Charge and Orbital Ordering in Pr_{0.5} Ca_{0.5} MnO_3 Studied by ^{17}O NMR

格式：pdf
大小：294.24 KB
文档页数：8

下载文档原格式

关于Formal

关于Formal Charge与Partial Charge的区别要知道，⼀种不管formal charge还是partial charge都不是实际能够直接经过实验看到的原⼦性质。

实际上分⼦不是由线将点连起来的，即使是同⼀个分⼦，不⼀样价键表达⽅式下，该分⼦中的formal charge可能定位不同（⽐如去质⼦化的羧酸，可以表⽰为开库勒式与芳⾹式，两种⽅式的formal charge定位完全不同），不⼀样的partial charge计算⽅法也会给同⼀个分⼦中的同⼀个原⼦分配不⼀样的电荷，⽐如苯环可以表⽰为[cH+]1[cH-][cH+][cH-][cH+][cH-]1。

两者的区别⾸先, 出于⽤价键表征分⼦的需要，formal charge 为整数.与原⼦价、键级以及连接性⼀起定义分⼦.第⼆，partial charge为浮点数，⽤在计算化学与分⼦模拟中。

它的值⽤来表⽰电⼦分布或分⼦的波函数，⽤⼀套分布于各个原⼦的点电荷来近似地的模拟分⼦的静电场。

Partial chargePartial atomic chargesPartial charges are created due to the asymmetric distribution of electrons in chemical bonds. The resulting partial charges are a property only of zones within the distribution, and not the assemblage as a whole. For example, chemists often choose to look at a small space surrounding the nucleus of an atom: When an electrically neutral atom bonds chemically to another neutral atom that is more electronegative, its electrons are partially drawn away. This leaves the region about that atom's nucleus with a partial positive charge, and it creates a partial negative charge on the atom to which it is bonded.In such a situation, the distributed charges taken as a group always carries a whole number of elementary charge units. Yet one can point to zones within the assemblage where less than a full charge resides, such as the area around an atom's nucleus. This is possible in part because particles are not like mathematical points--which must be either inside a zone or outside it--but are smeared out by the uncertainty principle of quantum mechanics. Because of this smearing effect, if one defines a sufficiently small zone, a fundamental particle may be both partly inside and partly outside it.UsesPartial atomic charges are used in molecular mechanics force fields to compute the electrostatic interaction energy using Coulomb's law. They are also often used for a qualitative understanding of the structure and reactivity of molecules. Methods of determining partial atomic chargesDespite its usefulness, the concept of a partial atomic charge is somewhat arbitrary, because it depends on the method used to delimit between one atom and the next (in reality, atoms have no clear boundaries). As a consequence, there are many methods for estimating the partial charges. According to Cramer (2002), all methods can be classified in one of four classes: Class I charges are those that are not determined from quantum mechanics, but from some intuitive or arbitraryapproach. These approaches can be based on experimental data such as dipoles and electronegativities.Class II charges are derived from partitioning the molecular wave function using some arbitrary, orbital based scheme.Class III charges are based on a partitioning of a physical observable derived from the wave function, such as electron density.Class IV charges are derived from a semiempirical mapping of a precursor charge of type II or III to reproduceexperimentally determined observables such as dipole moments.The following is a detailed list of methods, partly based on Meister and Schwarz (1994).Population analysis of wavefunctionsMulliken population analysisCoulson's chargesNatural chargesCM1, CM2, CM3 charge modelsPartitioning of electron density distributionsBader charges (obtained from an atoms in molecules analysis)Density fitted atomic chargesHirshfeld chargesMaslen's corrected Bader chargesPolitzer's chargesVoronoi Deformation Density chargesCharges derived from density-dependent propertiesPartial derived chargesDipole chargesDipole derivative chargesCharges derived from electrostatic potentialChelpChelpG, Breneman modelMK, Merz-KollmanCharges derived from spectroscopic dataCharges from infrared intensitiesCharges from X-ray photoelectron spectroscopy (ESCA)Charges from X-ray emission spectroscopyCharges from X-ray absorption spectraCharges from ligand-field splittingsCharges from UV-vis intensities of transition metal complexesCharges from other spectroscopies, such as NMR, EPR, EQRCharges from other experimental dataCharges from bandgaps or dielectric constantsApparent charges from the piezoelectric effectCharges derived from adiabatic potential energy curvesElectronegativity-based chargesOther physicochemical data, such as equilibrium and reaction rate constants, thermochemistry, and liquiddensities.Formal chargesFormal chargeIn chemistry, a formal charge (FC) is the charge assigned to an atom in a molecule, assuming that electrons in a chemical bond are shared equally between atoms, regardless of relative electronegativity.The formal charge of any atom in a molecule can be calculated by the following equation:FC = V - N - B/2Where V is the number of valence electrons of the atom in isolation (atom in ground state); N is the number of non-bonding electrons on this atom in the molecule; and B is the total number of electrons shared in covalent bonds with other atoms in the molecule.When determining the correct Lewis structure (or predominant resonance structure) for a molecule, the structure is chosen such that the formal charge (without sign) on each of the atoms is minimized.Formal charge is a test to determine the efficiency of electron distribution of a molecule. This is significant when drawing structures.Examples:Carbon in methane: FC = 4 - 0 - (8÷2) = 0Nitrogen in NO2-: FC = 5 - 2 - (6÷2) = 0double bonded oxygen in NO2-: FC = 6 - 4 - (4÷2) = 0single bonded oxygen in NO2- FC = 6 - 6 - (2÷2) = -1An alternative method for assigning charge to an atom taking into account electronegativity is by oxidation number. Other related concepts are valence which counts number of electrons that an atom uses in bonding and coordination number, the number of atoms bonded to the atom of interest.Contents1 Examples2 Alternative method3 Formal Charge vs. Oxidation State4 References5 External linksExamplesAmmonium NH4+ is a cationic species. By using the vertical groups of the atoms on the periodic table it is possible to determine that each hydrogen contributes 1 electron, the nitrogen contributes 5 electrons, and the charge of +1 means that 1 electron is absent. The final total is 8 total electrons (1 × 4 + 5 − 1). Drawing the Lewis structure gives an sp3 (4 bonds) hybridized nitrogen atom surrounded by hydrogen. There are no lone pairs of electrons left. Thus, using the definition of formal charge, hydrogen has a formal charge of zero (1- (0 + ½ × 2)) and nitrogen has a formal charge of +1 (5− (0 + ½ × 8)). After adding up all the formal charges throughout the molecule the result is a total formal charge of +1, consistent with the charge of the molecule given in the first place.Note: The total formal charge in a molecule should be as close to zero as possible, with as few charges on the molecule as possibleExample: CO2 is a neutral molecule with 16 total valence electrons. There are three different ways to draw the Lewis structureCarbon single bonded to both oxygen atoms (carbon = +2, oxygens = -1 each, total formal charge = 0)Carbon single bonded to one oxygen and double bonded to another (carbon = +1, oxygen double = 0, oxygen single = −1, total formal charge = 0)Carbon double bonded to both oxygen atoms (carbon = 0, oxygens = 0, total formal charge =0)Even though all three structures gave us a total charge of zero, the final structure is the superior one because there are no charges in the molecule at all.Alternative methodAlthough the formula given above is correct, it is often unwieldy and inefficient to use. A much quicker and still accurate method is to do the following:Draw a circle around the atom for which the formal charge is requested (as with carbon dioxide, below)Count up the number of electrons in the atom's "circle." Since the circle cuts the covalent bond "in half," each covalent bond counts as one electron instead of two.Subtract the number of electrons in the circle from the group number of the element (the Roman numeral from the older system of group numbering, NOT the IUPAC 1-18 system) to determine the formal charge.The formal charges computed for the remaining atoms in this Lewis structure of carbon dioxide are shown below. Again, this method is just as accurate as the one cited above, but is much easier to use. It is important to keep in mind that formal charges are just that-formal, in the sense that this system is a formalism. Atoms in molecules do not have "signs around their necks" indicating their charge. The formal charge system is just a method to keep track of all of the valence electrons that each atom brings with it when the molecule is formed.Formal Charge vs. Oxidation StateThe concept of oxidation states constitutes a competing method to assess the distribution of electrons in molecules. If the formal charges and oxidation states of the atoms in carbon dioxide are compared, the following values are arrived at:The reason for the difference between these values is that formal charges and oxidation states represent fundamentally different ways of looking at the distribution of electrons amongst the atoms in the molecule. With formal charge, the electrons in each covalent bond are assumed to be split exactly evenly between the two atoms in the bond (hence the dividing by two in the method described above). The formal charge view of the CO2 molecule is essentially shown below:The covalent (sharing) aspect of the bonding is overemphasized in the use of formal charges, since in reality there is a higher electron density around the oxygen atoms due to their higher electronegativity compared to the carbon atom. This can be most effectively visualized in an electrostatic potential map.With the oxidation state formalism, the electrons in the bonds are "awarded" to the atom with the greater electronegativity. The oxidation state view of the CO2 molecule is shown below:Oxidation states overemphasize the ionic nature of the bonding; most chemists agree that the difference in electronegativity between carbon in oxygen is insufficient to regard the bonds as being ionic in nature.In reality, the distribution of electrons in the molecule lies somewhere between these two extremes. The inadequacy of the simple Lewis structure view of molecules led to the development of the more generally applicable and accurate valence bond theory of Slater, Pauling, et al., and thenceforth the molecular orbital theory developed by Mulliken and Hund.。

Interference phenomena in radiation of a charged particle moving in a system with one-dimen

(10)
√ where k = ω ε/c. 2
III. GREEN’S FUNCTION
In this chapter we follow the approach of our previous paper [2]. For the bare Green’s function in momentum representation one has from (10) G0 (q ) = In the coordinate representation one has G0 (r) = − 1 ikr e 4πr (12) k2 1 − q 2 + iδ (11)
1
div A − ∇2 A +
iω ε(r, ω )ϕ(r, ω ) = 0, c (4)
ω2 ε(r, ω )A(r, ω ) = j (r, ω ) c2
where j (r, ω ) is the current associated with the moving charged particle j (r, ω ) = − 4πe v δ (x)δ (y )eiωz/v , v z c v (5)
(8)
Using (4) and (6) one can express the radiation tensor in terms of radiation potential ω2 δz ∂2 ˆi ∗ δ δ < A ( R, ω ) A ( R, ω ) > + < A ( R, ω ) A∗ (R, ω ) > z ˆ i z ˆ j r r r c2 ε ∂Rj ∂z r ∂2 ∂2 c2 ∂2 δz ˆj < < A∗ ( R, ω ) A ( R, ω ) > + A ( R, ω ) A∗ (R, ω ) > + r r r ε ∂Ri ∂z ω 2 ε2 ∂Ri ∂z ∂Rj ∂z r < Iij (R) >=

Spin dynamics of strongly-doped La_{1-x}Sr_xMnO_3

$Spin dynamics of strongly-doped La_{1-x}Sr_xMnO_3$

a r X i v :c o n d -m a t /9712191v 1 [c o n d -m a t .s t r -e l ] 16 D e c 1997Spin dynamics of strongly-doped La 1−x Sr x MnO 3L.Vasiliu-Doloc,J.W.Lynn,NIST Center for Neutron Research,National Institute of Standards and Technology,Gaithersburg,Maryland 20899andCenter for Superconductivity Research,University of Maryland,College Park,MD 20742Y.M.Mukovskii,A.A.Arsenov,D.A.ShulyatevMoscow Steel and Alloy Institute,Moscow 117936,RussiaCold neutron triple-axis measurements have been used to investigate the nature of the long-wavelength spin dynamics in strongly-doped La 1−x Sr x MnO 3single crystals with x =0.2and 0.3.Both systems behave like isotropic ferromagnets at low T ,with a gapless (E 0<0.02meV)quadratic dispersion relation E =E 0+Dq 2.The values of the spin-wave stiﬀness constant D are large (D T =0=166.77meV ·˚A 2for x =0.2and D T =0=175.87meV ·˚A 2for x =0.3),which directly shows that the electron transfer energy for the d band is large.D exhibits a power law behavior as a function of temperature,and ap-pears to collapse as T →T C .Nevertheless,an anomalously strong quasielastic central component develops and dominates the ﬂuctuation spectrum as T →T C .Bragg scattering in-dicates that the magnetization near T C exhibits power law behavior,with β≃0.30for both systems,as expected for a three-dimensional ferromagnet.75.25.+z,75.30.Kz,75.40.Gb,75.70.PaI.INTRODUCTIONSince the recent discovery of unusually large magne-toresistive eﬀects in perovskite manganites,the doped LaMnO 3class of materials 1has generated continued interest and has motivated experimental and theoreti-cal work devoted to understanding of the origin of this colossal magnetoresistance (CMR)phenomenon.The large variation in the carrier mobility originates from an insulator-metal transition that is closely associated with the magnetic ordering.The on-site exchange inter-action between the spins on the manganese ions is be-lieved to be strong enough to completely polarize the (e g )conduction electrons in the ground state,forming a “half-metallic”ferromagnet.However,hopping,and hence conduction,may only occur if the Mn core spins (formed by the d electrons in a t 2g orbital)on adjacent sites are parallel,which then directly couples ferromag-netic order with the electrical conductivity at elevated temperatures.This mechanism,known as the double ex-change mechanism,2was ﬁrst proposed in the 1950s,and has provided a good description of the evolution of the magnetic properties with band ﬁlling.However,in order to fully explain all the properties of the CMR materials,strong electron correlations,3and/or a strong electron-lattice coupling 4in diﬀerent polaronic approaches are in-voked.Cooperative Jahn-Teller (JT)distortions associ-ated with the Mn 3+JT ions have been evidenced from structural studies at low doping,where the system is in-sulating and antiferromagnetic,and may be an important contribution to orbital ordering,double exchange,and related spin ordering and transport properties observed at higher concentrations.As the doping concentration x increases,the static JT distortion weakens progressively and the system becomes metallic and ferromagnetic,with the CMR property observed for doping levels x >0.17.It is believed that in the absence of a cooperative eﬀect in this regime,local JT distortions persist on short time and length scales.These short-range correlations would contribute,together with the electron correlations,to cre-ate an eﬀective carrier mass necessary for large magne-toresistance.This unique class of half-metallic ferromag-nets provides an excellent opportunity to elucidate the inﬂuence of such correlations on the lattice and spin dy-namics,which can best be probed by inelastic neutron scattering.In the optimally doped regime with x ∼0.3it has been shown that the ground state spin dynamics is es-sentially that expected for a conventional metallic ferro-magnet described by an isotropic Heisenberg model 5−7.For the Ca-doped system,however,results obtained on polycrystalline samples 8have indicated a possible coex-istence of spin-wave excitations and spin diﬀusion in the ferromagnetic phase.In particular,it was suggested that the quasielastic component of the scattering that devel-ops rapidly as the Curie temperature is approached is associated with the localization of the e g electrons on the Mn 3+/Mn 4+lattice,and may be related to the for-mation of spin polarons in the system 9.Furthermore,it is this spin diﬀusion that drives the ferromagnetic phase transition rather than the thermal population of conven-tional spin waves.In the present publication we report diﬀraction and inelastic measurements of the spin dy-namics in the metallic ferromagnets La 0.8Sr 0.2MnO 3and La 0.7Sr 0.3MnO 3.II.EXPERIMENTThe single crystals used in the present neutron scatter-ing experiments were grown at the Steel and Alloys In-stitute in Moscow,using the ﬂoating zone method.The crystals weighed 2.25and 4.25g,respectively.The sam-ples were oriented such that the[100]and[010]axes of the rhombohedral R¯3c cell lie in the scattering plane.The neutron scattering measurements have been carried out on the NG-5(SPINS)cold neutron triple-axis spectrom-eter at the NIST research reactor.The(002)reﬂection of pyrolytic graphite(PG)was used as monochromator and analyser for measuring the low-energy part of the spin-wave spectrum.We have used aﬂat analyzer with aﬁxed ﬁnal energy E f=3.7meV,a cold Beﬁlter on the incident beam,and collimations40′-S-40′-130′in sequence from the neutron guide to detector.This conﬁguration oﬀered an energy resolution of∼0.15meV,together with good q-resolution.Each sample was placed in a helium-ﬁlled aluminum cell in a displex refrigerator.The sample tem-perature ranged from15to325K for La0.8Sr0.2MnO3, and from30to375K for La0.7Sr0.3MnO3,and was con-trolled to within0.1o.The crystal structure of both systems at room temper-ature and below is rhombohedral(R¯3c),with a0≃b0≃c0≃3.892˚A for x=0.2and a0≃b0≃c0≃3.884˚A for x=0.3.III.RESULTS AND DISCUSSIONFigure1shows the integrated intensity of the(100) Bragg reﬂection as a function of temperature for both samples.This reﬂection has aﬁnite nuclear structure factor,and therefore the intensity in the paramagnetic phase is nonzero.The increase in intensity below T C is due to magnetic scattering produced by the ferromag-netism of spins aligning on the manganese ions and yield-ing a magnetic structure factor.The solid curve is aﬁt of the points near T C to a power law.The bestﬁts give T C=305.1K and a critical exponentβ=0.29±0.01 for La0.8Sr0.2MnO3,and T C=350.8K andβ=0.30±0.02for La0.7Sr0.3MnO3.Both values of the critical ex-ponent are slightly below,but rather close to,the well known three-dimensional Heisenberg ferromagnet model value of∼1/3.We have investigated the spin dynamics in the(1,0,0) high-symmetry direction in both samples.The ground state spin dynamics for a half-metallic ferromagnet was not expected to diﬀer much from the conventional pic-ture of well deﬁned spin waves,and we found that the long wavelength magnetic excitations were in fact the usual spin waves,with a dispersion relation given by E=E0+Dq2,where E0represents the spin wave energy gap and the spin stiﬀness coeﬃcient is directly related to the exchange interactions.The spin-wave gap E0was too small to be measured directly in energy scans at the zone center,but very high-resolution measurements on the NG-5(SPINS)cold-neutron triple-axis spectrometer have allowed us to determine that E0<0.02meV for both systems,which demonstrates that these are”soft”isotropic ferromagnets.A previously reported value of E0=0.75meV for the x=0.3system6was obtained from an extrapolation of higher q data,not from direct high-resolution measurements as in the present case.The low-temperature values of the spin-wave stiﬀness constant D are large:D T=0=(166.77±1.51)meV·˚A2for x=0.2andD T=0=(175.87±5.00)meV·˚A2for x=0.3,and show that the electron transfer energy for the d band is large. The low temperature value of the spin stiﬀness constantgives a ratio D/k B T C∼6.34and5.82for the x=0.2and 0.3systems,respectively.Both values are quite large,as might be expected for an itinerant electron system.Figure2plots the temperature dependence of the spin-wave stiﬀness D.The data have been analysed in terms of two-spin-wave interactions in a Heisenberg ferromagnet within the Dyson formalism,10which predicts that the dynamical interaction between the spin waves gives,to leading order,a temperature dependence:D(T)=D0 1−v0S k B T2) ,(1)where v0is the volume of the unit cell,S is the aver-age value of the manganese spin,andζ(5l2is the moment deﬁned by 3D l n+2J(l) and which,compared to the square of the lattice parameter a2,gives information about the range of the exchange interaction.The solid curves in Fig.2areﬁts to Eq.1,and are in good agreement with the experimental data for reduced temperatures t=(T−T C)/T C up to t1≃-0.1for La0.8Sr0.2MnO3and -0.14for La0.7Sr0.3MnO3.Theﬁtted values ofT C ν′−β,where ν′is the critical exponent for a three-dimensional ferro-magnet.In the course of our measurements we have noticed that the central peak has a strong temperature depen-dence on approaching T C,while typically the central peak originates from weak temperature-independent nu-clear incoherent scattering.Figure3(a)shows two mag-netic inelastic spectra collected at300and325K,and reduced wave vector q=0.035away from the(100)re-ciprocal point in the La0.7Sr0.3MnO3(T C=351K).A ﬂat background of4.9counts plus an elastic incoherent nuclear peak of110counts,measured at30K,have been subtracted from these data.We can clearly see the de-velopment of the quasielastic component,comparable in intensity to the spin waves,and the temperature depen-dence of the strength of this scattering is shown in Fig. 3(b)as a function of temperature.We observe a signif-icant intensity starting at250K(∼100K below T C),and the scattering peaks at T C.At and above T C all the scattering is quasielastic.For typical isotropic ferro-magnets,such as Ni,Co,Fe,any quasielastic scattering below T C is too weak and broad to be observed directly in the data,and can only be distinguished by the use of polarized neutron techniques.In Fig.3(a)we can nev-ertheless see that the spectrum starts to be dominated by this quasielastic component at temperatures well be-low T C.The appearance in the ferromagnetic phase of a quasielastic component wasﬁrst observed on Ca-doped polycrystalline samples,8and it has been suggested that it is associated with the localization of the e g electrons on the Mn3+/Mn4+lattice,and may be related to the for-mation of spin polarons in the system.9We have observed a similar anomalous behavior of the central peak in the more lightly-doped system La0.85Sr0.15MnO3,11but for that doping weﬁnd that the central component becomes evident only much closer(∼25K)to the Curie temper-ature.Similar data have been obtained on both poly-crystalline and single crystal samples of the Ba-doped system.12It thus appears that the coexistence of spin-wave excitations and spin diﬀusion is a common charac-teristic for many perovskite manganites,and that it may be relevant for the giant magnetoresistance property of these systems.It is therefore important to pursue the study of this aspect with polarized neutron techniques, in order to determine the nature of theﬂuctuations in-volved in this new quasielastic component to theﬂuctu-ation spectrum.Research at the University of Maryland is supported by the NSF under Grant DMR97-01339and by the NSF-MRSEC,DMR96-32521.Experiments on the NG-5spectrometer at the NIST Research Reactor are sup-ported by the NSF under Agreement No.DMR94-23101.1G.H.Jonker and J.H.van Santen,Physica16,337 (1950);E.O.Wollan and W.C.Koehler,Phys.Rev.100, 545(1955);G.H.Jonker,Physica22,707(1956).2C.Zener,Phys.Rev.82,403(1951);P.W.Anderson and H.Hasegawa,Phys.Rev.100,675(1955);P.G.de Gennes,Phys.Rev.100,564(1955).3Y.Tokura,A.Urushibara,Y.Moritomo,T.Arima,A. Asamitsu,G.Kido,and N.Furukawa,J.Phys.Soc.Jpn. 63,3931(1994).lis,P.B.Littlewood,and B.I.Shraiman,Phys. Rev.Lett.74,5144(1995);lis,Phys.Rev.B 55,6405(1997).5T.G.Perring,G.Aeppli,S.M.Hayden,S.A.Carter,J.P. Remeika,and S.-W.Cheong,Phys.Rev.Lett.77,711 (1996).6M.C.Martin,G.Shirane,Y.Endoh,K.Hirota,Y. Moritomo,and Y.Tokura,Phys.Rev.B53,14285 (1996).7A.H.Moudden,L.Pinsard,L.Vasiliu-Doloc, A. Revcolevschi,Czech.J.Phys.46,2163(1996).8J.W.Lynn,R.W.Erwin,J.A.Borchers,Q.Huang,and A.Santoro,Phys.Rev.Lett.76,4046(1996).9J.W.Lynn,R.W.Erwin,J.A.Borchers,A.Santoro,Q. Huang,J.-L.Peng,R.L.Greene,J.Appl.Phys.81,5488 (1997).10D.C.Mattis,The theory of magnetism,Spinger-Verlag, Heidelberg,1981.11L.Vasiliu-Doloc,J.W.Lynn,A.H.Moudden,A.M.de Leon-Guevara,A.Revcolevschi,J.Appl.Phys.81,5491 (1997).12J.W.Lynn,L.Vasiliu-Doloc,S.Skanthakumar,S.N. Barilo,G.L.Bychkov and L.A.Kurnevitch,private com-munication.FIGURE CAPTIONSFIG.1.Temperature dependence of the integrated in-tensity of the(100)Bragg peak for(a)La0.8Sr0.2MnO3 and(b)La0.7Sr0.3MnO3.There is a nuclear contribution to this peak,and the additional temperature-dependent intensity originates from the onset of the ferromagnetic order at T C=305K for the x=0.2system,and T C= 350.8K for x=0.3.The solid curves areﬁts of the points near T C to a power law.FIG.2.Spin-wave stiﬀness coeﬃcient D in E=E0+Dq2 as a function of temperature for(a)La0.8Sr0.2MnO3and(b)La0.7Sr0.3MnO3.The solid curves areﬁts to Eq.(1).D appears to vanish at the ferromagnetic transition temperature,as expected for a conventional ferromagnet. The dashed curves areﬁts to a power law.FIG.3.(a)Constant-q magnetic inelastic spectra col-lected at300and325K and a reduced wave vector vector q=(0,0,0.035)for La0.7Sr0.3MnO3(T C=350.8K),and (b)temperature dependence of the integrated intensity of the quasielastic central component.The dominant eﬀect is the development of a strong quasielastic component in the spectrum.Above T C,all the scattering in this range of q is quasielastic.Fig.1:L.Vasiliu-Doloc et al.Fig.2:L.Vasiliu-Doloc et al.Fig.3:L.Vasiliu-Doloc et al.。

