Mixture of bosonic and spin-polarized fermionic atoms in an optical lattice

a r X i v :c o n d -m a t /0202055v 1 4 F eb 2002Stern-Gerlach Entanglement in Spinor Bose-EinsteinCondensates.S.Cruz-Barrios (1),M.C.Nemes(2,3∗)and A.F.R.de Toledo Piza (2)February 1,2008(1)Departamento de F´ısica At´o mica,Molecular y Nuclear,Aptdo 1065,41080Sevillaand Departamento de F´ısica Aplicada I,Universidad de SevillaSevilla,Spain(2)Departamento de F´ısica–Matem´a tica,Instituto de F´ısica,Universidade de S˜a o Paulo,C.P.66318,05315-970S˜a o Paulo,S.P.,Brazil(3)Departamento de F´ısica,ICEX,Universidade Federal de Minas Gerais,C.P.702,30161-970Belo Horizonte,M.G.,BrazilAbstractEntanglement of spin and position variables produced by spatially inhomogeneous magnetic fields of Stern-Gerlach type acting on spinor Bose-Einstein condensates may lead to interference effects at the level of one-boson densities.A model is worked out for these effects which is amenable to analytical calculation for gaussian shaped condensates.The resulting interference effects are sensitive to the spin polarization properties of the condensate.PACS number:03.75.FiThe classic Stern-Gerlach experiment[1]is currently understood as providing for the spin analysis of a beam of particles using the entanglement of spin and spatial degrees of freedom through the action of inhomogeneous magnetic fields and subsequent spatial analysis of the scattered flux[2].In this paper we explore effects resulting from this same type of entanglement when an essentially static spinor Bose-Einstein condensate with large coherence length is subjected to Stern-Gerlach field gradients.In the case of pure condensates that are sufficiently dilute so that mean field effects are a minor correction,the involved dynamics can be treated in a rather straightforward and simple way for appropriate,non-trivial field configurations using the ideas recently developed in ref.[3].A simple but still rather general model state for a pure spinor (spin 1for definiteness)condensate is one in which all bosons occupy one same single-boson spin-orbital u ( r ,σ),whereσ=−1,0,1is the spin variable.This state can be expressed in terms of the creation operatora†≡ σ d3r u( r,σ)ψ†σ( r),whereψσ( r)is the spinor bosonicfield operator,as|Ψ(N) =1N! a† N|0 .This state is completely characterized by its one-boson density,given byρ( r,σ; r′σ′)≡ Ψ(N)|ψ†σ′( r′)ψσ( r)|Ψ(N) =Nu( r,σ)u∗( r′,σ′).The spin and position degrees of freedom are entangled whenever the spin-orbital u( r,σ) does not have the product form u( r)χ(σ).A slightly more general form for a non-entangled one-body density isρ( r,σ; r′σ′)→u( r)u∗( r′)⊗ρ(s)(σ;σ′)≡ρ(pos)( r; r′)⊗ρ(s)(σ;σ′)(1) where the second factor,representing the spin density matrix,is allowed to be a mixed state. This information if of course not sufficient to craracterize the underlying many-boson state. Considering,as an example,a case in whichρ(s)(σ;σ′)is diagonal,with eigenvalues Nσand1σ=−1Nσ=N,both the pure N-boson state|{Nσ} =1N1!N0!N−1! σ a†σ Nσ|0 ,a†σ≡ d3r u( r)ψ†σ( r)(2)and the statistical mixture represented by the many-boson densityσ a†σ N|0 Nσimplemented in terms of a quantization axis different from that associated with the Stern-Gerlachfield will also produce one-body interference effects.Both of these schemes will be developed in what follows.The mechanism responsible for the one-body interference can be illustrated schematically in terms of a completely polarized“travelling”one-boson amplitudeφ( r,σ)=e i k· rV⊗|σz=0 .If thefield gradient is applied along the x-axis,rotation of the state changes the spin factor to(|σx=1 −|σx=−1 )/√√2 |σz=1 ±√2Vsin2κxwhich shows interference fringes parallel to the z-axis.Note,in particular,that this is independent of the initial momentum k of the travelling amplitude.Eventually,an analogy may be discerned between this mechanism and that involved in Bragg diffraction experiments involving Bose-Einstein condensates[5,6].More specifically,the coherent superposition of amplitudes with different momenta resulting from the action of the Stern-Gerlachfield after subsequent redefinition of the relevant quantization axis parallels that achieved through the action of the Bragg pulses in thefirst ref.