Magnetic, orbital and charge ordering in the electron-doped manganites

a r X i v :c o n d -m a t /0301048v 1 [c o n d -m a t .s t r -e l ] 6 J a n 2003Magnetic,orbital and charge ordering in the electron-doped manganitesTulika Maitra ∗1and A.Taraphder †2∗Max-Planck-Institut f¨u r Physik Komplexer Systeme N¨o thnitzer Str.3801187Dresden,Germany †Department of Physics &Meteorology and Centre for Theoretical Studies,Indian Institute of Technology,Kharagpur 721302India Abstract The three dimensional perovskite manganites R 1−x A x MnO 3in the range of hole-doping x >0.5are studied in detail using a double exchange model with degenerate e g orbitals including intra-and inter-orbital correlations and near-neighbour Coulomb repulsion.We show that such a model captures the observed phase diagram and orbital-ordering in the intermediate to large band-width regime.It is argued that the Jahn-Teller eﬀect,considered to be crucial for the region x <0.5,does not play a major role in this region,particularly for systems with moderate to large band-width.The anisotropic hopping across the degenerate e g orbitals are crucial in understanding the ground state phases of this region,an observation emphasized earlier by Brink and Khomskii.Based on calculations using a realistic limit of ﬁnite Hund’s coupling,we show that the inclusion of interactions stabilizes the C-phase,the antiferromagnetic metallic A-phase moves closer to x =0.5while the ferromagnetic phase shrinks in agreement with recent observations.The charge ordering close to x =0.5and the eﬀect of reduction of band-width are also outlined.The eﬀect of disorder and the possibility of inhomogeneous mixture of competing states have been discussed.PACS Nos.75.30.Et,75.47.Lx,75.47.Gk I.Introduction The colossal magnetoresistive manganites have been investigated with renewed vigour inthe recent past mainly because of their technological import.It was soon realized that these systems have a rich variety of unusual electronic and magnetic properties involving almost all the known degrees of freedom in a solid,viz.,the charge,spin,orbital and lattice degrees of freedom[1,2,3].Of particular interest have been the systems R 1−x A x MnO 3,where Rand A stand for trivalent rare-earth(e.g.,La,Nd,Pr,Sm)and divalent alkaline-earth ions (Ca,Sr,Ba,Pb etc.)respectively.Around the region0.17<x<0.4,electrical transport properties of these systems generically show extreme sensitivity towards external magnetic ﬁeld with a concomitant paramagnetic insulator(or poor metal)to ferromagnetic metal transition at fairly high temperatures[5,6,7].For a long time the dominant paradigm in the theory of this unusual magneticﬁeld-dependence of transport has been the idea of double exchange(DE)[8]involving the localized core spins(the three t2g electrons at each Mn site)coupled to the itinerant electrons in the Jahn-Teller split e g level via strong Hund’s exchange.It has been realized recently that such a simplifying theoretical framework may not be adequate in explaining several other related features involving transport,electronic and magnetic properties[9,10,11,12,13].It was already known that the observed structural distortions and magnetic and orbital orders in these systems in the region x≃0.5require interactions not included in the DE model[14,15,16].Owing to the observation of colossal magnetoresistance(CMR)in the region x<0.5in the relatively narrow band-width materials[6]at high temperatures,much of the attention was centred around this region.Only in the last few years CMR eﬀect has been observed in the larger band-width materials like Nd1−x Sr x MnO3[17,18]and Pr1−x Sr x MnO3[19,20] in the region x>0.5.If one counts the doping from the side x=1in R1−x A x MnO3where all Mn ions are in+4state,then doping by R y(y=1−x)introduces Mn+3ions carrying one electron in the e g orbitals.This region,therefore,is also called the electron-doped region. The charge,magnetic and orbital structures of the manganites in the electron-doped regime have already been found to be quite rich[2,4,21,22,23]and the coupling between all these degrees lead to stimulating physics[24].In the framework of the conventional DE model with one e g orbital,one would expect qualitatively similar physics for x∼0and x∼1[25].On the contrary,experiments reveal a very diﬀerent and assymetric picture for the phase diagram between the regions x<0.5andx>0.5.The lack of symmetry about x=0.5manifests itself most clearly in the magnetic phase diagram of these manganites.It has now been shown quite distinctly[18,32,27,34] that the systems Nd1−x Sr x MnO3,Pr1−x Sr x MnO3,La1−x Sr x MnO3are antiferromagnetically ordered beyond x=0.5while one observes either a metallic ferromagnetic state[7]ora charge ordered state with staggered charge-ordering[29,30]in the approximate range0.25<x<0.5.This charge ordered insulating state can be transformed into a ferromagnetic metallic state[19,31]by the application of magneticﬁelds.There are several diﬀerent types of AFM phases with their characteristic dimensionality of spin ordering observed in this 1−x Sr x MnO3shows A-type antiferromagnetic ground state(in which ferromagnetically aligned xy-planes are coupled antiferromagnetically)in the range0.52<x<0.58.It also shows a sliver of FM phase[27]immediately above x=0.5. In Nd1−x Sr x MnO3[34,18],the A-type spin structure appears at x=0.5and is stable upto x=0.62while in Pr1−x Sr x MnO3[19,26],this region extends from x=0.48to x=0.6.In all these cases,the phase that abuts the A-type antiferromagnet(AFM)in the region of higher hole-doping(x)is the C-type AFM state,in which antiferromagnetically aligned planes are coupled ferromagnetically.The C-type AFM phase occupies largest part of the phase diagram in this region.For even larger x,the C-phase gives way to the three dimensional antiferromagnetic G-phase.The systematics of the phase diagram changes considerably(except close to x=1)in these systems as a function of the bandwidth.Recently Kajimoto et al.[28]have quite succinctly summarized the phase diagrams of various manganites of varying bandwidths across the entire range of doping.Their phase diagram is reproduced inﬁg.1.The phase diagram changes considerably with changing bandwidth as shown in theﬁgure.We note that the narrow bandwidth compounds like Pr1−x Ca x MnO3,La1−x Ca x MnO3etc.exhibit a wide region of CE-type insulating charge-ordered state around x=0.5whereas the inter-mediate bandwidth material Nd1−x Sr x MnO3shows a conducting A-type antiferromagneticphase around x=0.5.As one moves towards the larger bandwidth compounds such as Pr1−x Sr x MnO3,La1−x Sr x MnO3,a small strip of ferromagnetic(F)metallic phase appears at x=0.5[27,28]followed by the A-type AFM state.In contrast with the narrow band-width manganites,the relatively wider bandwidth manganites generally show the following sequence of spin/charge ordering upon hole doping(in the entire range0≤x≤1):insulating A-type AFM→metallic FM→metallic A-type AFM→insulating C-type AFM andﬁnally insulating G-type AFM states.Clearly,the most important feature here is the absence of CE-type spin/charge ordering and the presence of a metallic A-type AFM state in these wider band-width compounds in the region close to x=0.5.It appears that the physics involved in the CE-type charge/spin ordering,important for the low band-width systems,is not quite as relevant in this case.In addition,it is also observed in the neutron diﬀraction studies that the metallic A-type AFM state is orbitally ordered[32,34]with predominant occupation of d x2−y2orbitals.The importance of orbital-ordering has been emphasized pre-viously in several other experimental[18,35,39,40]and theoretical[33,41,42,43,44,45,46] investigations.The crucial role of the e g orbitals and inter-orbital Coulomb interaction has been underlined by Takahashi and Shiba[50]from a study of the optical absorption spectra in the ferromagnetic metallic phase of the doped manganite La1−x Sr x MnO3.They point out that it is imperative to consider the transition between nearly degenerate and moder-ately interacting e g orbitals even in the hole-doped region in order to interpret the optical absorption spectra in La1−x Sr x MnO3.In a detailed observation carried out by Akimoto et al.[27]the electronic and magnetic properties of a heavily doped manganite R1−x Sr x MnO3with R=La1−z Nd z are studied by continuously changing the band-width.In this novel procedure they were able to control the band-width chemically by changing the average ionic radius by manipulating the ratio of La and Nd(i.e.,changing z).Substitution of the smaller Nd+3ions for the larger La+3 ions eﬀectively reduces the one-electron band-width.By increasing z chemically,they wereable to go continuously from the large band-width system La1−x Sr x MnO3down to the intermediate band-width system Nd1−x Sr x MnO3.For z<0.5,there is a metallic FM phase in the region0.5<x<0.52.From x≥0.54to about x=0.58the ground state is A-type antiferromagnetic metallic irrespective of the value of z,i.e.from La1−x Sr x MnO3 (z=0)all the way down to Nd1−x Sr x MnO3(z=1).They believe that the key factor that stabilizes the A-type AFM metallic state in a wide range of z is the structure of the two e g orbitals(d x2−y2and d3z2−r2)and the anisotropic hopping integral between them.There is no signature of charge-ordering or CE-type ordering below z=0.5for any x.The charge-ordered(CO)insulating state appears above z=0.5and around x=0.5primarily due to the commensuration(between the lattice periodicity and hole concentration)eﬀect in the low band-width systems.The ground state phase diagram for doped manganites in x−z plane(i.e.,doping versus band-width plane)is shown inﬁg.2after Akimoto et al.[27].The general inferences from all these measurements are that the physics of the electron-doped region is very diﬀerent from the hole-doped region.In this region,with decreasing band-width starting from La1−x Sr x MnO3down to Nd1−x Sr x MnO3,the F-phase shrinks,the A-phase and C-phase remain nearly unaﬀected.The A-phase disappears and the C-phase shrinks(with the possible growth of incommesurate charge order region as inﬁg.1)rapidly in the low band-width systems like La1−x Ca x MnO3and Pr1−x Ca x MnO3.The G-phase at the low electron-doping region seems to remain unaﬀected all through.It has been seen [27,34,35]that the gradual build up of the AFM correlations in the electron-doped region is pre-empted by the orbital ordering in the A-and C-phases.The e g orbitals and the anisotropic hopping of electrons between them[16,63],must indeed play a signiﬁcant role given the presence of orbital ordering in much of the phase diagram beyond x=0.5.It is also realized that the eﬀect of lattice could be ignored in theﬁrst approximation for these moderate to large band-width systems in this region of doping.All these point to the fact that the interactions that play a dominant role in the elctron-doped region are diﬀerent[36,37,38]from the ones that are considered crucial in the hole-doped side.There has been a large number of reports of charge ordering and inhomogeneous states [17,18,19,47,48,49,52,53]in the region x≃0.5.These states are quite abundant in the low band-width materials.The inhomogeneous states result primarily from the competing ground states[54](charge ordered/AFM and FM in this case)that lead to1st.order phase transitions with a discontinuity in the density as the chemical potential is varied.Such transitions are known to lead to phase separation in the canonical ensemble.Phase separation in this context has been dicussed in the literature for quite some time[51,55,56,57,58,61]. Such macroscopic phase separations are not stable against long range Coulomb interactions and tend to break up into microscopic inhomogeneities[55,59,60].There is also the well-known CE-type charge and spin ordering that has been seen at x=0.5in most of these systems[14,15,47]with low band-width.In both Nd1−x Sr x MnO3and P r1−x Sr x MnO3Kawano et al.[32]and Kajimoto et al. [28,34]have seenﬁnite temperature(T≃150K)ﬁrst order transitions at x=0.5from a ferromagnetic metal to an antiferromagnetic A-phase which is insulating but has quite low resistivity(immediately away from x=0.5it becomes A-type metal).In a neutron diﬀraction study Kajimoto et al.[28]have also observed that close to the boundary of the FM and A-type AFM metallic phases of P r1−x Sr x MnO3,an unusual stripe-like charge-order appears along with this weaklyﬁrst order transition.This stripe-like charge-order is distinctly diﬀerent from the staggered charge-ordering of the CE-type state.Very recently,an inhomegeneous mixture of micron-size antiferromagnetic grains(possibly charge-ordered)and similar sized ferromagnetic grains has been seen in electron diﬀraction and dark-ﬁeld imaging in the low band-width system La1−x Ca x MnO3at x=0.5[62]without any evidence of the long-range CE or any other macroscopic ordering. The ground state energies of these diﬀerent phases seem to be very close[67]in this region leading to a possibleﬁrst order phase transition and consequent phase seggregation.Apossible nanoscale phase separation between A-type AFM and ferromagnetic regions has recently been reported by Jirac et al.,[81]in the cintered ceramic samples of Pr0.44Sr56MnO3 doped with Cr(upto8percent).It is also observed that although both the ferromagnetic domains and A-type AFM host are independently metallic(though anisotropic for A-AFM), the resultant inhomohgeneous state is non-metallic.Almost all the experiments discussed above consider orbital ordering as the underlying reason for the various magnetic orders observed in the electron-doped regime.The anisotropy of the two e g orbitals and the nature of overlap integral between them[16,63]make the electronic bands low dimensional.Such anisotropic conduction in turn leads to anisotropic spin exchanges and diﬀerent magnetic structures.In the A-phase the kinetic energy gain of the electrons is maximum when the orbitals form a2D band in the xy-plane and maximize the in-plane ferromagnetic exchange interaction.However,in the z-direction AFM super-exchange interaction dominates due to the negligible overlap of d x2−y2and d3z2−r2orbitals. In addition,the presence of charge ordering and inhomegeneous or phase separated states, particularly around the commensurate densities,are suggestive of the vital role of Coulomb interactions in the manganites.The absence of CE-phase in the moderate to large band-width materials imply that the role of Jahn-Teller or static lattice distortions may not be as crucial in the electron-doped regime even in the region close to x=0.5.A model,for the electron-doped systems,therefore,should have as its primary ingredients,the two e g orbitals at each Mn site and the anisotropy of hopping between them.In addition,the Coulomb interactions are present,and their eﬀects on the charge,orbital and magnetic order are important[9,38,41,46,67].In the next section,we motivate a model recently proposed by Brink and Khomskii[36]for the electron-doped manganites and later extended by us [38]in order to take into account the eﬀects of local Coulomb interactions present in these systems.We extend this model further in the present work,study the magnetic and orbital orders in more detail,investigate the possibility of charge-ordering and phase separation anddiscuss their consequences.In sections II and III we present our calculations and results and compare them with experimental literature.We conclude with a brief discussion on the implications of our results.II.a.Degenerate Double-Exchange ModelEvidently the physics of the region x>0.5is quite diﬀerent from that in the x<0.5 for the manganites and one has to look at the electron-doped manganites from a diﬀerent perspective.In order to pay due heed to the compelling experimental and theoretical evidence in support of the vital role of the orbitals,Brink and Khomskii[36](hereafter referred to as BK)have proposed a model for the electron-doped manganites that incorporates the e g orbitals and the anisotropic hopping between them.In the undoped LaMnO3compound each Mn ion has one electron and acts as a Jahn-Teller centre,the e g orbitals are split and the system is orbitally ordered.Thus for the lightly(hole-)doped system one can at the ﬁrst approxmation ignore the orbital degree of freedom and apply a single band model like the conventional double exchange(DE)model to describe it.If,however,one proceeds from the opposite end and starts,for example,from the insulating CaMnO3compound where the empty e g orbitals of Mn+4ions are degenerate,then doping trivalent(La,Nd,Pr etc.)ions into CaMnO3results in adding electrons into the doubly degenerate e g manifold.In the doped manganites R1−x A x MnO3there are y=1−x number of electrons in the e g orbitals at each Mn site.Since each site has two e g orbitals,four electrons can be accommodated per site and hence the actualﬁlling(electron density)is y[we restrict ourselves to the region0.5≤x≤1.0(0.5≥y≥0) 8in the foregoing].Due to this low electron concentration and hence very few Jahn-Teller centres the e g band is mostly degenerate and the Jahn-Teller eﬀect is negligible to a leadingapproximation.The neglect of Jahn-Teller eﬀect is also justiﬁed from the experimental evidence presented above.The usual charge and spin dynamics of the conventional DE model then operate here too,albeit with an additional degree of freedom coming from the degenerate set of e g orbitals.This process has been described by BK as double exchange via degenerate orbitals.In order to capture the magnetic phases properly,the model has,in addition to the usual double exchange term,orbital degeneracy and the superexchange(SE)coupling between neighbouring t2g spins.At x=1(or y=0)end the e g band is completely empty and the physics is governed entirely by the antiferromagnetic exchange(superexchange)between the t2g spins at neighbouring sites.On doping,the band begins toﬁll up,the kinetic energy of electrons in the degenerate e g levels along with the attendant Hund’s coupling between t2g and e g spins begin to compete with the antiferromagnetic superexchange interaction leading to a rich variety of magnetic and orbital structures.The model used to describe the ground state properties of the electron-doped manganites contains the following termsH=J AF<ij>S i.S j−J HiS i.s i−<ij>σ,α,βtαβi,j c†i,α,σc j,β,σ(1)Theﬁrst term is the usual AF superexchange between t2g spins at nearest-neighbour sites,the second term represents the Hund’s exchange coupling between t2g and e g spins at each site and the third term stands for the hopping of electrons between the two orbitals [16,63,64](α,βtake values1and2for d x2−y2and d3z2−r2orbitals,corresponding to the choice of the phaseξi=0in Ref.[65]).The hopping matrix elements are determined by the symmetry of e g orbitals[16,63].Although similar in appearance to the conventional DE model the presence of orbital degeneracy together with the very anisotropic hopping matrix elements tαβij makes this model and its outcome very diﬀerent from the conventional DE model of Zener[8,25,68,69]with a single non-degenerate orbital.In the manner often used in literature[8]BK treated the t2g spins quasi-classically andthe Hund’s coupling was set to inﬁnity.At each site the spins were allowed to cant in the xz-plane leading to the eﬀective hopping matrix elements[8]t xy=tcos(θxy/2)and t z=tcos(θz/2).Hereθxy is the angle between nearest neighbour t2g spins in the xy−plane andθz is the same in the z−direction.The superexchange energy per state then becomesE SE=J AF S20√3t xy(cosk x+cosk y)−83(cosk x+cosk y)−4t z3(cosk x+cosk y)−4t z3(cosk x−cosk y)2)1we have plotted the bands for the A-phase in the presence of a small canting inﬁg.3a.Note that even in the presence of canting,there is almost no dispersion in the z-direction(Γ-Z and M-L directions).In the canted C-phase as well the band disperses little in the x and y directions and remains almost indistinguishable from the pure phase.The total energy is then obtained for a particularﬁlling by adding the superexchange contribution to the band energy.It is evident that the energy spectrum obtained depends on the underlying magnetic structure as well as the orbital-dependent(anisotropic)hopping ma-trix elements.This will lead to diﬀerent anisotropic magnetic structures at diﬀerent doping. The magnetic phase diagram in the(electron)doping y-t/J AF plane is then calculated by minimizing the total energy with respect toθxy andθz.The sequence of phases follows from the nature of the DOS modulated by the anisotropic overlap of orbitals as well as the DE mechanism.At very low doping(x∼1)BK get a stable A-type(canted)antiferromagnetic phase and on increasing the doping the systemﬁrst enters the C-phase and then depending on the value of t/J AF directly gets into the ferromagnetic phase or reenters the A-phase before becoming ferromagnetic at large doping.The presence of ferromagnetic phase at large doping and C-type antiferromagnetic order at the intermediate electron doping range is rightly captured in their model.Such a sequence of phases is indeed seen in the experimen-tal phase diagram in these systems.Quite remarkably the phase diagram has almost all the magnetic phases except the G-type antiferromagnetic one that is observed experimentally in these systems at low electron doping.The phase diagram of BK,unfortunately,has two major shortcomings in it.At very low electron-doping a canted A-type antiferromagnetic phase is obtained which is stable for all values of J AF whereas experimentally G-type anti-ferromagnetic phase is observed at this end.The stability of the G-phase around x→1is quite naturally expected on physial grounds.At the y=0(x=1)end there are no electrons in the e g band,the only interaction is the antiferromagnetic exchange between neighbouring t2g spins which should lead to the three dimensional G-type antiferromagnetic order.Theother problem is that of the limiting behaviour.When the antiferromagnetic exchange in-teraction is zero or very close to zero(i.e.t/J AF→∞)the system should be completely ferromagnetic,a feature which is also missed out in their phase diagram.It appears that the designation of the A-type ordering by BK was somewhat ambiguous and that might have led to the absence of the G-phase around x=1in their phase diagram. This is particularly relevant as the typical values of canting obtained by BK in their A-phase are quite large.In their convention for diﬀerent spin ordering,they chose to designate A-phase whenθxy<θz.It is apparent,therefore,that by this convention,a spin ordering with both the anglesθxy andθz close toπbutθxy<θz,could be designated as a canted A-phase.On the other hand,from the structure of spin arrangements,it should be more appropriately called a canted G-phase.Although G-phase with such large canting has not been seen experimentally(there is hardly any evidence of signiﬁcant canting in the region close to x=1).This ambiguity is easily resolved if in addition one considers orbital ordering which,however,was not included in their treatment.We discuss this in more detail later on with reference to our calculations.The limit of inﬁnite Hund’s coupling which BK worked with is unphysical for the man-ganites considered[3,9,65,67].Typical values reported in the experiments[3,4,23]and various model studies[9,41,65]and LDA calculations[67,70]do not suggest the spin spilit-tings of the e g band in various manganites to be very large.These are typically comparable to(or slightly larger than)the e g band-width.The scale of Coulomb correlations are most likely to be even higher[3,9].The other serious consequence of using such large values of Hund’s coupling is that the predictions about low energy excitations(like optical spectra, speciﬁc heat,spinﬂuctuation energy scales)are going to be inaccurate.BK’s calculation, though,serves as a starting point for improved theories.Based on their phase diagram BK argue that the degeneracy of orbitals and the anisotropy of hopping are crucial and the lattice(including Jahn-Teller(JT)eﬀect)is of secondaryimportance for the physics of electron-doped manganites.This was borne out by a more reﬁned calculation by Pai.In a more realistic treatment of the spin degrees of freedom,Pai [37]considered the limit ofﬁnite J H in the same model and succeeded in recovering the G-and F-phases.II.b.Double exchange and correlationWe mentioned earlier that by all estimates the Coulomb correlations in these systems are large[24,73,70]and it is not obvious,therefore,that the phase diagram obtained by BK will survive once these are introduced in the model.Neither of the treatments of BK or Pai includes the interactions present in the system,namely the inter-and intra-orbital Coulomb interactions as well as the longer-range Coulomb interactions.Although for low doping the local correlations are expected to be ineﬀective,with increase in doping they preferentially enhance the orbital ordering[38].This aﬀects the F-phase and alters the relative stability of the A-and C-phases.The longer-range part of the interactions would tend to localize the carriers and lead to charge ordering.It is,therefore,necessary to include them in the Hamiltonian and look for their eﬀects on the phase diagram.In the present work we have incorporated the onsite inter-and intra-orbital as well as the nearest neighbour Coulomb interactions in the model Hamiltonian and studied how these terms aﬀect the nature of magnetic phase diagram,orbital ordering and other properties of electron doped manganites.We also set out from the double exchange model with degenerate e g orbitals and the superexchange interaction between the neighbouring t2g spins.The addition of the correlation terms makes the model very diﬀerent from the ones considered by BK and Pai. Besides,the physics of charge ordering is beyond the scope of the models earlier considered.The model Hamiltonian we consider consists of two parts,theﬁrst part is the same as the Hamiltonian in eqn.(1)we discussed in the previous section.The second part,which is the interaction part,has onsite inter-and intra-orbital interaction and the nearest neighbourCoulomb interaction terms in it.The total Hamiltonian is thereforeH=H1+H intH1is the same as in eqn.(1)andH int=Uiαˆn iα↑ˆn iα↓+U′iσσ′ˆn i1σˆn i2σ′+V<ij>ˆn iˆn j.(5)In the above U,U′and V are the intra-and inter-orbital and the nearest neighbour Coulomb interaction strengths respectively.We treat the t2g spin subsystem quasi-classically as in BK(this is the usual practice in many of the treatments of the double exchange model [8,9,68]),but we choose to work with the more realistic limit ofﬁnite values of the Hund’s coupling.In an uncanted homogeneous ground state we choose S=S0exp(i Q.r)where the choice of Q determines the diﬀerent spin arrangements for the core(t2g)spins.For example,Q=(0,0,0)would be the pure ferromagnetic phase,Q=(π,π,π)gives the G-type antiferromagnetic phase,Q=(π,π,0)is for C-type antiferromagnetic phase and ﬁnally Q=(0,0,π)reproduces A-type antiferromagnetic phase.In the inﬁnite J H limit, the e g electron spins are forced to follow the t2g spins leading to the freezing of their spin degrees of freedom.Atﬁnite J H,however,the quantum nature of the transport allows for ﬂuctuations and the e g spin degrees of freedom,along with anisotropic hopping across the two orbitals,play a central role.For canted magnetic structures where the angle between two nearest-neighbour t2g spins is diﬀerent from that of the pure phases,S i is given by S i=S0(sinθi,0,cosθi)withθi taking all values between0andπ.The t2g spins are allowed to cant only in the xz−plane(this does not cause any loss of generality in the treatments that follow).We will discuss the canted structures at length in the foregoing.We begin our discussion by considering the model without the interaction terms U,U′and V.The interactions and their eﬀects will be dealt with in detail later.。

专业英语电子版教材

Chapter 3 Inorganic Chemistry (28)3.1 The Atomic Nature of Matter (28)3.2 Electronic Structure of Atoms (30)3.3 Periodicity of Atomic Properties (32)3.5 Molecular Geometry and Bonding Theories......................................................... 错误！未定义书签。

3.6 Chemical Reactions................................................................................................. 错误！未定义书签。

3.7 The Behavior of Gases ............................................................................................ 错误！未定义书签。

3.8 Aqueous Reactions and Solution Stoichiometry................................................... 错误！未定义书签。

3.9 Chemical Equilibrium ............................................................................................ 错误！未定义书签。

3.10 Thermochemistry.................................................................................................. 错误！未定义书签。

强激光与物质相互作用英语

强激光与物质相互作用英语Possible article:Interactions between Matter and Strong Laser LightIntroductionStrong laser light can produce remarkable effects on matter, ranging from heating and ionization to acceleration and fusion. Understanding these interactions is not only fascinating from a scientific perspective but also holdsgreat significance for energy, medical, and industrial applications. This article will overview the basic principles, mechanisms, and applications of the interaction betweenstrong laser light and matter.Basic PrinciplesLight is an electromagnetic wave, characterized by its wavelength, frequency, and amplitude. The behavior of a light wave can be described by Maxwell's equations, which relatethe electric and magnetic fields to the sources and media of the wave. When light interacts with matter, several phenomena can occur, depending on the frequency and intensity of thelight as well as the nature and state of the matter.One of the most important parameters of strong laserlight is its intensity, which is defined as the power of the light beam per unit area. The intensity can reach values of10^15 W/cm^2 or higher for modern lasers, which is equivalent to focusing the light energy of the Sun onto a tiny spot.Such high intensities can cause nonlinear effects, where the response of the matter depends on the square or higher powers of the electric field strength. Moreover, the highintensities can lead to relativistic effects, where themotion of the electrons in the matter becomes significant to the point of approaching the speed of light.Mechanisms of InteractionSeveral mechanisms can explain the interaction between strong laser light and matter. Some of the most importantones are:- Absorption: When a photon of the light energy is absorbed by an electron in the matter, the electron gains energy and may be excited to a higher energy level or even ionized from the atom or molecule. The probability of absorption depends on the frequency of the light and the electronic structure of the matter. For example, ultraviolet light is easily absorbed by molecules containing aromatic or conjugated rings, while infrared light is more likely to be absorbed by polar molecules.- Scattering: When a photon of the light energy collides with a particle in the matter, it may be scattered in different directions or absorbed and reemitted at a different frequency. Scattering can occur elastically, where the photon keeps its energy and only changes direction, or inelastically, wherethe photon loses or gains some energy in the process. Scattering can be used to diagnose the properties of matter, such as its size, shape, and composition.- Ionization: When the intensity of the light exceeds acertain threshold, called the ionization threshold, the probability of ionization increases dramatically. Ionization can lead to the formation of plasmas, which are collectionsof positively charged ions and free electrons that behave asa fluid with collective properties. Plasmas can emit intense radiation, generate magnetic fields, and accelerate chargedparticles to high energies.- Heating: When the light energy is absorbed by the matter, the temperature of the matter increases due to the excitation of the internal degrees of freedom, such as vibrations, rotations, or electronic transitions. The amount of heating depends on the rate of energy deposition and the thermal conductivity of the matter. Heating can be useful for a variety of applications, such as welding, cutting, and annealing.- Acceleration: When a strong laser light beam is focused onto a small target, the intense electric field can create a gradient of forces that pushes the surface electrons away from the center and attracts the ions towards it. This creates a net force that can accelerate the target towards the light source or even generate a shock wave. Acceleration can be used to produce high-energy particles, such as ions, electrons, and neutrons, which can be employed for medical imaging, cancer therapy, or material analysis.- Fusion: When two nuclei with positive charges are brought close enough, they can overcome their electrostatic repulsion and collide with enough kinetic energy to form a heavier nucleus. This process is called fusion and releases a large amount of energy, as predicted by Einstein's famous equation E=mc^2. Strong laser light can enhance the fusion rate by compressing and heating the nuclei to overcome the Coulomb barrier. Fusion can be a promising source of clean energy, but requires overcoming many technical and safety challenges.ApplicationsThe interaction between strong laser light and matter has numerous applications in science and technology. Some of the most promising ones are:- High-energy physics: Strong laser light can mimic and complement the experiments performed in particle accelerators, by producing high-energy particles with high precision and compactness. Strong laser light can also probe the quantum vacuum and test fundamental physics theories.- Material science: Strong laser light can modify and control the properties of materials, such as their surface texture, hardness, and conductivity. Strong laser light can alsocreate new materials by inducing rapid phase transitions orby synthesizing nanoparticles with specific shapes and sizes. - Medicine: Strong laser light can be used for non-invasive diagnostic imaging, such as optical coherence tomography, or for therapeutic treatments, such as laser surgery, cancer ablation, and photodynamic therapy.- Energy: Strong laser light can enhance the efficiency and safety of nuclear fusion, which could provide a virtually limitless and clean source of energy. Strong laser light can also enable the harvesting of renewable energy sources, suchas solar and wind, by improving their conversion and storage technologies.ConclusionThe interaction between strong laser light and matter is a fascinating and multidisciplinary field of research and innovation, with far-reaching implications for science, technology, and society. Exploring and harnessing these interactions requires advancements in laser technology, theoretical modeling, experimental techniques, and interdisciplinary collaborations. As the intensity of laser light continues to increase and its applications continue to expand, the future of this field looks bright and enlightening.。

Measurements of Cross Sections and Forward-Backward Asymmetries at the Z Resonance and Dete