[5].We now turn to the description of the dinamics of the spinor condensate under thefield gradient.We assume that when thefield is applied the condensate is dilute enough so that effects of the two-body interaction are negligible.The relevant dynamics is thus contained in a second-quantized Hamiltonian of the formH= σσ′ d3rψ†σ′( r) −¯h2∇2B( r)→ B(x,z)=(B+b1z)ˆz−b1xˆx.Typical values of the constants are B0∼50G and b1∼2.5G cm−1.As shown in ref[3],the dynamics can be implemented in terms of a set of semi-classical propagators associated to eigenvalues of the projection of the spin operator onto the direction of the local magneticfield.In view of the orders of magnitude given above,this direction differs negligibly from thefield z axis.Therefore,if this axis makes an angleθwith the quantization axis used to express the spin density,in order to apply the semi-classsical propagators one has to consider the rotated spin densityρ(s)(m;m′)= σσ′d∗σm(θ)ρ(s)(σ;σ′)dσ′m′(θ)so that the complete initial density is given asρ( r,m; r′m′)=ρ(pos)( r; r′)⊗ρ(s)(m;m′).Propagation to time t of each m component is then performed byx f,z f|U m(t)|x,z ≈ M¯h S claswhere the classical actionS clas=M2gmb1t(z+z f)−(gmb1)2the typical value quoted above.The resulting distribution closely resembles that given in ref.[4].We next consider a mid-course change of the Stern-Gerlachfield.After afirst stage described by the above expressions and lasting for a time t1a sudden rotation by an angle θB of B(x,z)is performed around the y axis.Strictly speaking,it is not important that the field values are maintained,so that the rotation can be achieved e.g.by superimposing an additional externalfield.The initial condition for the second stage of the evolution will be then,in the appropriatefield frameρ(2)( r,m; r′m′,t1)= m1m2d∗m1m(θB)ρ( r,m1; r′m2,t1)d m2m′(θB).The propagation to t>t1is handled analogously to thefirst stage,in terms of a propagator ˜U(t−t1),leading to afinal densitymρ(2)( r,m; r′m′,t)= d3r1 d3r2 r|˜U m(t−t1)| r1 ρ(2)( r1,m; r2,m′,t1) r2|˜U†m′(t−t1)| r′ . The corresponding spin-inclusivefinal spatial density is nowρ(inc)( r,t)= mρ(2)( r,m; r,m,t)=(4) = m m1m2 d3r1 d3r2 r|U mm1(t)| r1 ρ( r1,m1; r2,m2) r2|U†m2m(t)| r wherer|U mm′(t)| r′ = d3r1 r|˜U m(t−t1)| r1 d∗m′m(θB) r1|U m′(t1)| r′is the effective,spin non-diagonal propagator from time zero to time t.Note that,during thefirst stage,different m components are subjected to different boosts.After the rotation θB,the new m components will in general be associated with coherent superpositions of differently boosted spatial amplitudes,leading to interferece patterns in the observed spin inclusive one-boson density,as can be seen infig.1.This interference will be absent in the special case in which the spin density is diagonal in the reference frame defined by thefield acting in thefirst stage,due to the incoherent nature of the differently boosted components.Alternatively,we may let the system evolve as in thefirst stage for a time t,and then consider the resulting one-boson density spin-selected along a quantization axis differing from thefield z axis by a rotationθsel around the y axis.In this case the spatial one-boson density selected for the component m of the spin in the last frame will be given byρ(sel)( r,t)= m1m2d∗m1m(θsel)ρ( r,m1; r,m2,t)d m2m(θsel).(5) which will also show interference effects for the same general reasons discussed in the previous case.In particular,in the special case in which the spin density is diagonal in the reference5frame defined by thefield,no interference occurs in the one-boson density.An example of this case is shown infig.2.The initial(gaussian)spatial amplitudes leading to the patterns shown in Figs.1and2 have been taken as real,and therefore the initial velocityfield vanishes.The regime in which the two-body interaction effects becomes negligible is in general reached after release of the mean-field energy,which generates a non-vanishing velocityfield.The argument given above in order to illustrate the one-boson interference mechanism indicates that this initial velocity field does not change the interference pattern generated by the Stern-Gerlach boosts.This has in fact been verified in the calculations,by starting from narrower gaussians and letting them spread freely for the appropriate time before applying the magneticfield.In both cases,the typical fringe spacing is determined by the de Broglie wavelength associated with the relative velocities of the interfering amplitudes.This depends both on the value of the magneticfield gradient and on the duration of thefirst stage(in thefirst case above)or of the exposure time to thefield(in the second case).For the F=1states of85Rb,fringes of the order of several microns correspond to times of the order of1ms or shorter for b1∼1G cm−1.It should be stressed that the above analysis has been carried out at the level of the one-boson density.To the extent that laboratory observation is sensitive to many-boson correlations[7],further interference effects are to be expected.Notably,in the case of the pure many-boson initial state(2)the Monte Carlo procedure of ref.[7]will generate an in-terference pattern in the extended r,σspace even when the initial Stern-Gerlach boosts are applied along the z-axis,which is however invisible at the one-boson level.No many-body interferences occur,under these conditions,in the case of the mixed many-boson state(3), due to the incoherece of the different spin components.If,however,the initial Stern-Gerlach boost is applied along a direction different from the x-axis,each one of the incoherent, completely polarized spin components of the mixed many-boson state will generate an in-terference pattern which seeps down to the one-body level.The restriction to the one-body level appears thus as a“filter”on the richer domain of many-body effects.Acknowledgement.S.C.-B.has been partially supported by the Spanish CICyT, Project No.PB98-1111and by the Pr´o-Reitoria de Pesquisa of the Universidade de S˜a o Paulo,and M.C.N.has been partially supported by by the Funda¸c˜a o de Amparo`a Pesquisa do Estado de S˜a o Paulo(FAPESP)and by the Conselho Nacional de Desenvolvimento Cient´ıfico e Tecnol´o gico(CNPq).References[1]W.Gerlach and O.Stern,Z.Phys.8,110(1922);9,349(1922).[2]In this context,the coherence properties of the spatially separated components of thewave function have been extensively discussed in connection with the“reconstruction”of the initial spin state,see Z.Hradil,J.Summhammer,G.Badurek and H.Rauch, Phys.Rev.A62,014101(2000)and references therein.6[3]S.Cruz-Barrios and J.G´o mez-Camacho,Phys.Rev.A63,012101(2001).[4]M.D.Barrett,A.J.Sauer and M.S.Chapman,Phys.Rev.Lett.87,010404(2001).[5]M Kozuma,L.Deng,E.W.Hagley,J.Wen,L.Lutwak,K.Helmerson,S.L.Rolstonand W.D.Phillips,Phys.Rev.Lett.82,871(1999);M.Kozuma,Y.Suzuki,Y.Torii, T.Sugiura,T.Kuga E.W.Hagley and L.Deng,Science286,2309(1999);J.P.E.Sim-sarian,J.Denschlag,M.Edwards,C.W.Clark,L.Dend,E.W.Hagley,K.Helmerson, S.L.Holston and W.D.Phillips,Phys.Rev.Lett.85,2040(2000).[6]J.Stenger,S.Inouye,A.P.Chikkatur,D.M.Stamper-Kurn,D.E.Pritcahrd and W.Ketterle,Phys.Rev.Lett.82,4569(1999);S.Inouye,R.F.Lw,S.Gupta,T.Pfau,A.Grlitz,T.L.Gustavson,D.E.Pritcahrd and W.Ketterle,Phys.Rev.Lett.85,4225 (2000).[7]J.Javanainen and S.M.Yoo,Phys.Rev.Lett.76,161(1996).7Figure1:Contour plots(sizes given in µm)of the spin inclusive one-boson den-sity(4)integrated over y for the shown values of t1and t.The initial one-boson spin density is diagonal with eigenvalueratios3:1:1for spin z-components −1,0,+1respectively.The initial gaus-sian amplitude has b x=25µm and b y,z= 15µm.The anglesθandθB areπ/2and −π/2respectively.Magneticfield param-eters:B0=50G and b1=1.0G cm−1. Note that in(c)interference fringes are too narow for accurate representation.