a rXiv:h ep-e x /246v116Feb2EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH CERN-EP/2000-022February 04,2000Measurements of Cross Sections and Forward-Backward Asymmetries at the Z Resonance and Determination of Electroweak Parameters The L3Collaboration Abstract We report on measurements of hadronic and leptonic cross sections and leptonic forward-backward asymmetries performed with the L3detector in the years 1993−95.A total luminosity of 103pb −1was collected at centre-of-mass energies √s ≈m Z ±1.8GeV which corresponds to 2.5million hadronic and 245thousand leptonic events selected.These data lead to a signiﬁcantly improved determination of Z parameters.From the total cross sections,combined with our measurements in 1990−92,we obtain the ﬁnal results:m Z =91189.8±3.1MeV ,ΓZ =2502.4±4.2MeV ,Γhad =1751.1±3.8MeV ,Γℓ=84.14±0.17MeV .An invisible width of Γinv =499.1±2.9MeV is derived which in the Standard Model yields for the number of light neutrino species N ν=2.978±0.014.Adding our results on the leptonic forward-backward asymmetries and the tau polarisation,the eﬀective vector and axial-vector coupling constants of the neutral weak current to charged leptons are determined to be ¯g ℓV =−0.0397±0.0017and ¯g ℓA =−0.50153±0.00053.Includingour measurements of the Z →b ¯b forward-backward and quark charge asymmetries a value for theeﬀective electroweak mixing angle of sin 21IntroductionThe Standard Model(SM)of electroweak interactions[1,2]is tested with great precision by the experiments performed at the LEP and SLC e+e−colliders running at centre-of-mass energies,√on the treatment of the t-channel contributions in e+e−→e+e−(γ)and on technicalities of the ﬁt procedures,respectively.2The L3DetectorThe L3detector[13]consists of a silicon microvertex detector[14],a central tracking chamber, a high resolution electromagnetic calorimeter composed of BGO crystals,a lead-scintillator ring calorimeter at low polar angles[15],a scintillation counter system,a uranium hadron calorime-ter with proportional wire chamber readout and an accurate muon spectrometer.Forward-backward muon chambers,completed for the1995data taking,extend the polar angle coverage of the muon system down to24degrees[16]with respect to the beam line.All detectors are installed in a12m diameter magnet which provides a solenoidalﬁeld of0.5T in the central region and a toroidalﬁeld of1.2T in the forward-backward region.The luminosity is measured using BGO calorimeters preceded by silicon trackers[10]situated on each side of the detector.In the L3coordinate system the direction of the e−beam deﬁnes the z direction.The xy, or rφplane,is the bending plane of the magneticﬁeld,with the x direction pointing to the centre of the LEP ring.The coordinatesφandθdenote the azimuthal and polar angles.3Data AnalysisThe data collected between1993and1995are split into nine samples according to the year√and the centre-of-mass energy.Data samples atshowers are simulated with the GHEISHA[28]program.The performance of the detector, including ineﬃciencies and their time dependence as observed during data taking,is taken into account in the simulation.With this procedure,experimental systematic errors on cross sections and forward-backward asymmetries are minimized.4LEP Energy CalibrationThe average centre-of-mass energy of the colliding particles at the L3interaction point is calcu-lated using the results provided by the Working Group on LEP Energy[9].Every15minutes the average centre-of-mass energy is determined from measured LEP machine parameters,ap-plying the energy model which is based on calibration by resonant depolarisation[29].This model traces the time variation of the centre-of-mass energy of typically1MeV per hour.The average centre-of-mass energies are calculated for each data sample individually as luminosity weighted averages.Slightly diﬀerent values are obtained for diﬀerent reactions because of small diﬀerences in the usable luminosity.The errors on the centre-of-mass energies and their correlations for the1994data and for the two scans performed in1993and1995are given in form of a7×7covariance matrix in Table1.The uncertainties on the centre-of-mass energy for the data samples not included in this matrix,i.e.the1993and1995pre-scans,are18MeV and10MeV,respectively.Details of the treatment of these errors in theﬁts can be found in Appendix B.The energy distribution of the particles circulating in an e+e−-storage ring has aﬁnite width due to synchrotron oscillations.An experimentally observed cross section is therefore a convolution of cross sections at energies which are distributed around the average value in a gaussian form.The spread of the centre-of-mass energy for the L3interaction point as obtained from the observed longitudinal length of the particle bunches in LEP is listed in Table2[9]. The time variation of the average energy causes a similar,but smaller,eﬀect which is included in these numbers.All cross sections and forward-backward asymmetries quoted below are corrected for the energy spread to the average value of the centre-of-mass energy.The relative corrections on the measured hadronic cross sections amount to+1.7per mill(‰)at the Z pole and to−1.1‰and−0.6‰at the peak−2and peak+2energy,respectively.The absolute corrections on the forward-backward asymmetries are very small.The largest correction is−0.0002for the muon and tau peak−2data sets.The error on the energy spread is propagated into theﬁts,resulting in very small contributions to the errors of theﬁtted parameters(see Appendix B).The largest eﬀect is on the total width of the Z,contributing approximately0.3MeV to its error.During the operation of LEP,no evidence for an average longitudinal polarisation of the electrons or positrons has been observed.Stringent limits on residual polarisation during lumi-nosity runs are set such that the uncertainties on the determination of electroweak observables are negligible compared to their experimental errors[30].The determination of the LEP centre-of-mass energy in1990−92is described in Refer-ences[31].From these results the LEP energy error matrix given in Table3is derived.5Luminosity MeasurementThe integrated luminosity L is determined by measuring the number of small-angle Bhabha interactions e+e−→e+e−(γ).For this purpose two cylindrical calorimeters consisting of arraysof BGO crystals are located on either side of the interaction point.Both detectors are dividedinto two half-rings in the vertical plane to allow the opening of the detectors duringﬁlling ofLEP.A silicon strip detector,consisting of two layers measuring the polar angle,θ,and one layer measuring the azimuthal angle,φ,is situated in front of each calorimeter to preciselydeﬁne theﬁducial volume.A detailed description of the luminosity monitor and the luminosity determination can be found in Reference[10].The selection of small-angle Bhabha events is based on the energy depositions in adjacentcrystals of the BGO calorimeters which are grouped to form clusters.The highest-energy cluster on each side is considered for the luminosity analysis.For about98%of the cases a hitin the silicon detectors is matched with a cluster and its coordinate is used;otherwise the BGOcoordinate is retained.The event selection criteria are:1.The energy of the most energetic cluster is required to exceed0.8E b and the energy onthe opposite side must be greater than0.4E b,where E b is the beam energy.If the energyof the most energetic cluster is within±5%of E b the minimum energy requirement onthe opposite side is reduced to0.2E b in order to recover events with energy lost in the gaps between crystals.The distributions of the energy of the most energetic cluster andthe cluster on the opposite side as measured in the luminosity monitors are shown in Figure1for the1993data.All selection cuts except the one under study are applied.2.The cluster on one side must be conﬁned to a tightﬁducial volume:•32mrad<θ<54mrad;|φ−90◦|>11.25◦and|φ−270◦|>11.25◦.The requirements on the azimuthal angle remove the regions where the half-rings of thedetector meet.The cluster on the opposite side is required to be within a largerﬁducialvolume:•27mrad<π−θ<65mrad;|φ−90◦|>3.75◦and|φ−270◦|>3.75◦.This ensures that the event is fully contained in the detectors and edge eﬀects in the reconstruction are avoided.3.The coplanarity angle∆φ=φ(z<0)−φ(z>0)between the two clusters must satisfy|∆φ−180◦|<10◦.The distribution of the coplanarity angle is shown in Figure2.Very good agreement with theMonte Carlo simulation is observed.Four samples of Bhabha events are deﬁned by applying the tightﬁducial volume cut to oneof theθ-measuring silicon layers.Taking the average of the luminosities obtained from thesesamples minimizes the eﬀects of relative oﬀsets between the interaction point and the detectors. The energy and coplanarity cuts reduce the background from random beam-gas coincidences.The remaining contamination is very small:(3.4±2.2)·10−5.This number is estimated using the sidebands of the coplanarity distribution,10◦<|∆φ−180◦|<30◦,after requiring that neither of the two clusters have an energy within±5%of E b.The accepted cross section is determined from Monte Carlo e+e−→e+e−(γ)samples gen-√erated with the BHLUMI event generator at aﬁxed centre-of-mass energy ofs=91.25GeV the acceptedcross section is determined to be69.62nb.The statistical error on the Monte Carlo sample con-tributes0.35‰to the uncertainty of the luminosity measurement.The theoretical uncertainty on the Bhabha cross section in ourﬁducial volume is estimated to be0.61‰[12].The experimental errors of the luminosity measurement are small.Important sources of systematic errors are:geometrical uncertainties due to the internal alignment of the silicon detectors(0.15‰to0.27‰),temperature expansion eﬀects(0.14‰)and the knowledge on the longitudinal position of the silicon detectors(0.16‰to0.60‰).The precision depends on the accuracy of the detector surveys and on the stability of the detector and wafer positions during the diﬀerent years.The polar angle distribution of Bhabha scattering events used for the luminosity measure-ment is shown in Figure3.The structure seen in the central part of the+z side is due to the ﬂare in the beam pipe on this side.The imperfect description in the Monte Carlo does not pose any problem as it is far away from the edges of theﬁducial volume.The overall agreement between the data and Monte Carlo distributions of the selection quantities is good.Small discrepancies in the energy distributions at high energies are due to contamination of Bhabha events with beam-gas interactions and,at low energies,due to an imperfect description of the cracks between crystals.The selection uncertainty is estimated by varying the selection criteria over reasonable ranges and summing in quadrature the resulting contributions.This procedure yields errors between0.42‰and0.48‰for diﬀerent years.The luminosities determined from the four samples described above agree within these errors.The trigger ineﬃciency is measured using a sample of events triggered by only requiring an energy deposit exceeding30GeV on one side.It is found to be negligible.The various sources of uncertainties are summarized in bining them in quadra-ture yields total experimental errors on the luminosity of0.86‰,0.64‰and0.68‰in1993,1994 and1995.Correlations of the total experimental systematic errors between diﬀerent years are studied and the correlation matrix is given in Table5.The error from the theory is fully correlated.Because of the1/s dependence of the small angle Bhabha cross section,the uncertainty on the centre-of-mass energies causes a small additional uncertainty on the luminosity measure-ment.For instance,this amounts to0.1‰for the high statistics data sample of1994.This eﬀect is included in theﬁts performed in Section12and13,see Appendix B.The statistical error on the luminosity measurement from the number of observed small angle Bhabha events is also included in thoseﬁts.Table6lists the number of observed Bhabha events for the nine data samples and the corresponding errors on cross section measurements.√Combining all data sets taken in1993−95at6e+e−→hadrons(γ)Event SelectionHadronic Z decays are identiﬁed by their large energy deposition and high multiplicity in theelectromagnetic and hadron calorimeters.The selection criteria are similar to those applied in our previous analysis[4]:1.The total energy observed in the detector,E vis,normalised to the centre-of-mass energy√must satisfy0.5<E vis/√s′is the eﬀective centre-of-mass energy after initial state s′>0.1√s is estimated to be photon radiation.The acceptance for events in the data withnegligible.They are not considered as part of the signal and hence not corrected for.The interference between initial andﬁnal state photon radiation is not accounted for in the event generator.This eﬀect modiﬁes the angular distribution of the events in particular at very low polar angles where the detector ineﬃciencies are largest.However,the error from the imperfect simulation on the measured cross section,which includes initial-ﬁnal state interference as part of the signal,is estimated to be very small(≪0.1pb)in the centre-of-mass energyrange considered here.Quark pairs originating from pair production from initial state radiation√are considered as part of the signal if their invariant mass exceeds50%ofDiﬀerences of the implementation of QED eﬀects in both programs are studied and found tohave negligible impact on the acceptance.Hadronic Z decays are triggered by the energy,central track,muon or scintillation counter multiplicity triggers.The combined trigger eﬃciency is obtained from the fraction of events with one of these triggers missing as a function of the polar angle of the event thrust axis. This takes into account most of the correlations among triggers.A sizeable ineﬃciency is only observed for events in the very forward region of the detector,where hadrons can escape through the beam pipe.Trigger eﬃciencies,including all steps of the trigger system,between99.829% and99.918%are obtained for the various data sets.Trigger ineﬃciencies determined for data sets taken in the same year are statistically bining those data sets results in statistical errors of at most0.12‰which is assigned as systematic error to all data sets.The background from other Z decays is found to be small:2.9‰essentially only from e+e−→τ+τ−(γ).The uncertainty on this number is negligible compared to the total systematic error.The determination of the non-resonant background,mainly e+e−→e+e−hadrons,is based on the measured distribution of the visible energy shown in Figure5.The Monte Carlo program PHOJET is used to simulate two-photon collision processes.The absolute cross section isderived by scaling the Monte Carlo to obtain the best agreement with our data in the low end√of the E vis spectrum:0.32≤E vis/s is observed.This is in agreement with results of a similar calculation performed with the DIAG36program.Beam related background(beam-gas and beam-wall interactions)is small.To the extent that the E vis spectrum is similar to that of e+e−→e+e−hadrons,it is accounted for by determining the absolute normalisation from the data.As a check,the non-resonant background is estimated by extrapolating an exponential dependence of the E vis spectrum from the low energy part into the signal region.This method yields consistent results.Based on these studies we assign an error on the measured hadron cross section of3pb due to the understanding of the non-resonant background.This errorassignment is supported by our measurements of the hadronic cross section at high energies √(130GeV≤certainties which scale with the cross section and absolute uncertainties are separated because they translate in a diﬀerent way into errors on Z parameters,in particular on the total width. The scale error is further split into a part uncorrelated among the data samples,in this case consisting of the contribution of Monte Carlo statistics,and the rest which is taken to be fully correlated and amounts to0.39‰.The results of the e+e−→hadrons(γ)cross section measurements are discussed in Sec-tion10.7e+e−→µ+µ−(γ)Event SelectionThe selection of e+e−→µ+µ−(γ)in the1993and1994data is similar to the selection applied in previous years described in Reference[4].Two muons in the polar angular region|cosθ|<0.8 are required.Most of the muons,88%,are identiﬁed by a reconstructed track in the muon spectrometer.Muons are also identiﬁed by their minimum ionising particle(MIP)signature in the inner sub-detectors,if less than two muon chamber layers are hit.A muon candidate is denoted as a MIP,if at least one of the following conditions is fulﬁlled:1.A track in the central tracking chamber must point within5◦in azimuth to a cluster inthe electromagnetic calorimeter with an energy less than2GeV.2.On a road from the vertex through the barrel hadron calorimeter,at leastﬁve out of amaximum of32cells must be hit,with an average energy of less than0.4GeV per cell.3.A track in the central chamber or a low energy electromagnetic cluster must point within10◦in azimuth to a muon chamber hit.In addition,both the electromagnetic and the hadronic energy in a cone of12◦half-opening angle around the MIP candidate,corrected for the energy loss of the particle,must be less than 5GeV.Events of the reaction e+e−→µ+µ−(γ)are selected by the following criteria:1.The event must have a low multiplicity in the calorimeters N cl≤15.2.If at least one muon is reconstructed in the muon chambers,the maximum muon momen-tum must satisfy p max>0.6E b.If both muons are identiﬁed by their MIP signature there must be two tracks in the central tracking chamber with at least one with a transverse momentum larger than3GeV.3.The acollinearity angleξmust be less than90◦,40◦or5◦if two,one or no muons arereconstructed in the muon chambers.4.The event must be consistent with an origin of an e+e−-interaction requiring at least onetime measurement of a scintillation counter,associated to a muon candidate,to coincide within±3ns with the beam crossing.Also,there must be a track in the central tracking chamber with a distance of closest approach to the beam axis of less than5mm.As an example,Figure11shows the distribution of the maximum measured muon momen-tum for candidates in the1993−94data compared to the expectation for signal and backgroundprocesses.The acollinearity angle distribution of the selected muon pairs is shown in Figure12. The experimental angular resolution and radiation eﬀects are well reproduced by the Monte Carlo simulation.The analysis of the1995data in addition uses the newly installed forward-backward muon chambers.Theﬁducial volume is extended to|cosθ|<0.9.Each event must have at least one track in the central tracking chamber with a distance of closest approach in the transverse plane of less than1mm and a scintillation counter time coinciding within±5ns with the beam crossing.The rejection of cosmic ray muons in the1995data is illustrated in Figure13.For events with muons reconstructed in the muon chambers the maximum muon momentum must be larger than2µ+µ−(γ)are summarised in Table8.Resonant four-fermionﬁnal states with a high-mass muon pair and a low-mass fermion pair are accepted.These events are considered as part of the signal if the invariant mass of√the muon pair exceeds0.5,(2)σF+σBwhereσF is the cross section for events with the fermion scattered into the hemisphere which is forward with respect to the e−beam direction.The cross section in the backward hemisphere is denoted byσB.Events with hard photon bremsstrahlung are removed from the sample by requiring that the acollinearity angle of the event be less than15◦.The diﬀerential cross section in the angular region|cosθ|<0.9can then be approximated by the lowest order angular dependence to suﬃcient precision:dσ8 1+cos2θ +A FB cosθ,(3) withθbeing the polar angle of theﬁnal state fermion with respect to the e−beam direction.For each data set the forward-backward asymmetry is determined from a maximum likeli-hoodﬁt to our data where the likelihood function is deﬁned as the product over the selected events labelled i of the diﬀerential cross section evaluated at their respective scattering angle θi:L= i 3strongly depends on the number of muon chamber layers used in the reconstruction.The charge confusion is determined for each event class individually.The average charge confusion probability,almost entirely caused by muons only measured in the central tracking chamber, is(3.2±0.3)‰,(0.8±0.1)‰and(1.0±0.3)‰for the years1993,1994and1995,respectively, where the errors are statistical.The improvement in the charge determination for1994and 1995reﬂects the use of the silicon microvertex detector.The correction for charge confusion is proportional to the forward-backward asymmetry and it is less than0.001for all data sets.To estimate a possible bias from a preferred orientation of events with the two muons measured to have the same charge we determine the forward-backward asymmetry of these events using the track with a measured momentum closer to the beam energy.The asymmetry of this subsample is statistically consistent with the standard measurement.Including these like-sign events in the1994sample would change the measured asymmetry by0.0008.Half of this number is taken as an estimate of a possible bias of the asymmetry measurement from charge confusion in the1993−94data.The same procedure is applied to the1995data and the statistical precision limits a possible bias to0.0010.Diﬀerences of the momentum reconstruction in forward and backward events would cause a bias of the asymmetry measurement because of the requirement on the maximum measured muon momentum.We determine the loss of eﬃciency due to this cut separately for forward and backward events by selecting muon pairs without cuts on the reconstructed momentum.No signiﬁcant diﬀerence is observed and the statistical error of this comparison limits the possible eﬀect on the forward-backward asymmetry to be less than0.0004and0.0009for the1993−94 and1995data,respectively.Other possible biases from the selection cuts on the measurement of the forward-backward asymmetry are negligible.This is veriﬁed by a Monte Carlo study which shows that events not selected for the asymmetry measurement,but inside theﬁducial volume and withξ<15◦,do not have a diﬀerent A FB value.The background from e+e−→τ+τ−(γ)events is found to have the same asymmetry as the signal and thus neither necessitates a correction nor causes a systematic uncertainty.The eﬀect of the contribution from the two-photon process e+e−→e+e−µ+µ−,further reduced by the tighter acollinearity cut on the measured muon pair asymmetry,can be neglected.The forward-backward asymmetry of the cosmic ray muon background is measured to be−0.02±0.13using the events in the sideband of the distribution of closest approach to the interaction point. Weighted by the relative contribution to the data set this leads to corrections of−0.0007and +0.0003to the peak−2and peak+2asymmetries,respectively.On the peak this correction is negligible.The statistical uncertainty of the measurement of the cosmic ray asymmetry causes a systematic error of0.0001on the peak and between0.0003and0.0005for the peak−2and peak+2data sets.The systematic uncertainties on the measurement of the muon forward-backward asymmetry are summarised in Table9.In1993−94the total systematic error amounts to0.0008at the peak points and to0.0009at the oﬀ-peak points due to the larger contamination of cosmic ray muons.For the1995data the determination of systematic errors is limited by the number of events taken with the new detector conﬁguration and the total error is estimated to be0.0015.In Figure15the diﬀerential cross sections dσ/dcosθmeasured from the1993−95data sets are shown for three diﬀerent centre-of-mass energies.The data are corrected for detector acceptance and charge confusion.Data sets with a centre-of-mass energy close to m Z,as well as the data at peak−2and the data at peak+2,are combined.The data are compared to the diﬀerential cross section shape given in Equation3.The results of the total cross section and forward-backward asymmetry measurements in e+e−→µ+µ−(γ)are presented in Section10.8e+e−→τ+τ−(γ)Event SelectionThe selection of e+e−→τ+τ−(γ)events aims to select all hadronic and leptonic decay modes of the tau.Z decays into tau leptons are distinguished from other Z decays by the lower visible energy due to the presence of neutrinos and the lower particle multiplicity as compared to hadronic Z pared to our previous analysis[4]the selection of e+e−→τ+τ−(γ) events is extended to a larger polar angular range,|cosθt|≤0.92,whereθt is deﬁned by the thrust axis of the event.Event candidates are required to have a jet,constructed from calorimetric energy de-posits[36]and muon tracks,with an energy of at least8GeV.Energy deposits in the hemisphere opposite to the direction of this most energetic jet are combined to form a second jet.The two jets must have an acollinearity angleξ<10◦.There is no energy requirement on the second jet.High multiplicity hadronic Z decays are rejected by allowing at most three tracks matched to any of the two jets.In each of the two event hemispheres there should be no track with an angle larger than18◦with respect to the jet axis.Resonant four-fermionﬁnal states with a high mass tau pair and a low mass fermion pair are mostly kept in the sample.The multiplicity cut aﬀects only tau decays into three charged particles with the soft fermion close in space leading to corrections of less than1‰.If the energy in the electromagnetic calorimeter of theﬁrst jet exceeds85%,or the energy of the second jet exceeds80%,of the beam energy with a shape compatible with an electromagnetic shower the event is classiﬁed as e+e−→e+e−(γ)background and hence rejected. Background from e+e−→µ+µ−(γ)is removed by requiring that there be no isolated muon with a momentum larger than80%of the beam energy and that the sum of all muon momenta does not exceed1.5E b.Events are rejected if they are consistent with the signature of two MIPs.To suppress background from cosmic ray events the time of scintillation counter hits asso-ciated to muon candidates must be within±5ns of the beam crossing.In addition,the track in the muon chambers must be consistent with originating from the interaction point.In Figures16to19the energy in the most energetic jet,the number of tracks associated to both jets,the acollinearity between the two jets and the distribution of|cosθt|are shown for the1994data.Data and Monte Carlo expectations are compared after all cuts are applied, except the one under study.Good agreement between data and Monte Carlo is observed.Small discrepancies seen in Figure17are due to the imperfect description of the track reconstruction eﬃciency in the central chamber.Their impact on the total cross section measurement is small and is included in the systematic error given below.Tighter selection cuts must be applied in the region between barrel and end-cap part of the BGO calorimeter and in the end-cap itself,reducing the selection eﬃciency(see Figure19). This is due to the increasing background from Bhabha scattering.Most importantly the shower shape in the hadron calorimeter is also used to identify candidate electrons and the cuts on the energy of theﬁrst and second jet in the electromagnetic end-cap calorimeter are tightened to 75%of the beam energy.。

物理学专业英语

华中师范大学物理学院物理学专业英语仅供内部学习参考！2014一、课程的任务和教学目的通过学习《物理学专业英语》，学生将掌握物理学领域使用频率较高的专业词汇和表达方法，进而具备基本的阅读理解物理学专业文献的能力。

通过分析《物理学专业英语》课程教材中的范文，学生还将从英语角度理解物理学中个学科的研究内容和主要思想，提高学生的专业英语能力和了解物理学研究前沿的能力。

培养专业英语阅读能力，了解科技英语的特点，提高专业外语的阅读质量和阅读速度；掌握一定量的本专业英文词汇，基本达到能够独立完成一般性本专业外文资料的阅读；达到一定的笔译水平。

要求译文通顺、准确和专业化。

二、课程内容课程内容包括以下章节：物理学、经典力学、热力学、电磁学、光学、原子物理、统计力学、量子力学和狭义相对论三、基本要求1.充分利用课内时间保证充足的阅读量（约1200~1500词/学时），要求正确理解原文。