-100-5050100(a) t1=0. ms, t=15. ms-100-5050100(b) t1=.5 ms, t=15.5 ms-75-50-250255075100 -75-50-25255075100(c) t1=5.5. ms, t=20.5 ms8Figure2:Contour plots(sizes given in µm)of the m=+1spin selected one-boson density(5)integrated over y for theshown values of t.The initial one-boson spin density is a pure s z=−1state.The anglesθandθsel areπ/4andπ/2respec-tively.Gaussian andfield parameters are the same as in Fig. 1.Note that in(b) interference fringes are too narow for ac-curate representation.-40-200204060 -30-20-1010203040(a) t=.5 ms-60-40-2002040 -10102030405060(b) t=12 ms9。

a r X i v :c o n d -m a t /0504155v 1 [c o n d -m a t .m e s -h a l l ] 7 A p r 2005Observation of spin-wave characteristics in the two-dimensional ferromagneticordering of in-plane spinsM.K.Mukhopadhyay 1,M.K.Sanyal 1,T.Sakakibara 2,V.Leiner 3,R.M.Dalgliesh 4,and ngridge 41Surface Physics Division,Saha Institute of Nuclear Physics,1/AF,Bidhannagar,Kolkata 700064,India.2Institute for Solid State Physics,University of Tokyo,Kashiwanoha,Kashiwa,Chiba 277-8581,Japan.3Lehrstuhl f¨u r Experimentalphysik,Ruhr-Universit¨a t Bochum,D44780Bochum,Germany.4ISIS,Rutherford Appleton Laboratory,Chilton,Didcot,Oxfordshire OX110QX,UK(Dated:February 2,2008)The role of dipolar interactions and anisotropy are important to obtain,otherwise forbidden,ferro-magnetic ordering at finite temperature for ions arranged in two-dimensional (2D)arrays (monolay-ers).Here we demonstrate that conventional low temperature magnetometry and polarized neutron scattering measurements can be performed to study ferromagnetic ordering of in-plane spins in 2D systems using a multilayer stack of non-interacting monolayers of gadolinium ions.The spontaneous magnetization is absent in the heterogenous magnetic phase observed here and the saturation value of the net magnetization was found to depend on the applied magnetic field.The net magnetiza-tion rises exponentially with lowering temperature and then reaches saturation following a T ln(βT )dependence.These findings verify predictions of the spin-wave theory of 2D in-plane spin system with ferromagnetic interaction and will initiate further theoretical development.PACS numbers:75.70.Ak,75.60.Ej,75.50.XxFerromagnetic materials confined in ultra-thin films and multilayered structures are being studied extensively for the development of high-density magnetic data stor-age devices and to refine our basic knowledge in low-dimensional physics [1,2,3,4].Recent advances in growth techniques such as molecular beam epitaxy and magnetization (M )measurement techniques based on the magneto-optical Kerr effect have enabled us to measure small magnetic signals as a function of applied magnetic field (H )and temperature (T )even from one atomic monolayer of a ferromagnetic material and a wide range of ordering effects has been observed [5,6,7,8,9,10].These measurements have also demonstrated the exis-tence of a spontaneous magnetization and have revealed hysteresis curves in two-[5]and one-dimensional [9]sys-tems,where magnetic ions are arranged in a grid or in a line within a monolayer.A recently generalized theorem [3,4]showed,following spin-wave theory,that long-range ferromagnetic order and hence spontaneous magnetization cannot exist at finite temperature in a two-dimensional systems provided spin-spin interactions are isotropic and short range.A theoretical formalism [7,8,11,12]and computer simulations [6,10]have been developed to include anisotropy and dipolar interactions to explain the apparent contradiction between theory and experiment in low-dimensional systems.A 2D array of magnetic ions with lattice parameter ‘a ’of spins S can be described by a Hamiltonian,H =H ex +H d +H k(1)The strength of the three terms arise from exchange,dipolar and magneto-crystalline anisotropic interactions respectively,and have been approximated by expressing[6,7]these terms in equivalent magnetic field units as,2µB H ex =JS ,2µB H d =4παgS ,2µB H k =6KS (2)In the above expression α(∼1)depends on the lat-tice type and g is equal [6]to (2µB )2/a 3.K is the anisotropy constant.The magnetization reduction due to thermally activated spin waves was calculated with this Hamiltonian and one obtains a non-zero temperature for long-range ferromagnetic ordering as a gap of width∆z =2µB H effk opens up at the bottom of the spin wave spectrum for an easy-magnetization axis (z )perpendic-ular to the film plane.The easy-magnetization axis is determined by the sign of the effective anisotropy field (H effk =H k −H d )defined [7]byH effk =13(3)This explains the observation of hysteresis curves in a monolayer with spins oriented normal to the surface [5,6,9].However,the situation is quite different forspins oriented in an in-plane direction with H effk <0as the spin-wave spectrum remains gapless.The long-range character of the dipole interactions was found [11]to be responsible for creating a pseudo-gap ∆xy =(πSg/2)6|K eff|J/(πgT c ))and out-of-plane spins (with β=2K B/∆z=1/T c).Here A=K B/(4πJS2)and M0is the saturation value of the net magnetization that de-pends on thefield applied to carry out measurements [12].Below T c spin wave theory predicts[7]an enhance-ment of M(T)as[1−A exp(−1/(βT))]and[1−CTν] for out-of-plane and in-plane ordering respectively where C depends on∆xy andνexpected[6,7,11]to be3/2. For0<|K eff|<π2g2/(6J)in-plane spins can not stabi-lize in a homogeneous phase as the magneto-crystalline anisotropy becomes large enough to pull some of the spins in the out-of-plane direction and create a ripple like in-stability[6,7].It is known that both the average magne-tization M(T)as well as the initial susceptibilityχ(T)is proportional to the physical extent of the ordered phase l⋆that minimizes the zero-field energy[6]and can be written asM∝Hl⋆andχ∝l⋆with l⋆∝exp(−γT)(5) It is expected that at low enough temperature,l⋆reaches saturation either because l⋆becomes comparable to the sample size or due to a freezing of the ripple walls.The net magnetization M(T)of the ordered domains then should follow the spin-wave prediction(Eq.(4))to reach saturation.Here we present the verification of this theoreti-cal prediction of2D ferromagnetic ordering of in-plane spins using Langmuir-Blodgett(LB)films of gadolinium stearate.The presence of a large multilayer stack of non-interacting monolayers of gadolinium has enabled us to carry out conventional quantitative magnetization mea-surements at sub-Kelvin temperatures.We could also use polarized neutron scattering measurements[13,14], to show that the ordered phase of the in-plane spins is inhomogeneous and that the monolayers remain uncor-related even when the net magnetization reaches a satu-ration value.In the metal-organic structure formed by LB tech-niques[15,16,17],gadolinium ions are separated by ap-proximately5˚A within a monolayer to form a distorted hexagonal2D lattice and the monolayers are separated from each other by49˚A by organic chains(Fig.1).Films having50such monolayers of gadolinium ions were de-posited on1mm thick Si(001)substrates and character-ized using x-ray reflectivity technique,as discussed earlier [17].Neutron reflection measurements(refer Fig.2)were carried out on the CRISP reflectometer at the Rutherford Appleton Laboratory(RAL),UK using a cold,polychro-matic neutron beam[18,19]and at the ADAM beamline [20,21]of the Institut Laue-Langevin(ILL),Grenoble, France,using a monochromatic cold neutron beam.In Fig.2(b)we have shown spin-polarized neutron reflectiv-ity data taken at2K by applying a magneticfield of13 kOe along an in-plane direction(refer Fig.1).It is known that,if the polarization of the neutrons defined to be par-allel(+)or antiparallel(-)to the appliedfield direction (along+y axis)[13,14,22],the intensity of a multilayer Bragg peak in this geometry increases with effective scat-tering length b eff=b±Aµy with A=0.2695×10−4˚A/µB.In the left inset of Fig.2(b)we have shown inten-sity profiles of parallel(+)and anti parallel(-)incident neutrons at thefirst peak position.The average of(+) and(-)profiles represent the non-magnetic contribution to the reflectivity.Systematic analysis of all these pro-files provide us the value ofµy,the component of aver-age moment per gadolinium ion along+y direction.The obtained values ofµy as a function of H at4.2K and at1.75K using the CRISP and ADAM spectrometers respectively are shown in Fig.2(a)along with data ob-tained from the magnetization measurements[17]at2K and5K.Results of these two independent measurements show that the obtained average saturated moment per gadolinium ion is much less than the expected7µB and confirms the existence of a heterogeneous phase.In the right inset of Fig.2(b)we have shown the transverse dif-fuse neutron scattering intensity profile at thefirst Bragg peak.The hyper-geometric line shape profile confirms that the in-plane correlation is logarithmic in nature and that the interfaces are conformal[23,24].It should be noted that unlike in x-ray measurements the scattering here originates primarily from the metal heads.The line shape and the associated parameters were found to be independent of T,H and hence exhibit the absence of conformality in the magnetic correlations between inter-faces.This again confirms that the LBfilms represent a collection of isolated2D spin-membranes of gadolinium ions.Now we present the results of conventional magneti-zation measurements carried out at sub-Kelvin temper-ature to understand the nature of the ordering.These measurements were performed in a conventional way by measuring forces exerted on a sample situated in a spa-tially varying magneticfield with a Faraday balance[25]. In Fig.2(a)we have shown M vs.H data taken at100mK and500mK temperature in an in-plane(+y)direction. This data reconfirms the absence of hysteresis and re-manence(M=0at H=0).The saturation value of the net magnetization at100mK and500mK found to be 12.7×10−6emu/mm2∼=5.4µB/Gd atom;much lower than the expected7.0µB/Gd atom for a homogeneous ferromagnetic phase.In Fig.3(a)we have shown the magnetization data taken with differentfields as a function of tempera-ture.At higher temperatures these data werefitted with Eq.(5),and the expected exponential dependence is also observed in the magnetization data extracted from our neutron reflectivity measurements(inset of Fig.3(a)). The values ofγobtained fromfitting were found to in-crease with the reduction of H and at0.25kOe it is found to be2.162K−1.It is also observed that at a lowerfield, the magnetization at afixed temperature is nearly pro-portional to the appliedfield(5.03×10−7at0.25kOe3and1.29×10−6emu/mm2at0.5kOe and at a tem-perature0.9K)as predicted for inhomogeneous striped phases(refer Eq.(5)).The amount of majority phase grows exponentially as we lower the temperature for each appliedfield but below a certain temperature this growth stops as the walls of the majority phase freeze.Below this temperature measured data do not follow Eq.(5) and the net magnetization of the majority phase M(T) increases with lowering temperature following the ther-mally activated spin waves as given in Eq.(4).Wefit-ted all the data with Eq.(4)and obtained M0values as0.9×10−6,1.6×10−6,3.2×10−6,4.5×10−6,7.9×10−6,9.5×10−6emu/mm2with0.15,0.25,0.5,1.0,2.5, 5.0kOe magneticfields respectively.These saturation values of net magnetization indicate that the percent-age of the ferromagnetic phase is increasing from7.1% to74.8%as we approach the maximum saturation value of net magnetization obtained of12.7×10−6emu/mm2 (∼=5.4µB/Gd atom)as shown in Fig.2(a).We extracted the value of exchange J as8.76×10−19erg(or H ex= 0.165kOe)from thefitted value of A(=1.02K−1)for the0.25kOe data.We obtainedβas3.4for all the data and hence|K eff|was calculated to be1.7×10−19erg (or H effk=0.19kOe)for0.25kOe data giving T c=26 mK.In this calculation g was6.88×10−18erg,assum-ing that one gadolinium atom occupies2.5˚A×20˚A2,as obtained from neutron and x-ray analysis(refer Fig.1). This proves that we are dealing with an inhomogeneous phase as0<|K eff|<K c(=8.89×10−17erg).Al-though Eq.