2.泛读适量课外相关英文读物，要求基本理解原文主要内容。

3.掌握基本专业词汇（不少于200词）。

4.应具有流利阅读、翻译及赏析专业英语文献，并能简单地进行写作的能力。

四、参考书目录1 Physics 物理学 (1)Introduction to physics (1)Classical and modern physics (2)Research fields (4)V ocabulary (7)2 Classical mechanics 经典力学 (10)Introduction (10)Description of classical mechanics (10)Momentum and collisions (14)Angular momentum (15)V ocabulary (16)3 Thermodynamics 热力学 (18)Introduction (18)Laws of thermodynamics (21)System models (22)Thermodynamic processes (27)Scope of thermodynamics (29)V ocabulary (30)4 Electromagnetism 电磁学 (33)Introduction (33)Electrostatics (33)Magnetostatics (35)Electromagnetic induction (40)V ocabulary (43)5 Optics 光学 (45)Introduction (45)Geometrical optics (45)Physical optics (47)Polarization (50)V ocabulary (51)6 Atomic physics 原子物理 (52)Introduction (52)Electronic configuration (52)Excitation and ionization (56)V ocabulary (59)7 Statistical mechanics 统计力学 (60)Overview (60)Fundamentals (60)Statistical ensembles (63)V ocabulary (65)8 Quantum mechanics 量子力学 (67)Introduction (67)Mathematical formulations (68)Quantization (71)Wave-particle duality (72)Quantum entanglement (75)V ocabulary (77)9 Special relativity 狭义相对论 (79)Introduction (79)Relativity of simultaneity (80)Lorentz transformations (80)Time dilation and length contraction (81)Mass-energy equivalence (82)Relativistic energy-momentum relation (86)V ocabulary (89)正文标记说明：蓝色Arial字体（例如energy）：已知的专业词汇蓝色Arial字体加下划线（例如electromagnetism）：新学的专业词汇黑色Times New Roman字体加下划线（例如postulate）：新学的普通词汇1 Physics 物理学1 Physics 物理学Introduction to physicsPhysics is a part of natural philosophy and a natural science that involves the study of matter and its motion through space and time, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic disciplines, perhaps the oldest through its inclusion of astronomy. Over the last two millennia, physics was a part of natural philosophy along with chemistry, certain branches of mathematics, and biology, but during the Scientific Revolution in the 17th century, the natural sciences emerged as unique research programs in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry,and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms of other sciences, while opening new avenues of research in areas such as mathematics and philosophy.Physics also makes significant contributions through advances in new technologies that arise from theoretical breakthroughs. For example, advances in the understanding of electromagnetism or nuclear physics led directly to the development of new products which have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.Core theoriesThough physics deals with a wide variety of systems, certain theories are used by all physicists. Each of these theories were experimentally tested numerous times and found correct as an approximation of nature (within a certain domain of validity).For instance, the theory of classical mechanics accurately describes the motion of objects, provided they are much larger than atoms and moving at much less than the speed of light. These theories continue to be areas of active research, and a remarkable aspect of classical mechanics known as chaos was discovered in the 20th century, three centuries after the original formulation of classical mechanics by Isaac Newton (1642–1727) 【艾萨克·牛顿】.University PhysicsThese central theories are important tools for research into more specialized topics, and any physicist, regardless of his or her specialization, is expected to be literate in them. These include classical mechanics, quantum mechanics, thermodynamics and statistical mechanics, electromagnetism, and special relativity.Classical and modern physicsClassical mechanicsClassical physics includes the traditional branches and topics that were recognized and well-developed before the beginning of the 20th century—classical mechanics, acoustics, optics, thermodynamics, and electromagnetism.Classical mechanics is concerned with bodies acted on by forces and bodies in motion and may be divided into statics (study of the forces on a body or bodies at rest), kinematics (study of motion without regard to its causes), and dynamics (study of motion and the forces that affect it); mechanics may also be divided into solid mechanics and fluid mechanics (known together as continuum mechanics), the latter including such branches as hydrostatics, hydrodynamics, aerodynamics, and pneumatics.Acoustics is the study of how sound is produced, controlled, transmitted and received. Important modern branches of acoustics include ultrasonics, the study of sound waves of very high frequency beyond the range of human hearing; bioacoustics the physics of animal calls and hearing, and electroacoustics, the manipulation of audible sound waves using electronics.Optics, the study of light, is concerned not only with visible light but also with infrared and ultraviolet radiation, which exhibit all of the phenomena of visible light except visibility, e.g., reflection, refraction, interference, diffraction, dispersion, and polarization of light.Heat is a form of energy, the internal energy possessed by the particles of which a substance is composed; thermodynamics deals with the relationships between heat and other forms of energy.Electricity and magnetism have been studied as a single branch of physics since the intimate connection between them was discovered in the early 19th century; an electric current gives rise to a magnetic field and a changing magnetic field induces an electric current. Electrostatics deals with electric charges at rest, electrodynamics with moving charges, and magnetostatics with magnetic poles at rest.Modern PhysicsClassical physics is generally concerned with matter and energy on the normal scale of1 Physics 物理学observation, while much of modern physics is concerned with the behavior of matter and energy under extreme conditions or on the very large or very small scale.For example, atomic and nuclear physics studies matter on the smallest scale at which chemical elements can be identified.The physics of elementary particles is on an even smaller scale, as it is concerned with the most basic units of matter; this branch of physics is also known as high-energy physics because of the extremely high energies necessary to produce many types of particles in large particle accelerators. On this scale, ordinary, commonsense notions of space, time, matter, and energy are no longer valid.The two chief theories of modern physics present a different picture of the concepts of space, time, and matter from that presented by classical physics.Quantum theory is concerned with the discrete, rather than continuous, nature of many phenomena at the atomic and subatomic level, and with the complementary aspects of particles and waves in the description of such phenomena.The theory of relativity is concerned with the description of phenomena that take place in a frame of reference that is in motion with respect to an observer; the special theory of relativity is concerned with relative uniform motion in a straight line and the general theory of relativity with accelerated motion and its connection with gravitation.Both quantum theory and the theory of relativity find applications in all areas of modern physics.Difference between classical and modern physicsWhile physics aims to discover universal laws, its theories lie in explicit domains of applicability. Loosely speaking, the laws of classical physics accurately describe systems whose important length scales are greater than the atomic scale and whose motions are much slower than the speed of light. Outside of this domain, observations do not match their predictions.Albert Einstein【阿尔伯特·爱因斯坦】contributed the framework of special relativity, which replaced notions of absolute time and space with space-time and allowed an accurate description of systems whose components have speeds approaching the speed of light.Max Planck【普朗克】, Erwin Schrödinger【薛定谔】, and others introduced quantum mechanics, a probabilistic notion of particles and interactions that allowed an accurate description of atomic and subatomic scales.Later, quantum field theory unified quantum mechanics and special relativity.General relativity allowed for a dynamical, curved space-time, with which highly massiveUniversity Physicssystems and the large-scale structure of the universe can be well-described. General relativity has not yet been unified with the other fundamental descriptions; several candidate theories of quantum gravity are being developed.Research fieldsContemporary research in physics can be broadly divided into condensed matter physics; atomic, molecular, and optical physics; particle physics; astrophysics; geophysics and biophysics. Some physics departments also support research in Physics education.Since the 20th century, the individual fields of physics have become increasingly specialized, and today most physicists work in a single field for their entire careers. "Universalists" such as Albert Einstein (1879–1955) and Lev Landau (1908–1968)【列夫·朗道】, who worked in multiple fields of physics, are now very rare.Condensed matter physicsCondensed matter physics is the field of physics that deals with the macroscopic physical properties of matter. In particular, it is concerned with the "condensed" phases that appear whenever the number of particles in a system is extremely large and the interactions between them are strong.The most familiar examples of condensed phases are solids and liquids, which arise from the bonding by way of the electromagnetic force between atoms. More exotic condensed phases include the super-fluid and the Bose–Einstein condensate found in certain atomic systems at very low temperature, the superconducting phase exhibited by conduction electrons in certain materials,and the ferromagnetic and antiferromagnetic phases of spins on atomic lattices.Condensed matter physics is by far the largest field of contemporary physics.Historically, condensed matter physics grew out of solid-state physics, which is now considered one of its main subfields. The term condensed matter physics was apparently coined by Philip Anderson when he renamed his research group—previously solid-state theory—in 1967. In 1978, the Division of Solid State Physics of the American Physical Society was renamed as the Division of Condensed Matter Physics.Condensed matter physics has a large overlap with chemistry, materials science, nanotechnology and engineering.Atomic, molecular and optical physicsAtomic, molecular, and optical physics (AMO) is the study of matter–matter and light–matter interactions on the scale of single atoms and molecules.1 Physics 物理学The three areas are grouped together because of their interrelationships, the similarity of methods used, and the commonality of the energy scales that are relevant. All three areas include both classical, semi-classical and quantum treatments; they can treat their subject from a microscopic view (in contrast to a macroscopic view).Atomic physics studies the electron shells of atoms. Current research focuses on activities in quantum control, cooling and trapping of atoms and ions, low-temperature collision dynamics and the effects of electron correlation on structure and dynamics. Atomic physics is influenced by the nucleus (see, e.g., hyperfine splitting), but intra-nuclear phenomena such as fission and fusion are considered part of high-energy physics.Molecular physics focuses on multi-atomic structures and their internal and external interactions with matter and light.Optical physics is distinct from optics in that it tends to focus not on the control of classical light fields by macroscopic objects, but on the fundamental properties of optical fields and their interactions with matter in the microscopic realm.High-energy physics (particle physics) and nuclear physicsParticle physics is the study of the elementary constituents of matter and energy, and the interactions between them.In addition, particle physicists design and develop the high energy accelerators,detectors, and computer programs necessary for this research. The field is also called "high-energy physics" because many elementary particles do not occur naturally, but are created only during high-energy collisions of other particles.Currently, the interactions of elementary particles and fields are described by the Standard Model.●The model accounts for the 12 known particles of matter (quarks and leptons) thatinteract via the strong, weak, and electromagnetic fundamental forces.●Dynamics are described in terms of matter particles exchanging gauge bosons (gluons,W and Z bosons, and photons, respectively).●The Standard Model also predicts a particle known as the Higgs boson. In July 2012CERN, the European laboratory for particle physics, announced the detection of a particle consistent with the Higgs boson.Nuclear Physics is the field of physics that studies the constituents and interactions of atomic nuclei. The most commonly known applications of nuclear physics are nuclear power generation and nuclear weapons technology, but the research has provided application in many fields, including those in nuclear medicine and magnetic resonance imaging, ion implantation in materials engineering, and radiocarbon dating in geology and archaeology.University PhysicsAstrophysics and Physical CosmologyAstrophysics and astronomy are the application of the theories and methods of physics to the study of stellar structure, stellar evolution, the origin of the solar system, and related problems of cosmology. Because astrophysics is a broad subject, astrophysicists typically apply many disciplines of physics, including mechanics, electromagnetism, statistical mechanics, thermodynamics, quantum mechanics, relativity, nuclear and particle physics, and atomic and molecular physics.The discovery by Karl Jansky in 1931 that radio signals were emitted by celestial bodies initiated the science of radio astronomy. Most recently, the frontiers of astronomy have been expanded by space exploration. Perturbations and interference from the earth's atmosphere make space-based observations necessary for infrared, ultraviolet, gamma-ray, and X-ray astronomy.Physical cosmology is the study of the formation and evolution of the universe on its largest scales. Albert Einstein's theory of relativity plays a central role in all modern cosmological theories. In the early 20th century, Hubble's discovery that the universe was expanding, as shown by the Hubble diagram, prompted rival explanations known as the steady state universe and the Big Bang.The Big Bang was confirmed by the success of Big Bang nucleo-synthesis and the discovery of the cosmic microwave background in 1964. The Big Bang model rests on two theoretical pillars: Albert Einstein's general relativity and the cosmological principle (On a sufficiently large scale, the properties of the Universe are the same for all observers). Cosmologists have recently established the ΛCDM model (the standard model of Big Bang cosmology) of the evolution of the universe, which includes cosmic inflation, dark energy and dark matter.Current research frontiersIn condensed matter physics, an important unsolved theoretical problem is that of high-temperature superconductivity. Many condensed matter experiments are aiming to fabricate workable spintronics and quantum computers.In particle physics, the first pieces of experimental evidence for physics beyond the Standard Model have begun to appear. Foremost among these are indications that neutrinos have non-zero mass. These experimental results appear to have solved the long-standing solar neutrino problem, and the physics of massive neutrinos remains an area of active theoretical and experimental research. Particle accelerators have begun probing energy scales in the TeV range, in which experimentalists are hoping to find evidence for the super-symmetric particles, after discovery of the Higgs boson.Theoretical attempts to unify quantum mechanics and general relativity into a single theory1 Physics 物理学of quantum gravity, a program ongoing for over half a century, have not yet been decisively resolved. The current leading candidates are M-theory, superstring theory and loop quantum gravity.Many astronomical and cosmological phenomena have yet to be satisfactorily explained, including the existence of ultra-high energy cosmic rays, the baryon asymmetry, the acceleration of the universe and the anomalous rotation rates of galaxies.Although much progress has been made in high-energy, quantum, and astronomical physics, many everyday phenomena involving complexity, chaos, or turbulence are still poorly understood. Complex problems that seem like they could be solved by a clever application of dynamics and mechanics remain unsolved; examples include the formation of sand-piles, nodes in trickling water, the shape of water droplets, mechanisms of surface tension catastrophes, and self-sorting in shaken heterogeneous collections.These complex phenomena have received growing attention since the 1970s for several reasons, including the availability of modern mathematical methods and computers, which enabled complex systems to be modeled in new ways. Complex physics has become part of increasingly interdisciplinary research, as exemplified by the study of turbulence in aerodynamics and the observation of pattern formation in biological systems.Vocabulary★natural science 自然科学academic disciplines 学科astronomy 天文学in their own right 凭他们本身的实力intersects相交，交叉interdisciplinary交叉学科的，跨学科的★quantum 量子的theoretical breakthroughs 理论突破★electromagnetism 电磁学dramatically显著地★thermodynamics热力学★calculus微积分validity★classical mechanics 经典力学chaos 混沌literate 学者★quantum mechanics量子力学★thermodynamics and statistical mechanics热力学与统计物理★special relativity狭义相对论is concerned with 关注，讨论，考虑acoustics 声学★optics 光学statics静力学at rest 静息kinematics运动学★dynamics动力学ultrasonics超声学manipulation 操作，处理，使用University Physicsinfrared红外ultraviolet紫外radiation辐射reflection 反射refraction 折射★interference 干涉★diffraction 衍射dispersion散射★polarization 极化，偏振internal energy 内能Electricity电性Magnetism 磁性intimate 亲密的induces 诱导，感应scale尺度★elementary particles基本粒子★high-energy physics 高能物理particle accelerators 粒子加速器valid 有效的，正当的★discrete离散的continuous 连续的complementary 互补的★frame of reference 参照系★the special theory of relativity 狭义相对论★general theory of relativity 广义相对论gravitation 重力，万有引力explicit 详细的，清楚的★quantum field theory 量子场论★condensed matter physics凝聚态物理astrophysics天体物理geophysics地球物理Universalist博学多才者★Macroscopic宏观Exotic奇异的★Superconducting 超导Ferromagnetic铁磁质Antiferromagnetic 反铁磁质★Spin自旋Lattice 晶格，点阵，网格★Society社会，学会★microscopic微观的hyperfine splitting超精细分裂fission分裂，裂变fusion熔合，聚变constituents成分，组分accelerators加速器detectors 检测器★quarks夸克lepton 轻子gauge bosons规范玻色子gluons胶子★Higgs boson希格斯玻色子CERN欧洲核子研究中心★Magnetic Resonance Imaging磁共振成像，核磁共振ion implantation 离子注入radiocarbon dating放射性碳年代测定法geology地质学archaeology考古学stellar 恒星cosmology宇宙论celestial bodies 天体Hubble diagram 哈勃图Rival竞争的★Big Bang大爆炸nucleo-synthesis核聚合，核合成pillar支柱cosmological principle宇宙学原理ΛCDM modelΛ-冷暗物质模型cosmic inflation宇宙膨胀1 Physics 物理学fabricate制造，建造spintronics自旋电子元件，自旋电子学★neutrinos 中微子superstring 超弦baryon重子turbulence湍流，扰动，骚动catastrophes突变，灾变，灾难heterogeneous collections异质性集合pattern formation模式形成University Physics2 Classical mechanics 经典力学IntroductionIn physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces. The study of the motion of bodies is an ancient one, making classical mechanics one of the oldest and largest subjects in science, engineering and technology.Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. Besides this, many specializations within the subject deal with gases, liquids, solids, and other specific sub-topics.Classical mechanics provides extremely accurate results as long as the domain of study is restricted to large objects and the speeds involved do not approach the speed of light. When the objects being dealt with become sufficiently small, it becomes necessary to introduce the other major sub-field of mechanics, quantum mechanics, which reconciles the macroscopic laws of physics with the atomic nature of matter and handles the wave–particle duality of atoms and molecules. In the case of high velocity objects approaching the speed of light, classical mechanics is enhanced by special relativity. General relativity unifies special relativity with Newton's law of universal gravitation, allowing physicists to handle gravitation at a deeper level.The initial stage in the development of classical mechanics is often referred to as Newtonian mechanics, and is associated with the physical concepts employed by and the mathematical methods invented by Newton himself, in parallel with Leibniz【莱布尼兹】, and others.Later, more abstract and general methods were developed, leading to reformulations of classical mechanics known as Lagrangian mechanics and Hamiltonian mechanics. These advances were largely made in the 18th and 19th centuries, and they extend substantially beyond Newton's work, particularly through their use of analytical mechanics. Ultimately, the mathematics developed for these were central to the creation of quantum mechanics.Description of classical mechanicsThe following introduces the basic concepts of classical mechanics. For simplicity, it often2 Classical mechanics 经典力学models real-world objects as point particles, objects with negligible size. The motion of a point particle is characterized by a small number of parameters: its position, mass, and the forces applied to it.In reality, the kind of objects that classical mechanics can describe always have a non-zero size. (The physics of very small particles, such as the electron, is more accurately described by quantum mechanics). Objects with non-zero size have more complicated behavior than hypothetical point particles, because of the additional degrees of freedom—for example, a baseball can spin while it is moving. However, the results for point particles can be used to study such objects by treating them as composite objects, made up of a large number of interacting point particles. The center of mass of a composite object behaves like a point particle.Classical mechanics uses common-sense notions of how matter and forces exist and interact. It assumes that matter and energy have definite, knowable attributes such as where an object is in space and its speed. It also assumes that objects may be directly influenced only by their immediate surroundings, known as the principle of locality.In quantum mechanics objects may have unknowable position or velocity, or instantaneously interact with other objects at a distance.Position and its derivativesThe position of a point particle is defined with respect to an arbitrary fixed reference point, O, in space, usually accompanied by a coordinate system, with the reference point located at the origin of the coordinate system. It is defined as the vector r from O to the particle.In general, the point particle need not be stationary relative to O, so r is a function of t, the time elapsed since an arbitrary initial time.In pre-Einstein relativity (known as Galilean relativity), time is considered an absolute, i.e., the time interval between any given pair of events is the same for all observers. In addition to relying on absolute time, classical mechanics assumes Euclidean geometry for the structure of space.Velocity and speedThe velocity, or the rate of change of position with time, is defined as the derivative of the position with respect to time. In classical mechanics, velocities are directly additive and subtractive as vector quantities; they must be dealt with using vector analysis.When both objects are moving in the same direction, the difference can be given in terms of speed only by ignoring direction.University PhysicsAccelerationThe acceleration , or rate of change of velocity, is the derivative of the velocity with respect to time (the second derivative of the position with respect to time).Acceleration can arise from a change with time of the magnitude of the velocity or of the direction of the velocity or both . If only the magnitude v of the velocity decreases, this is sometimes referred to as deceleration , but generally any change in the velocity with time, including deceleration, is simply referred to as acceleration.Inertial frames of referenceWhile the position and velocity and acceleration of a particle can be referred to any observer in any state of motion, classical mechanics assumes the existence of a special family of reference frames in terms of which the mechanical laws of nature take a comparatively simple form. These special reference frames are called inertial frames .An inertial frame is such that when an object without any force interactions (an idealized situation) is viewed from it, it appears either to be at rest or in a state of uniform motion in a straight line. This is the fundamental definition of an inertial frame. They are characterized by the requirement that all forces entering the observer's physical laws originate in identifiable sources (charges, gravitational bodies, and so forth).A non-inertial reference frame is one accelerating with respect to an inertial one, and in such a non-inertial frame a particle is subject to acceleration by fictitious forces that enter the equations of motion solely as a result of its accelerated motion, and do not originate in identifiable sources. These fictitious forces are in addition to the real forces recognized in an inertial frame.A key concept of inertial frames is the method for identifying them. For practical purposes, reference frames that are un-accelerated with respect to the distant stars are regarded as good approximations to inertial frames.Forces; Newton's second lawNewton was the first to mathematically express the relationship between force and momentum . Some physicists interpret Newton's second law of motion as a definition of force and mass, while others consider it a fundamental postulate, a law of nature. Either interpretation has the same mathematical consequences, historically known as "Newton's Second Law":a m t v m t p F ===d )(d d dThe quantity m v is called the (canonical ) momentum . The net force on a particle is thus equal to rate of change of momentum of the particle with time.So long as the force acting on a particle is known, Newton's second law is sufficient to。

Orbital polarization in LiVO_2 and NaTiO_2

a rX iv:c ond-ma t/971223v1[c ond-m at.str-el]18D ec1997EUROPHYSICS LETTERS Europhys.Lett.,(),pp.()Orbital polarization in LiVO 2and NaTiO 2S.Yu.Ezhov 1,V.I.Anisimov 1,H.F.Pen 2,D.I.Khomskii 2,G.A.Sawatzky 21Institute of Metal Physics,GSP-170,Ekaterinburg,Russia 2Laboratory of Applied and Solid State Physics,Materials Science Centre,Univer-sity of Groningen,Nijenborgh 4,9747AG Groningen,The Netherlands (received ;accepted )PACS.71.15Mb –Density functional theory,local density approximation.PACS.71.27+a –Strongly correlated electron systems;heavy fermions.PACS.71.20−b –Electron density of states and band structure of crystalline solids.Abstract.–We present a band structure study of orbital polarization and ordering in the two-dimensional triangular lattice transition metal compounds LiVO 2and NaTiO 2.It is found that while in NaTiO 2the degeneracy of t 2g orbitals is lifted due to the trigonal symmetry of the crystal and the strong on cite Coulomb interaction,in LiVO 2orbital degeneracy remains and orbital ordering corresponding to the trimerization of the two-dimensional lattice develops.It is well known that transition metal compounds with orbital degeneracy will in some way restructure to remove that orbital degeneracy in the ground state.Well known is the example of a two-fold orbitally degenerate case of divalent Cu in octahedral symmetry with one hole in a e g -like orbital.A similar case is trivalent Mn in O h symmetry as in the now well known collossal magnetoresistance materials.In these so called strong Jan Teller systems local lattice distortions determine the type of orbital ordering.It is also well established that the relative spatial orientation of occupied orbitals on neighboring ions determines not only the magnitude but also the sign of the exchange interactions governing the magnetic structure of the system [1].In the early 3d transition metal compounds only the t 2g orbitals are occupied leaving us with three-fold degeneracy in the cases of Ti 3+and V 3+with one and two 3d electrons respectively assuming also O h symmetry.In contrast to the e g orbitals thebonding to the neighboring O 2p orbitals is much weaker,bandwidths are much smaller and therefore the removal of the orbital degeneracy may be more subtle.It has for example recently been suggested that the orbital degeneracy in LiVO 2can be lifted by a particular kind of orbital ordering driven by the nearest neighbor exchange interactions [2].The orbital ordering proposed there is one which simultaniously removes the frustration in the spin Hamiltonian of this triangular two-dimensional lattice and results in a non magnetic singlet ground state.Another much discussed two-dimensional triangular lattice spin system is NaTiO2with spin 1trigonal,and in that case the t2g level is split into a nondegenerate A1g and double degenerateS.E gbethe√2)(√4Fig.3.upperwithlocalpointsoneband90◦,sotheand a more delicate quantitative analysis is needed to clarify this problem.In the right panel ofﬁg.2the partial DOS for decomposition of the t2g band into orbitals of the A1g and E g symmetry are presented.One can see that the situation can not be described in the simple terms of A1g-E g”splitting”:both curves have the same width and they are approximately in the same energy region.We can estimate the actual splitting of the A1g and E g levels by calculating the values of the centres of gravity of these bands.In the case of NaTiO2with one d electron the center of gravity of the A1g band is0.1eV lower than that of the E g band.As a result the occupied part of t2g band has slightly more A1g character than E g,and the occupancy of orbitals are.25and.20per spin-orbital for A1g and for each E g correspondingly.This means that the degeneracy of the t2g orbitals is essentially lifted but the splitting is still much less than the band widths.This small splitting is non theS.EZHOV et al.:ORBITAL POLARIZATION IN LiVO2AND NaTiO25Fig.4.–The t2g holes from LDA+U calculations for LiVO2.Only V atoms for one triangle in a hexagonal plane are drawn.The view is from the point directly above V-triangleless important since as we will see below if we turn on the d-d Coulomb interaction in LDA+U the A1g band will be occupied and the E g unocupied now with a splitting mainly due to U. However the choice as to which band is occupied and which one not is dictated by the small crystalﬁeld splitting.The above result would also indicate that the A1g-E g local excitation energy would be only0.1eV or so and would contribute to charge conserving excitonic-like excitations.In this LDA+U calculation the d-d Coulomb interaction was found to be3.6eV (taking into account the screening of t2g electrons by e g electrons[12])which is much larger than the t2g band width and leads to the localization of a single d electron in the A1g orbital.The LDA+U calculations were carried out for both antiferromagnetic and ferromagnetic cases.For the AFM case we choose the simplest magnetic order with four nearest neighbors out of the six in the basal plane having anti-parallel spin orientation and other two parallel. Independent of the spin ordering a single d electron in the t2g shell of the Ti ion turned out to be localized in the A1g orbital.The occupation numbers for the majority spin are0.9 for A1g and0.1for E g for both FM and AFM cases.The Ti(3d)projected density-of-states obtained from LDA+U calculations is shown inﬁg.3(a).So we can say from theﬁg.3(a)that the LDA+U solution for NaTiO2is almost fully orbitally polarized.One can see from eq.1 that the A1g orbital(d3z2−r2inﬁg.3(a))is symmetric in the hexagonal Ti-Ti plane and the occupation of this orbital leads to the isotropic exchange.This indicates that NaTiO2would still behave like a frustrated spin system.In the case of LiVO2the centre of gravity of the A1g band is only0.025eV lower then the centre of gravity of the E g band,and the resulting occupancies are0.37and0.36for A1g and for each E g-orbitals correspondingly.In this situation orbital degeneracy is not lifted,since we now have two electrons one in a A1g and one in a E g orbital,because the Hunds rule exchange6EUROPHYSICS LETTERS strongly favours the high spin state.As a result the appearance of some kind of orbital order can be expected.In[2,13,14]the formation of local spin singlets on trimers containing V-atom triangles was suggested as the model explaining the low-temperature nonmagnetic behavior of LiVO2.Those spin singlets were stabilized by a speciﬁc orbital order[2].The LDA+U method is based on a mean-ﬁeld approximation and can not fully reproduce the essentially many-electron singlet wave function,especially the correct energy diﬀerence of singlet-triplet conﬁgurations.However a single Slater determinant trial wave function can still describe the basic relationship between spin and orbital degrees of freedom.To imitate trimer spin singlets we performed LDA+U calculations with spin-order of the type”up-down-zero”on every triangle(closed circles on theﬁg.1).The self-consistent calculations resulted in the orbital order of the same type as proposed in[2]from model calculations[ﬁg.3(b)]:on every V atom the occupied orbitals are xz and yz if in a local coordinate system z axis is directed towards the oxygen atom sitting just above the center of V-triangle,and x and y axes are directed towards other oxygens of an octahedron(ﬁg.1).We should also mention the fact that the LDA+U calculations give the correct semiconducting state for LiVO2[ﬁg.3(b)]instead of a metallic state from”normal”LDA(left panel ofﬁg.2).Inﬁg.4the angular distribution of the t2g hole is presented as was obtained from the LDA+U calculations.It indicates the same orbital order proposed in[2](ﬁg.1(a)in[2]):xz and yz orbitals are occupied,the t2g hole is in xy orbital in a local coordinate system of every V atom.Both LiVO2and NaTiO2were regarded as candidates for realization of Anderson’s”res-onating valence bond”systems with a quantum liquid of randomly distributed spin singlet pairs.Our results show that while in LiVO2more complicated trimer spin singlets with corresponding orbital order are formed,no orbital order due to the crystalﬁeld lifting of the orbital degeneracy is present in NaTiO2,and its magnetic properties are most probably explained by a nondegenerate model,so that it is indeed a good candidate for Anderson’s RVB state.What then is the nature of the structural phase transition observed in NaTiO2at T c=250,remains an open question.Summarizing,we have shown that the degeneracy of the t2g-orbitals in NaTiO2is lifted because of the trigonal symmetry of the crystal and the large d-d Coulomb interaction and no orbital ordering occurs.In LiVO2orbital degeneracy remains in spite of the same trigonal distortion as in NaTiO2,and in eﬀect the orbital ordering consistent with the trimerization of the two-dimensional lattice takes place.***We thank Dr.S.J.Clarke for providing us with the detailed data of the NaTiO2crystal structure prior to publication.This investigation was supported by the Russian Foundation for Fundamental Investigations(RFFI grant9602-16167)and by the Netherlands Organization for Fundamental Research on Matter(FOM),withﬁnancial support by the Netherlands Organization for the advance of Pure Science(NWO).REFERENCES[1]K.I.Kugel and D.I.Khomskii,p.,25231(1982).[2]H.F.Pen,J.van den Brink,D.I.Khomskii,G.A.Sawatzky,Phys.Rev.Lett.,781323(1997).[3]P.W.Anderson,Science,2351196(1987);P.W.Anderson,Mater.Res.Bull.,8153(1973).[4]P.F.Bongers,Ph.D.thesis,(University of Leiden)1957.[5]K.Kobayashi,K.Kosuge,S.Kashi,Mater.Res.Bull.,495(1969);L.P.Cardoso,D.E.Cox,T.A.Hewston,B.L.Chamberland,J.Solid State Chem.,72234(1988).S.EZHOV et al.:ORBITAL POLARIZATION IN LiVO2AND NaTiO27[6]K.Terakura,T.Oguchi,A.R.Williams,J.K¨u bler,Phys.Rev.B,304734(1984).[7]Andersen O.K.,Phys.Rev.B,123060(1975).[8]P.Hoenberg,W.Kohn,Phys.Rev.,136B864(1964);W.Kohn,L.J.Sham,Phys.Rev.,140A1133(1965).[9]V.I.Anisimov,J.Zaanen,Andersen O.K.,Phys.Rev.B,44943(1991);V.I.Anisimov,F.Aryasetiawan,A.I.Lichtenstein,J.Phys.:Condens.Matter,9767(1997).[10]Katsushiro Imai,Hiroshi Sawa,Masayoshi Koike,Masashi Hasegawa,Humihiko Takei,J.Solid State Chem.,114184(1995).[11]S.J.Clarke,A.C.Duggan,A.J.Fowkes,A.Harrison,R.M.Ibberson,M.J.Rosseinsky,m.,(1996)409;S.J.Clarke,(private communication).[12]V.I.Anisimov,O.Gunnarsson,Phys.Rev.B,437570(1991);W.E.Pickett,S.E.Erwin,E.C.Ethridge,(Preprint No.condens-matter/9611225).[13]G.B.Goodenough,Magnetism and the Chemical bond,(Interscience Publishers,N.Y.)1963p.269.[14]G.B.Goodenough,G.Dutta,and A.Manthiram,Phys.Rev.B.,4310170(1991).。

Complex magnetic interactions and charge transfer effects in highlyorderedNixFe1-x nano-wires

Complex magnetic interactions and charge transfer effectsin highly ordered Ni x Fe1Àx nano-wiresShu-Jui Chang,Chao-Yao Yang,Hao-Chung Ma,Yuan-Chieh Tseng nDepartment of Materials Science&Engineering,National Chiao Tung University,1001Ta Hsueh Road,Hsin-Chu30010,Taiwan,ROCa r t i c l e i n f oArticle history:Received23October2012Received in revised form12November2012Available online3December2012Keywords:NiFeNano-wiresXMCDCharge transfera b s t r a c tThis work investigates the subtle magnetic interactions within the Ni x Fe1Àx(x¼0.3,0.5,and1.0)nano-wires by probing spin-dependent behaviors of the two constituted elements.The wires were fabricatedby electro-deposition and an anode aluminum oxide template to produce free-standing nature,and theNi–Fe interactions were probed by x-ray magnetic spectroscopy across a BCC-FCC structuraltransition.The wires’magneto-structural properties were predominated by Ni,as reﬂected by adecrease but an increase in total magnetization and FCC x-ray intensity with increasing x,even if the Femoment increased simultaneously.Upon annealing,a prominent charge transfer,together with thechanges of spin-dependent states,took place in the Ni and Fe3d orbitals,and a structural disorderingwas also obtained,for the wires at x¼0.3.The charge transfer led to a local magnetic-compensation forthe two elements,explaining the minor change in total magnetization for x¼0.3probed by avibrational sample magnetometer.When x was increased to0.5,however,the charge transfer becameinactive due to persistent structural stability supported by Ni,albeit resulting in nearly invariantmagnetization similar to that of x¼0.3.The complexity of the Ni–Fe interactions varied with thecomposition and involved the modiﬁcations of the coupled magnetic,electronic and structural degreesof freedom.The study identiﬁes the roles of Ni and Fe as unequally-inﬂuential in Ni x Fe1Àx,whichprovides opportunities to re-investigate the compound’s properties concerning its technologicalapplications.&2012Elsevier B.V.All rights reserved.1.IntroductionBecause permalloy(Ni80Fe20)[1,2]and invar(Ni65Fe35)[3,4]alloys are the central components of many modern technologies,shaping Ni x Fe1Àx into various forms in a controllable manner,andinvestigating the varying properties corresponding to the shapinghave captured great research popularity.Although the propertiesof Ni x Fe1Àx have been reported in several systems[5,6],probingNi–Fe interactions in nanostructures continues to provide aplayground for realizing the compound’s fundamental properties,as well as for developing principles to create the functionalstructures.Motivated by this cause,we combined pulse-electrodepositionand an anodic aluminum oxide(AAO)template to fabricateNi x Fe1Àx nano-wires with a precise control over the size andshape.The wires’coupled magnetic,electronic and structuraldegrees of freedom that determine the wires’macroscopic mag-netism were realized by the element-speciﬁc probes of Ni and Fe.An annealing-induced,spin-dependent Ni–Fe charge transfereffect was especially focused in this study.The modiﬁcations inmicroscopic magnetism,and associated electronic re-establish-ments,are often neglected if changes in macroscopic magnetismare imperceptible.Nevertheless,the invisible electronic interac-tions are essential,as they drive the magnetic ordering,alsoserving as the cause for many anomalous effects.This is a seriousconcern in Ni x Fe1Àx,because the compound disobeyed the Slater–Pauling prediction[7,8]at certain compositions,depending on thesystem and treatment[9,10].This implies that the magnetism ofNi x Fe1Àx is not simply the sum of the local moments of Ni and Febut rather depends on the local interactions of the two.Theinteractions may vary with x,because increasing x altered thecrystallographic structure of Ni x Fe1Àx[5,6].The underlying phy-sics is still under debate due to incomplete understanding ofNi x Fe1Àx and hence is worthy of exploration.Using x-ray magnetic spectroscopy,we successfully discrimi-nated the magnetisms of Ni and Fe with varying x.Further,employing rapid thermal annealing(RTA)we were able to createstructural instability,and examine the correlation between thestructural instability and the wires’magnetic and electronicresponses with x-dependency,based on the isolated Ni(Fe)behaviors.We discovered aﬂow of spins from Fe to Ni3dconduction band when the structural stability was lost,despiteContents lists available at SciVerse ScienceDirectjournal homepage:/locate/jmmmJournal of Magnetism and Magnetic Materials0304-8853/$-see front matter&2012Elsevier B.V.All rights reserved./10.1016/j.jmmm.2012.11.037*Corresponding author.Tel.:þ88635731898;fax:þ88635724727.E-mail address:yctseng21@.tw(Y.-C.Tseng).Journal of Magnetism and Magnetic Materials332(2013)21–27the total magnetization of the wires remaining almost unaltered. This resulted in a decrease but an increase in Fe and Ni local moments,together with the changes of the electronic states of the two.The element-speciﬁc probe uncovered the local magnetic-compensation of the wires invisible to the conventional probes, perfectly explaining the minor change in magnetization upon annealing.However,such phenomenon was absent when the structural stability was persistent,which can be related to the increased dominance of Ni.In summary this work investigates the properties of the Ni x Fe1Àx bimetallic wires from a microscopic picture.This work subverts our thoughts that the two elements are equally-inﬂuential in Ni x Fe1Àx,and therefore opens research opportunities concerning the compound’s properties from both technical and fundamental aspects.2.ExperimentalPulse-electrodeposition method combined with an AAO tem-plate were used to fabricate highly aligned Ni x Fe1Àx nano-wires with varying compositions(x¼0.3,0.5,and1).To do so,a commercial AAO featuring60m m in thickness and0.25m m in pore-diameter(aspect-ratio¼300)was patterned by a Ti/Cu electrode only on one side using a sputtering facility,where Ti served as an adhesion layer between the AAO and the Cu seed layer.The AAO inter-pore distance was about0.45m m.The Cu seed layer of the Ti/Cu electrode was not completely homoge-neous,so an extra Cu-electrodeposition on the AAO/Ti/Cu was followed to provide better quality of Cu,operating at a deposition current of15mA and a deposition time of1.5h.Afterwards,the AAO/Ti/Cu was immersed into a deposition bath containing FeSO4Á7H2O,NiSO4Á6H2O,H3BO3and ascorbic acid,subjected to an electrodeposition operated at30mA and a total duration of 20min.The deposition was pulse-based,with an interval of1s between current-on and-off,at which on and off were both held for1s in an alternating manner for the entire deposition.Since the pulse-delay time(T off)was kept constant,the anomalous co-deposition of Ni and Fe that may result in a higher deposition rate of Fe,as suggested by Salem et al.[11],was not expected in our case.The concentrations of Ni and Fe were controlled by the use of FeSO4Á7H2O and NiSO4Á6H2O,and were identiﬁed by energy dispersive spectrometry(EDX),subsequent to the removal of the wires from the substrate.The EDX analysis only showed Ni and Fe signals,which excluded the possibility that Cu electrode may form the alloy with NiFe upon annealing.RTA of3001C-2min was applied to the samples,and the annealed samples were compared with the non-annealed ones in terms of all analyses.The samples’morphologies,crystallographic structures and magnetic proper-ties were identiﬁed using a scanning electron microscope(SEM), an x-ray diffraction(XRD)facility and a vibrating sample magneto-meter(VSM),respectively,all without the AAO protec-tion.The wires’magnetic easy-axis was found to be the long-axis, so the magnetic hysteresis(M–H)curves presented here were all taken from the long-axis measurements.A high-resolution trans-mission electron microscope(HRTEM,JEM-2100F,operated at 200keV)was used to probe the microstructure of the wires.To further understand the wires’magnetism with elemental speciﬁ-city,x-ray absorption spectroscopy(XAS)and x-ray magnetic circular dichrosim(XMCD)taken with total electron yield(TEY) and totalﬂuorescence yield(TFY)modes were employed to probe the spin-dependent states of Ni and Fe,at BL11A,National Synchrotron Radiation Research Center(NSRRC).The XMCD spectra were taken by having the x-ray photon wave-vector parallel to the wires’long-axis under an appliedﬁeld of1T.This forced the Ni and Fe moments to be measured in a way parallel to the wires’easy-axis,which promised a quantitative comparison with the VSM data.Each XAS/XMCD spectrum presented in this work was the average of more than5data points collected on different spots of the same sample,and the deviation was very minor among the spectra,which suggests the sample homogene-ity to be of reliable quality.Finally,spin(S z)and orbital(L z) moments were estimated by sum-rule analysis[12]to elucidate the Ni and Fe moments in a detailed way.The use of n3d in sum-rule analysis was carefully treated,as detailed in the text, considering the varying electronic states of Ni and Fe.3.Results and discussionFig.1(a)shows the SEM image of the Ni x Fe1Àx nano-wires on the Ti/Cu electrode after the AAO removal,where the high-ordering,free-standing nature of the wires can be clearly assessed.The wires’dimensions were precisely controlled by the AAO and they were identical for all compositions in order to have a quantitative comparison in magnetic properties.Upon the RTA,the morphologies of the wires remain unaltered as con-ﬁrmed by Fig.1(b).The isolations of the wires were well preserved as demonstrated by SEM with a larger magniﬁcation.Weﬁrst focus on the wires without the RTA treatment. Fig.2(a)shows the x-dependent M–H curves for the wires.The saturationﬁeld and coerciveﬁeld of the wires highly depend on the manufacturing recipe[13–15],aspect-ratio[16]and pore-diameter[11,14,17,18].In our case,the saturationﬁeld is larger than5000Oe and the coerciveﬁeld is about75Oe inaverage.Fig.1.(a)Cross-sectional SEM image of the as-deposited Ni x Fe1Àx nano-wires and (b)top-viewed SEM image of the annealed Ni x Fe1Àx nano-wires,with a larger magniﬁcation.S.-J.Chang et al./Journal of Magnetism and Magnetic Materials332(2013)21–27 22The wires appear to lose saturation magnetization (M s )with increasing x .This suggests that the role of Ni is to reduce the wire’s magnetization,agreeing well with the general picture of the Slater–Pauling curve [9,10].Element-speciﬁc M –H curves performed over the L 3-edges of Ni and Fe are given in Fig.2(b).The Ni and Fe share similar ﬁeld-dependency as shown in the M –H curves probed by the VSM (Fig.2(a)),suggesting that the two elements are coherent in magnetization reversal.A HRTEM image demonstrating a homogeneous polycrystalline microstructure for x ¼0.5is shown in Fig.2(c).Similar micrograph is seen in other samples (hence,not provided),in agreement with the literatures [9,18]reporting that the electro-deposition generally produces a polycrystalline microstructure for nano-materials.Upon the introduction of Ni,a structural transition takes place,changing from mainly BCC (x ¼0.3)[19],then BCC þFCC (x ¼0.5)[5,17,20]and ﬁnally to FCC (x ¼1.0)[21],as shown in Fig.2(d).The structural transition can be tracked by the transition of the characteristic peaks;i.e.,the Fe BCC-(110)setting at 45.23degree (x ¼0.3),then shifting to a lower angle of 44.15degree corre-sponding to the BCC–FCC mixed case (x ¼0.5),and ﬁnally relocat-ing at a higher angle of 44.76degree assigned by Ni FCC-(111)(x ¼1.0).The transition of the characteristic peaks is consistent with Glaubitz et al.[5]also dealing with a BCC -FCC transition in the Ni x Fe 1Àx thin ﬁlms.It came to our attention that the structural ordering of the Fe-rich sample is weaker than that of the Ni-rich sample,from the fact that the Fe-rich sample’s (x ¼0.3)XRD intensity is less pronounced than that of the Ni (x ¼1.0)one.One may notice that the intensity of Cu (111)increases with increasing x ,therefore arguing that the crystallization of Ni could have been facilitated by a better crystallized Cu electrode,rather than an intrinsic property of Ni itself.However,all the AAO/Ti/Cu substrates were prepared in the same batch and the quality-variation was very minor.This can be validated by the comparable peak intensities of Cu (200)and Cu (220)from sample to sample.Therefore,the enhanced intensity of Cu (111)could be explained as having an overlap with the Ni (111)but not the quality-variation of the electrode.Thus,the results imply that the Ni FCC is more energetically favored within the wire struc-ture.This could explain the dominance of Ni over the wire’s magnetic properties as detailed below,considering that the structural and magnetic properties are often coupled in magnetic materials [22–25].The Ni and Fe XAS spectra with varying x are presented in Fig.3(a)and (b),respectively.Both Ni and Fe are found to be oxidized by the evidence of edge-splitting.In general,Fe is more sensitive to oxidation than Ni due to a higher oxidation potential [26],and the oxidation that can be easily acquired at the L 3as this edge,especially with the TEY XAS,is renowned for ﬁngerprinting the chemical state of Fe [27–30].In XAS,x -dependency is almost imperceptible for Ni and Fe.However,XMCD reﬂecting the Ni and Fe moments exhibits opposite dependencies with x .In Fig.4(a),the Ni XMCD intensity is found to decrease with increasing x .Conversely,the Fe XMCD intensity not only increases but also turns to be more metallic-like with increasing x ,as presented in Fig.4(b).For x ¼0.5in particular,its Fe XMCD line-shape deviates from those of Fe 2O 3and Fe 3O 4[27,28]but is rather similar to metallic Fe [5,12],which suggests that the oxidation is minor for this concentration.Also,from the TEM results (not shown)we did not obtain any oxidized layer at the wire’s surface.For Fe,the XAS with light oxidation but the XMCD with a metallic spectral shape can be found in Tsai et al.[29]and Kim et al.[30],for the cases of CoFeB/MgO thin ﬁlms and Fe substrate,respectively,very similar to our situation.In both references Fe was treated to be metallic and ferromagnetic considering the limited oxidation effect,and therefore the same principle can be followed for x ¼0.5here.However,the Fe oxidation cannot be neglected in x ¼0.3,as the oxidation effect is evident in the XMCD spectralshape.Fig.2.(a)x -Dependent M –H curves.(b)TFY M –H curves of Fe (black)and Ni (red)for x ¼0.5,and the same curve is seen in x ¼0.3.(c)HRTEM image of x ¼0.5.Similar polycrystalline microstructure is seen in x ¼1.0and 0.3.(d)x -dependent XRD patterns.For the FCC–BCC mixed phase case as x ¼0.5,the characteristic peaks are hard to identify so they are not indexed.However,for x ¼0.3,the characteristic peaks are close to Fe BCC so they are indexed.(For interpretation of the references to color in this ﬁgure legend,the reader is referred to the web version of this article.)S.-J.Chang et al./Journal of Magnetism and Magnetic Materials 332(2013)21–2723Fig.4(c)presents the x -dependent sum-rule analyses (S z þL z )for Ni and Fe.Qualitatively,the microscopic analyses from the sum rule are consistent with the macroscopic analyses from the VSM throughout the paper,indicating the reliability of the analyses.The sum-rule results suggest that Ni and Fe exhibit contrary dependencies,where the Fe moment increases,whereas the Ni moment decreases,with increasing x .The increased Fe moment can be explained by the more metallic and enhanced Fe XMCD as x increases from 0.3to 0.5(Fig.4(b)),while the decreased Ni moment can be understood as the suppressed XMCD signal,with increasing x ,after spectral normalization [31].The weighted sum of Ni and Fe presumably equals to the total magnetization of Ni x Fe 1Àx ,which decays with increasing x .It is noteworthy that the same trend has been discovered in Fig.8of Glaubitz et al.[5].Both Glaubitz’s and our results show the fact that despite Ni x Fe 1Àx following the Slater–Pauling prediction for magnetism,Ni and Fe take contrary paths locally,in spite of their coherent magnetization reversal.Interestingly,despite unclear mechanism for the decreased Ni moment with increasing x ,when concentration is weighted Ni’s magnetic strength is still sufﬁcient to pull down the wire’s total magnetization matching the Slater–Pauling prediction.In combination with the XRD (Fig.2(c)),Ni seems to be more dominant than Fe in terms of magnetic and structural degrees of freedom,as will be further validated by the results from the RTA in the following.Now we turn focus to the RTA effects particularly for x ¼0.3and 0.5samples.Fig.5(a)and (b)presents the M –H curves and XRD patterns for x ¼0.3affected by the RTA,respectively.The saturation magnetization drops by only 5%with the RTA,so the magnetism is affected by the treatment in a very minor way.However,for x ¼0.3,notable changes are obtained in the Ni/Fe XAS (Fig.5(c)and (d)),with the Ni and Fe XAS white-line intensities being suppressed and enhanced,respectively.The XAS here corresponds to the Ni/Fe 2p -3d photo-excitation process with the white-line intensity reﬂecting the available vacancy in the 3d orbital.Since Ni exhibits suppressed intensity than that of Fe,it indicates a charge transfer from Fe to Ni via orbital hybridization that results in higher d-band vacancy of Fe,i.e.,a more oxidized state for Fe but a more reduced state for Ni,under the inﬂuence of the RTA.The more oxidized state for Fe is due to a more pronounced intensity in L 3pre-edge,while a more reduced state for Ni is linked to the suppressed XAS along with the disappearance of the shoulders around the edges.The charge transfer consequently modiﬁes the spin-polarizations of the two constituents as reﬂected by their XMCD,as given in Fig.5(e)and (f).For Ni,the suppressed XAS gives rise to an enhanced XMCD as a consequence.Conversely,oscillation emerges in the Fe XMCD around the L 3,indicating a highly oxidized Fe as Fe 2O 3and Fe 3O 4[27,28].In Fig.5(b),the Fe BCC is found to disappear after the RTA.In fact,a heavily smeared peak near Cu (111)is barely detectable in the XRD of the annealed x ¼0.3,which can be due to the disappeared Fe (110).This indicates that some degrees of structural ordering still persist upon RTA to support the magnetic hysteresis observed in Fig.5(a),but it is difﬁcult to be identiﬁed due to limited resolution of the x-ray facility,so we rather prefer to claim the phase to be close to amorphous.This is unusual because the heat treatment usually facilitates the crystallization of the materials especially in bulk forms.However,since the Ni x Fe 1Àx is formed in nano-wires,the large thermal stress raised by the RTA in a very short period is unlikely to be relieved within such a low and conﬁned dimension,and therefore causes deterioration of the structure,especially when the structural ordering is intrinsically weak prior to the RTA.Here,the Ni–Fe charge transfer occurs with the disappear-ance of Fe (110),perhaps due to more overlapped Ni/Fe 3d electron wave-functions with the structural disordering,and examples of structural-disordering induced charge transfer can be referred to from Refs.[32–34].Since the magnetic and structural properties are strongly coupled,the annealing-induced structural disordering would modify the magnetism of Ni x Fe 1Àx accordingly.Interestingly,though the modiﬁcation is obscure with a macroscopic probe,it is unambiguously probed by a microscopic one,hence revealing the importance of the latter.Fig.6presents the sum-rule results (S z þL z )for Ni and Fe before and after the RTA,for x ¼0.3.Considering the substantial changes in the chemical states of Ni and Fe,n 3d for both metallic and fully oxidized (Ni 2þ,Fe 3þ)cases were used in various combinations to examine if any deviation in the trend of (S z þL z )is seen.The deviation was less than 15%for the extreme case and had no signiﬁcant inﬂuence on the trend.The results reveal that the charge transfer is spin-dependent,resulting in a decrease but an increase in the Fe and Ni moments.Therefore,the minor magnetization change probed by the VSM (Fig.5(a))can be understood as a local magnetic-compensation.It arises from the spin exchange between the two elements with the loss of structural stability,a phenomenon invisible to the conventional measurement.For x ¼0.5,the magnetization also drops imperceptibly after the RTA,as shown in Fig.7(a).However,the induced structural disordering is less pronounced than that of x ¼0.3,as the char-acteristic peaks of the mixed-phase are still visible in Fig.7(b),especially the peak near Cu(111).The persistence of structural stability deactivates the electronic modiﬁcations of Ni and Fe,as reﬂected by their XAS provided in Fig.7(c)and (d),respectively.Fig.3.x -Dependent (a)Ni L 2,L 3XAS and (b)Fe L 2,L 3XAS.S.-J.Chang et al./Journal of Magnetism and Magnetic Materials 332(2013)21–2724Fig.4.x -Dependent (a)Ni L 2,L 3XMCD and (b)Fe L 2,L 3XMCD.All spectra are normalized to the integrations of corresponding XAS spectra.(c)Sum-rule (S z þL z )analyses for Ni,Fe,and weighted Ni þFe,with x -dependency.In (c),lines through data points are guides for the eyes,and the scale of the y -axis is selectively presented for the purpose ofclarity.Fig.5.(a)M –H curves (b)XRD patterns (c)Ni L 2,L 3XAS (d)Fe L 2,L 3XAS (e)Ni L 2,L 3XMCD and (f)Fe L 2,L 3XMCD,for x ¼0.3before and after the RTA treatment.S.-J.Chang et al./Journal of Magnetism and Magnetic Materials 332(2013)21–2725Here,the Ni XAS remains unaltered,but a minor deviation is obtained in the Fe XAS after the RTA,and a likeness is seen in their XMCD (Fig.7(e)and (f)).The identical Ni XAS before and after the RTA suggests no electronic-modiﬁcation;i.e.,no charge transfer in the Ni conduction band.Thus,the limited change in the Fe XAS can be realized as the minor oxidation at the surface,instead of the electron removal as that happened at x ¼0.3.Apparently,thecharge transfer effect is both composition-and structure-dependent.It only occurs when the structural stability is lost such as x ¼0.3.However,for x ¼0.5,the charge transfer is invisible,due to the robust structural stability supported by the larger fraction of the Ni FCC.The results indicate that the properties of Ni x Fe 1Àx are complex,involving the interactions among the magnetic,structural and electronic degrees of freedom which all vary with x ,and are probably hard to be predicted by the Slater–Pauling curve alone.In particular,the role of Ni is found to be supreme in Ni x Fe 1Àx as it dominates the total magnetization and structural stability,and thus its inﬂuence should be more weighted than Fe,which is essential for attempts to tailor the properties of Ni x Fe 1Àx .In bimetallic magnetic compounds,we ﬁnd that if one of the constituents dominates the magnetic properties,there must be at least a physical parameter,such as crystal or electronic structure itinerantly coupled with the magnetism of the dominant consti-tuent,to support its dominance.For example,in Yang et al.[23]only 6%of Co doping was sufﬁcient to alter the magnetic phase of the Ni rod along with the change of microstructure from nano-crystalline to polycrystalline.In Telling et al.[35],Co was more magnetically dominant than Mn in Co 2MnAl,due to a smaller gap in the Co minority spin-band.Even in the theoretical work Wang et al.[36]pointed out that in a Cu–Co bimetallic clustersystem,Fig.6.Sum-rule (S z þL z )analyses for Ni,Fe,for x ¼0.3before and after the RTA treatment.The scale of the y -axis is selectively presented for the purpose ofclarity.Fig.7.(a)M –H curves (b)XRD patterns (c)Ni L 2,L 3XAS (d)Fe L 2,L 3XAS (e)Ni L 2,L 3XMCD and (f)Fe L 2,L 3XMCD,for x ¼0.5before and after the RTA treatment.In (b),Mix,Mix 0and Mix 00represent the three characteristic peaks of the BCC–FCC mixed phase just near the characteristic peaks of Cu,and these peaks are still observable after the RTA.S.-J.Chang et al./Journal of Magnetism and Magnetic Materials 332(2013)21–2726the introduction of Cu atoms would cause a dramatic enhance-ment of magnetism due to geometrical characters.All these phenomena suggest that,in a bimetallic system the physical proximity effects would lose balance if any two physical degrees of freedom of one constituent are more coupled than the other constituent.This will lead to the dominance of the constituent with the stronger coupling,if one of its degrees of freedom is elaborated.Assigning this principle to our case,we elaborate the structural instability to imbalance the physical proximity effect between Ni and Fe,which sharply discriminates the electronic responses of the two.Correlating the structural information with the local and macroscopic magnetism,it is easy to observe the dominance of Ni in Ni x Fe1Àx.Finally,the invariant magnetizations with the RTA for x¼0.3and0.5,therefore,need to be described by different microscopic pictures.For the former,it results from the spin exchange between Ni and Fe.However,the latter is char-acterized by the static,inactive interactions between the two elements as a result of the persistent structural stability.4.ConclusionIn this study we have demonstrated how Ni–Fe magnetic interactions inﬂuenced the Ni x Fe1Àx nano-wires’magneto-structural properties,by isolating the Ni and Fe elemental behaviors while the wires underwent the structural transition. The inﬂuences of the two elements were found to be incompar-able,with Ni being superior to Fe in terms of magnetic and structural properties.Upon RTA,the wires at x¼0.3became amorphous,where the Ni and Fe moments compensated mutually by exchanging the3d electrons.This reasoned the nearly unal-tered magnetization of the wires.A similar macroscopic behavior was seen at x¼0.5,while its invariant magnetization needed to be described as the inactive electronic interaction between the two elements,because of persistent structural properties resulting from a larger fraction of Ni.AcknowledgmentThe authors appreciate the assistances on HRTEM,XMCD,and electro-deposition from Dr.C.M.Liu,Dr.H.J.Lin and Mr.K.M. Chen,respectively.This work is supported by the National Science Council of Taiwan,under Grant no.NSC98-2112-M-009022-MY3. References[1]M.Kl¨aui,Journal of Physics:Condensed Matter20(2008)313001.[2]C.L.Dennis,R.P.Borges,L.D.Buda,U.Ebels,J.F.Gregg,M.Hehn,E.Jouguelet,K.Ounadjela,I.Petej,I.L.Prejbeanu,M.J.Thornton,Journal of Physics: Condensed Matter14(2002)R1175–262.[3]O.Yamada, cheisserie,Journal of the Physical Society of Japan53(1984)729–734.[4]E.F.Wassermann,Journal of Magnetism and Magnetic Materials100(1991)346.[5]B.Glaubitz,S.Buschhorn,F.Brussing,R.Abrudan,H.Zabel,Journal of Physics:Condensed Matter23(2011)254210.[6]B.Singh,C.L.Ho,Y.C.Tseng,C.T.Lo,Journal of Nanoparticle Research14(2012)706.[7]J.Crangle,G.C.Hallam,Proceedings of the Royal Society A272(1963)119.[8]R.F.Willis,N.J.Gilman,Europhysics Letters69(2005)411.[9]K.H.Lee,H.Y.Lee,W.Y.Jeung,W.Y.Lee,Journal of Applied Physics91(2002)8513.[10]A.Cai,H.Zhang,H.Hua,Z.Zhang,Nanotechnology13(2002)627.[11]M.S.Salem,P.Sergelius,R.Zierold,J.M.Montero Moreno,D.G¨orlitz,K.ielsch,Journal of Materials Chemistry22(2012)8549.[12]C.T.Chen,Y.U.Idzerda,H.J.Lin,N.V.Smith,G.Meigs,E.Chaban,G.H.Ho,E.Pellegrin,F.Sette,Physical Review Letters75(1995)152.[13]F.E.Atalay,H.Kaya,Journal of Alloys and Compounds469(2009)458.[14]S.Aravamudhan,J.Singleton,Journal of Physics D:Applied Physics42(2009)115008.[15]C.G.Wu,H.L.Lin,Journal of Solid State Electrochemistry10(2006)198.[16]H.R.Khan,K.Petrikowski,Journal of Magnetism and Magnetic Materials213(2000)526.[17]Q.Liu,J.Wang,Z.Yan,D.Xue,Physical Review B72(2005)144412.[18]F.Tain,J.Zhu,D.Wei,Journal of Physical Chemistry C111(2007)12699.[19]J.B.Wang,X.Z.Zhou,Nanotechnology15(2004)485.[20]Y.B.Zhu,Y.Wang,X.Y.Zhang,G.W.Qin,International Journal of RefractoryMetals and Hard Materials25(2007)275.[21]X.W.Wang,G.T.Fei,Journal of Physical Chemistry B109(2005)24326.[22]C.C.Huang,C.C.Lo,Y.C.Tseng,C.M.Liu,C.Chen,Journal of Applied Physics109(2011)113905.[23]C.Y.Yang,C.C.Huang,Y.C.Tseng,C.M.Liu,C.Chen,Journal of Applied Physics110(2011)073913.[24]C.Magen,L.Morellon,P.A.Algarabel,M.R.Ibarra,C.Ritter,A.O.Pecharsky,K.A.Gschneidner Jr.,V.K.Pecharsky,Physical Review B70(2004)224429.[25]D.Haskel,Y.B.Lee,B.N.Harmon,Z.Islam,ng,G.Srajer,Ya.Mudryk,K.A.Gschneidner Jr.,V.K.Pecharsky,Physical Review Letters98(2007) 247205.[26]//ox_potential.htm S.[27]E.Pellegrin,M.Hagelstein,S.Doyle,H.O.Moser,J.Fuchs, D.Vollath,S.Schuppler,M.A.James,S.S.Saxena,L.Niesen,O.Rogojanu,G.A.Sawatzky,C.Ferrero,M.Borowski,O.Tjernberg,N.B.Brookes,Physica Status Solidi(b)215(1999)797.[28]L.Signorini,L.Pasquini,F.Boscherini,E.Bonetti,I.Letard,S.Brice-Profeta,P.Saincavit,Nuclear Instruments and Methods in Physics Research Section B 246(2006)20.[29]W.C.Tsai,S.C.Liao,H.C.Hou,C.T.Yen,Y.H.Wang,H.M.Tsai,F.H.Chang,H.J.Lin,i,Applied Physics Letters100(2012)172414.[30]D.H.Kim,H.J.Lee,G.Kim,Y.S.Koo,J.H.Jung,H.J.Shin,J.-Y.Kim,J.-S.Kang,Physical Review B79(2009)033402.[31]All XMCD spectra presented in this work were normalized to the integrationsof corresponding XAS spectra,which was to guarantee the comparison based on an atomic absorption.[32]N.R.Khasanova, F.Izumi,M.Shida, B.C.Chakoumakos, E.Ohshima,M.Kikuchi,Syono,Physica C269(1996)115.[33]S.A.Bewick,R.A.Pascal,D.M.Ho,Z.G.Soos,M.Masino,Journal of ChemicalPhysics122(2005)024710.[34]M.Zhang,M.R.Anderson,Langmuir10(1994)2807.[35]N.D.Telling,P.S.Keatley,G.van der Laan,R.J.Hicken, E.Arenholz,Y.Sakuraba,M.Oogane,Y.Ando,K.Takanashi, A.Sakuma,T.Miyazaki, Physical Review B78(2008)184438.[36]J.Wang,G.Wang,X.Chen,W.Lu,J.Zhao,Physical Review B66(2002)014419.S.-J.Chang et al./Journal of Magnetism and Magnetic Materials332(2013)21–2727。

1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。

a r X i v :c o n d -m a t /0208592v 1 [c o n d -m a t .s t r -e l ] 30 A u g 2002Charge and Orbital Ordering in Pr 0.5Ca 0.5MnO 3Studied by17O NMRA.Yakubovskii,1,2A.Trokiner,2S.Verkhovskii,3A.Gerashenko,3and D.Khomskii 41Russian Research Centre ”Kurchatov Institute”,Moscow,123182Russia2Laboratoire de Physique du Solide,E.S.P.C.I.,Paris,France3Institute of Metal Physics,Russian Academy of Sciences,620219Ekaterinburg,Russia4Laboratory of Solid State Physics,Groningen University,Netherlands The charge and orbital ordering in Pr 0.5Ca 0.5MnO 3is studied for the ﬁrst time by 17O NMR.This local probe is sensitive to spin,charge and orbital correlations.Two transitions exist in this system:the charge and orbital ordering at T CO =225K and the antiferromagnetic (AF)transition at T N =170K .Both are clearly seen in the NMR spectra measured in a magnetic ﬁeld of 7T .Above T CO there exists only one NMR line with a large isotropic shift,whose temperature dependence is in accordance with the presence of ferromagnetic (FM)correlations.This line splits into two parts below T CO ,which are attributed to diﬀerent types of oxygen in the charge/orbital ordered state.The interplay of FM and AF spin correlations of Mn ions in the charge ordered state of Pr 0.5Ca 0.5MnO 3is considered in terms of the hole hopping motion that is slowed down with decreasing temperature.The developing ﬁne structure of the spectra evidences,that there still exist charge-disordered regions at T CO >T >T N and that the static (t >10−6s )orbital order is established only on approaching T N .The CE-type magnetic correlations develop gradually below T CO ,so that at ﬁrst the AF correlations between checkerboard ab-layers appear,and only at lower temperature -CE correlations within the ab-planes.PACS numbers:75.30.Et,74.40.-s,76.60.CqI.INTRODUCTIONThe charge ordering phenomena in the hole-doped R 1−x A x MnO 3(R is a trivalent rare-earth ion and A is a divalent alkaline-earth ion)have been a subject of ex-tensive studies due to intriguing interplay of the charge,orbital and spin degrees of freedom.The charge ordered (CO)state is formed due to localization of the mobile e g -holes.Above T CO the e g -holes provide FM correlations be-tween electron spins of neighboring manganese ions through the double-exchange (DE)mechanism proposed by Zener [1].Pr 1−x Ca x MnO 3(0.3≤x ≤0.75)oxides are the most suitable for investigation of the CO state since the onsets of the charge (T CO )and spin (T N )or-der are well separated in temperature.This doped oxide has an orthorhombic structure (space group,P bnm )in a wide temperature and magnetic ﬁeld (<20T )range.It remains in the semiconducting state with no admix-ture of FM metal phase as opposed to Pr 1−x Sr x MnO 3,La 1−x Ca x MnO 3and La 1−x Sr x MnO 3[2],[3].In the CO structure of Pr 1−x Ca x MnO 3with x ∼0.5the in-plane pattern of Mn 3+and Mn 4+ions may be represented asa checkerboard related to the corresponding t 3g e 1g and t 3g electronic conﬁgurations of Mn (Fig.1).The lobes of a certain number of occupied e g -orbitals are ordered in the direction of the Mn 3+-O-Mn 4+bond to maximize DE coupling.Whereas the AF superexchange t 2g −t 2g cou-pling is a dominating magnetic interaction for Mn 4+and Mn 3+which e g -lobes are aligned perpendicular to the Mn 3+-O-Mn 4+bond.At x ∼0.5the competition of these exchange couplings results in the AF spin ordering of CE-type with T N <T CO .The associated Jahn-Teller (JT)distortions of MnO 6octahedra double the unit cellalong b-axis of the orthorhombic (P bnm )lattice.The ideal CE type charge/orbital order implies FM zigzag ar-rangement of the ordered e g (3x 2−r 2)and e g (3y 2−r 2)or-bitals of Mn 3+ions in ab-plane.The neighboring zigzags are AF-coupled,the ordering in c-direction is also anti-ferromagnetic.Recent resonant x-ray scattering [4],electron mi-croscopy [5]and neutron diﬀraction [6],[7]studies of Pr 0.5Ca 0.5MnO 3have shown that the orbital order (OO)below T N =170K results in an orbital domain state commensurate with the lattice.This commensurate OO becomes metastable above T N .Its melting is observed in diﬀraction studies as a commensurate-incommensurate (C-IC)transition at T C −IC ∼(180−200)K >T N .With further increase of temperature the partial orbital dis-order turns on the FM spin ﬂuctuations which become dominating near T CO ≈250K [8].The C-IC transition was considered in terms of the e g -orbital polarization soft mode.The e g -orbital completely polarized along Mn-O bond corresponds to the amplitude of the wave at a given Mn 3+ion [6]and its wave vector q ={0,1/2−ε,0}was considered as the order parameter of the transition.Further discussion of the CO state requires more de-tailed microscopic data related to the distribution of spin density and to its dynamic regime in the CO state of man-ganite.Studies of spatial ﬂuctuations of charge/orbital order with diﬀraction experiments [6],[7]is restricted to short correlation times τc <10−12s .Whereas NMR experiments enable studying time-dependent spin ﬂuctu-ations at much longer τc .In this work we have studied the spin correlations of the neighboring Mn ions developed in the paramagnetic charge ordered (CO PM)state of Pr 0.5Ca 0.5MnO 3by measuring the 17O NMR spectra.Oxygen atoms be-2ing placed between two Mn ions bring valuable infor-mation about the spin/orbital conﬁguration of the near-est Mn ions.As expected the nuclear spin of oxygen (17I=5/2)probes its magnetic state through the dipo-lar and transferred hyperﬁne magneticﬁelds that de-pend on the spin/orbital conﬁguration of the neighboring Mn ions[9].The55Mn nucleus is a less suitable NMR probe for this task for the following reasons.First,the NMR spectrum of Mn4+ion(t3g electron conﬁguration) is available only at low temperatures in the metastable CO AF phase.On the other hand,NMR of Mn3+(t3g e1g) is hard to detect due to extremely high nuclear spin-spin relaxation rate apparently controlled by abnormal low-frequency spin dynamic of the localized e g-electrons. This17O NMR report is focused on the study of the development of the charge/orbital ordering in Pr0.5Ca0.5MnO3.The main result is that in Pr0.5Ca0.5MnO3the CE-type magnetic correlations de-velop gradually below T CO:ﬁrst those between ab-layers arise and only at lower temperature the correlations within ab-planes appear.The static(τc>10−6s)orbital order is established only on approaching T N.II.EXPERIMENTALWe used a powder sample of Pr0.5Ca0.5MnO3prepared by traditional ceramic technology.The powder was en-riched with17O isotope up to≈25%.The single-phase nature of the enriched sample was conﬁrmed by the x-ray diﬀraction and Raman scattering studies at room tem-perature.17O NMR measurements were carried out on a phase-coherent NMR pulse Bruker spectrometer over the tem-perature range of80−330K in magneticﬁeld of7T. In thisﬁeld the onset of the CO and AF spin order-ing was found to shift slightly down to T CO≈225K and T N≈170K compared to reported data at zeroﬁeld and in accordance with H-dependence of T CO reported in Ref.[3].NMR spectra were obtained for a loose-packed powder sample with point-by-point frequency sweep mea-surements,the intensity of the spin-echo signal formed with the pulse sequence(π/2)−τdel−(π/2)-echo be-ing measured.The width of theπ/2-exciting pulse was t p=(2−4.5)µs and the distance between pulses varied in the range ofτdel=(40−80)µs.For each frequency,the amplitude of the exciting rf-pulse was adjusted in order to optimize the echo signal intensity while keeping the pulse durationﬁxed.All the echo-intensities were corrected to τdel≈0by measuring the rate of echo-decay at diﬀerent frequencies of the broad spectrum.All the spectra for T<T CO were measured during cooling down from room temperature to avoid the hysteresis uncertainties.The 17O NMR signal in H2O was used as a frequency refer-ence to determine the shift of NMR line in our sample.III.RESULTS AND DISCUSSIONA.The charge disordered paramagnetic state Figure2shows the17O NMR spectra of Pr0.5Ca0.5MnO3measured in the PM state.In the charge disorder paramagnetic state(CD PM)for T>T CO≈225K the main signal(∼95%)in the spectrum is a rather asymmetric line.It has a positive and extremely large magnetic shift exceeding6%even at the highest measured temperature,T=330K with respect to those observed in nonmagnetic compounds. An additional line of small intensity(∼5%)is present at zero NMR-shift.It is supposed to originate from a small amount of the Ca-based oxides,which arise as spurious precipitations during the solid-state reaction synthesis. It’s well known that a small concentration of spurious phase formed with light atoms like Ca is hard to detect by x-ray.Let us now consider the quadrupolar and magnetic shift interactions of the oxygen nuclear spin with its en-vironment.The oxygen atoms are located at the cor-ners of octahedra with Mn at the center.The non-cubic local symmetry of oxygen sites leads to the in-teraction of17O electric quadrupole moment(eQ)with electricﬁeld gradient(eV ZZ).The resulting17O NMR spectrum is expected to split into2I+1lines sepa-rated by the quadrupole frequencyνQ=3e2Q3La 0.5Ca 0.5MnO 3,which becomes FM-metal in the ﬁeld of 4Tbelow T ≈220K [11].The slope of the K vs χplot corresponds to the local magnetic ﬁeld H loc =µB ∆K/∆χ≈1·104Oe/µB (the χ-data are taken from Fig.4in Ref.[6].It exceeds the magnitude of the classic dipolar ﬁeld (H dip )induced at oxygen by the magnetic moments of the neighboring Mn ions:H dip =2g e µB s z (Mn )r 3Mn −O.(1)At room temperature H dip may be estimated as H dip ≈1200Oe where χis deﬁned per spin from Ref.[6].The corresponding estimated anisotropic contribution to the total NMR line shift {−0.8%,−0.8%,1.6%}is much less than the experimental value.Thus we assume that the classic dipole interaction of 17O nucleus with the eﬀective magnetic moments 2g e µB s z (Mn ) of the nearest Mn has no strong inﬂuence on the total shape of the spectrum.The most probable origin of the observed giant isotropic magnetic shift K iso ≡(2K ⊥+K )/3is the Fermi contact interaction of the nuclear spin 17I with the transferred s-spin density of electrons participating both in the Mn-O-Mn bonding and in superexchange coupling of the neighboring Mn,K iso =8π17γa (2s )f s s z (Mn )(2)Here g e µB s z (Mn ) =χH ,a (2s )=17γ H F C (2s )=0.15cm −1is the isotropic hyperﬁne coupling constant for oxygen ion [12],[13].H F C is the corresponding hyperﬁne magnetic ﬁeld due to the Fermi-contact interaction with electron located on 2s-orbital with wave function ψ2s (r ).Following [14],[9]the corresponding isotropic spin den-sity transferred at oxygen from neighboring Mn ions may be deﬁned in terms of the factor f s =H loc,iso /2H F C (2s ).This quantity estimated from (2)results in a rather large magnitude of the eﬀective fractional occupancy of O(2s)orbitals by unpaired spins.We found f s =0.01for insulating PM state of Pr 0.5Ca 0.5MnO 3.For compar-ison the LDA+U band structure calculation results in f s =0.003−0.007for the FM-ordered state of LaMnO 3[15].Another possible isotropic hyperﬁne interaction is the core-polarization term which provides H loc ≃3·104Oe [16]when assuming that the doped electron is fully lo-calized within the oxygen 2p-orbital.But this is not the case above T CO in Pr 0.5Ca 0.5MnO 3.Thus this interac-tion may be neglected for the light oxygen atom.The noncubic local symmetry of oxygen sites gives rise to an anisotropic part of the magnetic shift tensor K ax =(K −K ⊥)/3.The most reasonable contribution to K ax is the magnetic dipole-dipole hyperﬁne interac-tion of 17I with electrons on 2p σπ,orbitals,which spin occupancies ’up’and ’down’become diﬀerent throughthe polarizing interactions with neighboring manganese.The corresponding magnetic shift tensor K dip may be expressed through the fractional spin density transfer f α s z (Mn ) on O-2p αorbital from paramagnetic neigh-boring Mn-ion [9]as:K (2p σ)=−2K ⊥(2p σ)=45<r −3>2p (f σ−f π)χ(Mn )(4)Taking <r −3>2p =4.97a.u.[13]for neutral oxygen atom we obtain a rather large positive value (f σ−f π)≈0.04.The direct observation of the positive value of (f σ−f π)proves for the ﬁrst time that the p σ-orbital directed along the Mn-O bond is more polarized than the two other p π-orbitals.We showed before that the 17O NMR line position in the CD PM state is mainly determined by the isotropic transferred hyperﬁne coupling,arising from the hy-bridization of Mn(3d)and O(2s)orbitals.In the ideal P bnm structure there is no overlap of Mn(t 2g )-O(2s)or-bitals due to their orthogonality,while e g -orbitals of Mn have a rather strong overlap with s-orbital of neighboring oxygen as shown in Fig.1.Hereafter we restrict ourselves to the eﬀects of overlap and covalency between Mn(e g )and O(2s)orbitals.B.The charge ordered paramagnetic stateJust below T CO the 17O NMR spectrum is substan-tially broadened.It splits into two parts as shown in Fig.2.The low-frequency spectrum in the range of K =(−2÷+10%is asymmetric (A-line).Its width decreases gradually as the temperature approaches T N .The high-frequency spectrum is approximately twice larger in in-tensity and forms a rather complicated pattern which center of gravity is shifted to extremely large positive K >20%.At T =170K ≃T N it splits into two broad lines (B-and C-line)of about equal intensity and peaked at K B ≈40%and K C ≈55%,respectively.According to x-ray and neutron diﬀraction studies [6],the CO and OO of the CE-type becomes commensurate in the CO PM phase only near T N .If the domain struc-ture of the OO [4],[6]is ignored,one ﬁnds four groups of the oxygen atoms diﬀerentiated by the charge and/or by the direction of occupied e g -orbital of the nearest-neighboring Mn-ions.The ﬁrst and the second groups are formed by apical oxygen located between two Mn 3+-ions (O1-site,shown in Fig.1)or between Mn 4+(O2/O3-site),respectively.Note that the s z -projections of elec-tron spins are AF correlated for neighboring Mn from4adjacent ab-planes.A third group is formed by oxygen (O4)in the ab-plane which participates in the AF cou-pling of neighboring Mn4+,Mn3+from adjacent zigzags. The last group(O5)is formed by oxygen in the ab-plane located between two FM coupled Mn4+and Mn3+ions in-side a zigzag.The concentration of each type of oxygen atoms obeys the”structural”ratio1:1:2:2.In order to assign A-C-lines measured in the CO PM phase we analyzeﬁrst the spectra near T N with resolved structure.We compare the”structural”ratio with the experimental”NMR line intensity”ratio,which is close to2:2:2.We also take into account that the lo-cal magneticﬁelds at diﬀerent oxygen sites are formed through the Mn-O-Mn exchange interactions which are short-range in space.In CO PM phase the eﬀective mag-netic moment of Mn(shown in Fig.1by arrows)is deﬁned by its projection g eµB s z on the direction of the exter-nal magneticﬁeld.In turn it controls the sign of the corresponding17O NMR shift contributed by each of the two neighboring Mn.A-line is attributed to the apical(O1and O2/O3) sites whereas B-and C-lines-to the in-plane ones.The magnetic shift of the A-line is small,and the localﬁeld at the corresponding17O is comparable in magnitude to the classic dipolarﬁeld estimated above(1).At these apical sites the hyperﬁne magnetic shifts(2-4)are greatly reduced since both neighboring Mn-ions are in the same valence state and their eﬀective magnetic mo-ments g eµB s z are AF correlated in the CO PM phase of CE-type.Let us now consider the high-frequency part of the spectra.C-line demonstrating the largest positive shift may be attributed to oxygen positioned in O5sites whereas B-line is presumably due to oxygen located in O4sites.Indeed for oxygen in O5site the transferred s-wave spin density is maximal since within the zigzag the lobe of the partially occupied e g(m l=0)orbital of Mn3+ ion points toward the neighboring oxygen.Furthermore the two neighboring Mn ions are FM correlated.For O4 we deﬁnitely expect a rather large transferred hyperﬁne ﬁeld for the following reason.Although the spins of Mn in adjacent zigzags are antiparallel,the O4oxygen is”sand-wiched”between Mn3+and Mn4+ions with diﬀerent spin values and diﬀerent orbital occupations,i.e.with diﬀer-ent covalency.So that the transferred polarization from these two Mn ions should not compensate as they do for the apical oxygen(O1,O2/O3).This should again re-sult in a substantial shift,although smaller than for O5. Moreover the transferred s-wave polarization from Mn4+ ion is expected to be negative due to eﬀects of covalent mixing with the empty e g-orbitals[17].As reviewed in [18]the charge transfer from the occupied O-2s orbital to the empty eg-orbital is spin dependent.It is regulated by the intra-atomic exchange coupling with electrons on t g-orbitals.Thus in the CO PM phase the static s-wave polariza-tion is directed along H,and the isotropic shift at O5 site may be expressed similarly to(2)through the corre-sponding transferred spin densities f s,3+ s z(Mn3+) orf s,4+ s z(Mn4+) of the neighboring Mn(with f s,3+>0 and f s,4+<0):K iso(O5)=8π3g eµB|ψ2s(0)|2{0.25f s,3+ s z(Mn3+) −f s,4+ s z(Mn4+) }(6) The sign”+”/”−”in(5),(6)takes into account the fact that FM/AF spin correlations of the neighboring Mn3+and Mn4+ions are considered as static in the time interval which is much longer that the inverse split-ting of the B-and C-line(∼10−8s)of the spectrum atT=170K≈T N,when the CO and OO are completely formed in PM state.This agrees with the fact that theO(2s)-polarization is provided predominantly by theσ-overlap with the e g-orbitals of Mn,and Pauli blockingof part of e g-orbitals in Mn3+gives stronger polariza-tion than in the case of Mn4+,where both2s↑and2s↓-electrons of O2-may virtually hop to Mn4+so that the net oxygen polarization due to covalency with Mn4+will be smaller than for Mn3+-neighbor and negative.For crude estimate of the transferred s-spin density we have assumed in(5),(6)that theσ-overlap of e g(m l=0) orbital of Mn3+with2s-orbital of O5in zigzag of the CE-type charge and orbital ordered phase is twice larger than the overlap with corresponding2s-orbital of oxy-gen O4located between the neighboring zigzags in ab-plane.(Of course under detailed consideration it should depend on interatomic distance and on the bending of the Mn3+-O bond in the tilted and JT distorted MnO6octa-hedra.)Inserting the value of the peak position of B-line (K iso=40%)and C-line(K iso=55%)into expressions (6),(5)respectively we get that the transferred s-wave polarization from Mn3+ion is positive and its absolute value exceeds about4times the corresponding negative polarization transferred from Mn4+|f s,4+ s z(Mn4+) |. The large diﬀerence in spin densities transferred from Mn3+/Mn4+ions indicates a substantial delocalizationof the”e g-hole”within the hybridized e g(Mn3+)-2pσ(O) orbital[19].It shows that a pure ionic approach where the e g-hole is completely localized at the Mn3+ion is a very rough approximation to describe in detail the CO and OO in doped manganite.Unfortunately the spatial distribution of the Fermi contact hyperﬁneﬁelds results in a large broadeningof the separate NMR lines in spectrum measured atT<T CO.It masks the anisotropy of the magnetic shift tensor and does not permit to trace the transfer of the2p-spin density at oxygen in the CO PM phase,i.e.to address the orbital order more directly by studying po-larization of a given p-orbital.5C.The antiferromagnetic stateDiﬀerent localﬁelds for apical oxygen in O1and (O2/O3)sites are expected only in the spin-ordered phase below T N.In the AF phase the AF moment cant-ing takes place when a rather high magneticﬁeld(7T)is applied.The canted moment of Mn in adjacent ab-planes will create at the apical oxygen an additional localﬁeld dependent on the valence state of neighboring Mn.At O1 sites the neighboring Mn3+ions create a larger isotropic magnetic shift than Mn4+ions do at O2/O3sites.In-deed,as shown in Fig.4at T=100K A-line splits into two lines of roughly equal intensity.A loose packed pow-der sample in a strong enough externalﬁeld may be con-sidered as partially oriented with c H.It should be noted that the observed splitting(4MHz)is not a result of the classic dipolarﬁelds of the neighboring Mn ions since the diﬀerence in their eﬀective magnetic moments is too small(µeff=2.7µB for Mn3+and2.2µB for Mn4+as estimated from Fig.4in Ref.[6]).The only slight additional broadening of the NMR spectra even around T N/2evidences that the line shift is mainly determined by the short-range CO and OO which have been completely formed in the CO PM phase at T→T N.Below110K it appears that the optimal rf pulse duration increases about twice from the low to the high frequency part of the A-line as illustrated in Fig.5. The same feature was found for the high-frequency spec-trum when the B-and C-lines are resolved.This striking eﬀect of the nonmagnetic ligand atom on the echo forma-tion may be related to a rather strong isotropic hyperﬁne interaction between17O nuclear spin and the Mn electron spin system with long-range AF spin order.The detailed analysis of the spectra measured below T N requires ad-ditional studies which are now in progress.D.Development of charge and orbital ordering Based on the site assignment considered above we pro-pose the following picture of the development of spin cor-relation in the Pr0.5Ca0.5MnO3CO PM phase as seen by17O NMR.In the low-temperature part of the CO PM phase the NMR spectrum represents the spin den-sity distribution on oxygen ions.Its value is determined not just by the Mn eﬀective magnetic moment but,to a greater extent,by the type of spin correlations of the neighboring Mn atoms.The presence of several lines in NMR spectrum,which can be attributed to the various oxygen sites in the lattice,shows that the correspond-ing spin correlations and eﬀective magnetic moment of the neighboring cations do not change at the time scale t≥10/(∆ω)≈10−6s(∆ω-line splitting)[20].The ther-mally activated hopping of e g-holes seems to be the main mechanism changing the charge state of the ion(Mn3+-Mn4+)and the spin correlations between the neighboring ions,which results in the”melting”of OO in CO PM phase.With increasing temperature theﬁne structure of the spectrum is smeared as the corresponding correlation time(τc)of the speciﬁc hoping becomes comparable with (∆ω)−1.As a result the various spin conﬁgurations are no more distinguishable at higher temperature.The splitting of the NMR spectrum just below T CO into the A-and(B+C)-lines may be explained as follows. As has been mentioned above the oxygen nuclei respon-sible for A-line are located between two AF correlated Mn ions from adjacent ab-plane whereas those responsi-ble for(B+C)-line have two neighboring Mn ions in the same ab-plane.The resolution of A-line shows that just below T CO the correlation time of the AF correlated spin of neighboring Mn from adjacent ab-planes becomes long compared to the NMR time scale.By contrast(B+C)-line is still unresolved just below T CO.Thus in the ﬁrst stage of the charge ordering the three-dimensional (3D)motion of eg-electrons transforms preferentially into a two-dimensional(2D)hopping within the ab-planes. Such an ordering phase transition may be considered as the nucleation of AF ordered clusters which grow at the expense of the CD PM phase which dominates above T CO.Furthermore as the temperature decreases and the unresolved(B+C)-line is shifted toward high frequency a shoulder appears on the low frequency part(see spectra for T≈200K at Fig.2).The temperature dependence of this signal follows the same Curie-Weiss law as the peak in the CD PM phase(dashed line in Figs.2,3). Its relative intensity decreases with temperature and be-comes negligible only near T N.This may indicate that almost down to T N traces of the CD PM phase remain in the CO PM phase.The proposed NMR interpretation of the ordering in the CO PM phase is in a good agreement with the main results of the resonant x-ray[4]and neutron diﬀraction studies[6],[7],[8].It should be noted that the time scales required to get a quasi-static picture of charge dis-tribution in NMR(t nmr>10−6s)and in neutron diﬀrac-tion(t nd∼10−12s)experiments are very diﬀerent.Both methods conﬁrm the presence of FM correlations between Mn as dominant spinﬂuctuations in the CD PM phase which reduce in intensity below T CO.In the neutron scattering experiments the short-range FM correlations are considered as a static whereas it is seen still as a low-frequency dynamic phenomenon in the NMR spec-tra.In conclusion,the distribution of spin density and the development of the charge and orbital ordering in the paramagnetic state of Pr0.5Ca0.5MnO3were studied for theﬁrst time by means of17O NMR.It is shown that the main interaction of oxygen is the isotropic hyperﬁne Fermi-contact interaction with the s-electron spin den-sity transferred from the nearest-neighboring Mn ions. The resulting magnetic line shift is very sensitive to both the electronic conﬁguration of the neighboring cation (Mn+3/Mn4+)and to their speciﬁc spin-pair correlations that develop on cooling in the charge and orbital ordered PM phase.It is shown that with increasing temperature the melting of the orbital orderingﬁrst develops within the ab-plane whereas the AF correlations between Mn6ions in adjacent layers are more stable and disappear only when T approaches T CO.AcknowledgmentsWe are very grateful to Prof.A.Kaul for supplying us the starting Pr0.5Ca0.5MnO3material and to Dr.A.In-yushkin for17O isotope enrichment.The work is sup-ported partly by Russian Foundation for Basic Research (Grant02-02-16357a)as well as by CRDF RP2-2355and INTAS01-2008Grants.We are especially grateful for support of A.Y.by ESPCI.[1]C.Zener,Phys.Rev.82,403(1951).[2]Z.Jirak,S.Krupicka,Z.Simsa,M.Dlouha,and Z.Vratislav,J.Magn.Magn.Mater.53,153(1985).[3]Y.Tomioka,A.Asamitsu,H.Kuwahara,Y.Morimoto,Y.Tokura,Phys.Rev.B53,R1689(1996).[4]M.v.Zimmerman,C.S.Nelson,J.P.Hill,D.Gibbs,H.Nakao,Y.Wakabayashi,Y.Murakami,Y.Tokura,Y.Tomioka,T.Arima,C.-C.Kao,Phys Rev B64,064411 (2001);M.v.Zimmerman, C.S.Nelson,J.P.Hill, D.Gibbs,M.Blume,D.Casa,B.Keimer,Y.Murakami,C.-C.Kao, C.Venkataraman,T.Cog,Y.Tomioka,Y.Tokura,Phys Rev B64,195113(2001).[5]S.Mori,T.Katsufuji,N.Yamamoto,C.H.Chen,S-W.Cheong,Phys Rev B59,13573(1999).[6]Z.Jirak,F.Damay,M.Hervieu,C.Martin,B.Raveau,G.Andre,F.Bouree,Phys.Rev.B61,1181(2000).[7]R.Kajimoto,H.Yoshizawa,Y.Tomioka,Y.Tokura,Phys Rev B63,212407(2001).[8]R.Kajimoto,T.Kakeshita,Y.Oohara,H.Yoshizawa,Y.Tomioka,Y.Tokura,Phys Rev B58,R11837(1998). [9]E.A.Turov,M.P.Petrov,Nuclear Magnetic Resonance inFerro-and Antiferromagnets(Halsded Press,New York, 1972).[10]it might be noted that a rough estimate for quadrupolecoupling of oxygen in PrCaMnO3falls in the range of17νQ=(0.95- 1.6)MHz reported for other oxides with perovskite or layered-perovskite crystal structure like(BaK)(PbBi)O3[E.Oldﬁeld,Ch.Coretsopoulos,S.Yang,L.Reven,H.Ch.Lee,J.Shore,O.H.Han, E.Ramli, D.Hinks,Phys.Rev.B40(1989)6832];[Yu.Piskunov et al.,Phys.Rev.B65,134518(2002)];YBaCuO[M.Takigawa et al.,Phys.Rev.Let.63,1865 (1989)].[11]Y.Yoshinari,P.C.Hammel,J.D.Thompson,S-W.Cheong,Phys.Rev.B60,9275(1999).[12]D.E.O’Reilly,T.Tsang,J.Chem.Phys.40,734(1963).[13]S.Fraga,J.Karwowski,K.M.S.Saxena,Handbookof Atomic Data(Elsevier Scientiﬁc Pub.,Amsterdam, 1976).[14]R.J.Shulman,V.Jaccarino,Phys.Rev.108,1219(1957).[15]I.S.Elﬁmov(private communication).[16]M.Karplus and G.K.Fraenkel,J.Chem.Phys.35,1312(1961).[17]R.E.Watson,A.J.Freeman,Phys.Rev.134,A1526(1964).[18]R.E.Watson, A.J.Freeman,in Hyperﬁne Interactions,edited by A.J.Freeman and R.B.Frankel(Acad.Press N.Y.-Ldn,1967)p.345.[19]V.I.Anisimov,I.S.Elﬁmov,M.A.Korotin,K.Terakura,Phys.Rev.B55,15494(1997).[20]A.Abragam,The Principles of Nuclear Magnetism3with◦-Mn3+--O5).Theparamag-relative to。