(4)describes the temperature dependence of the magnetization for ferromagnetic ordering of both in-plane and out-of-plane spins,the argument of the loga-rithmic function can become less than1only for in-plane ordering.Unusually low values of H ex and H effk with a rather large value of H d(=16.3kOe)makeβT<1even for T>T c–this situation has not been reported ear-lier to the best of our knowledge.It is interesting to note that all the magnetization data shown in Fig.3(a) attains respected saturation values M0at temperature T0=1/β(≃0.29K)and a maximum magnetization at temperature T m=1/(eβ)(≃0.108K).Our experimen-tal uncertainties below100mK prohibit us from com-menting on any reduction of magnetization below this T m but Eq.(4)withβT<1,all the data isfitted quite well. Further theoretical development is required to under-stand the thermal activation of spin-waves with in-plane ordering especially as we approach below T c(=26mK). In Fig.3(b)we have shown zero-field-cooled(ZFC)and field-cooled(FC)magnetization data taken with0.15kOe and0.5kOefield along with thefitted curve from Eq.(4). We observe a blocking temperature(T b)of125mK be-low which there is branching in both the ZFC and FC data.This result reconfirms that the observed ferromag-netic ordering requires an externalfield to stabilize and such a low T b indicates the existence of very small spin clusters in the ZFC phase.Application of thefield lowers the activation energy required for the randomly oriented domains to increase the number of spins in the ferro-magnetically ordered majority phase and increases the activation energy of the reverse transition[6].As a re-sult we do not observe T b in the measured temperature range for0.5kOe.In conclusion,we have demonstrated that polarized neutron scattering and conventional magnetization mea-surements can be used to study2D ferromagnetic order-ing of in-plane spins using a stack of magnetically uncor-related spin-membranes formed with gadolinium stearate LBfilm.The in-plane ordering observed here shows that a spontaneous magnetization is absent even at100mK and saturation value of the net magnetization increases with a lowering in temperature.The magnetization is found to increase exponentially with a lowering in tem-perature due to the exponential increase of the physical extent of the ferromagnetic domains in the heterogeneous phase.The ferromagnetic domains ultimately saturate following T ln(βT):characteristic of thermally activated spin-waves and are found to be valid for evenβT≤1. We believe these experimental results will initiate further theoretical development.[1]A.Aharoni,Introduction to the theory of Ferromagnetism(Oxford University Press)2000.[2]C.M.Schneider,and J.Kirschner,Handbook of surfacescience(eds.K.Horn,and M.Scheffler),511,(Elsevier, Amsterdam,2000).[3]N.D.Mermin and H.Wagner,Phys.Rev.Lett.17,1133(1966);17,1307(1966).[4]P.Bruno,Phys.Rev.Lett.87,137203(2001).[5]H.J.Elmers,G.Liu,and U.Gradmann,Phys.Rev.Lett.63,566(1989);H.J.Elmers,Intern.J.Mod.Phys.B9, 3115(1995).[6]K.De’Bell,A.B.Maclsaac,J.P.Whitehead,Rev.Mod.Phys.72,225(2000).[7]P.Bruno,Phys.Rev.B43,6015(1991).[8]A.Kashuba,and V.L.Pokrovsky,Phys.Rev.Lett.70,3155(1993).[9]P.Gambardella,A.Dallmeyer,K.Maiti,M.C.Malagoli,W.Eberhardt,K.Kern,and C.Carbone,Nature(Lon-don)416,301(2002).[10]A.B.MacIsaac,J.P.Whitehead,M.C.Robinson,andK.De’Bell,Phys.Rev.B51,16033-16045(1995).[11]S.V.Male’eV,Sov.Phys.JETP bf43,1240(1976).[12]P.Bruno,Mat.Res.Soc.Sym.Proc.231,299(1992).[13]C.G.Shull,and J.S.Smart,Phys.Rev.76,1256(1949).[14]G.P.Felcher,Phys.Rev.B24,R1595(1981).[15]M.K.Sanyal,M.K.Mukhopadhyay,M.Mukherjee,A.Datta,J.K.Basu,and J.Penfold,Phys.Rev.B65, 033409(2002).[16]J.K.Basu,and M.K.Sanyal,Phys.Rep.363,1(2002).[17]M.K.Mukhopadhyay,M.K.Sanyal,M.D.Mukadam,S.M.Yusuf,and J.K.Basu,Phys.Rev.B68,174427 (2003).[18]J.Penfold,and R.K.Thomas,J.Phys.:Condens.matter4Figure captions:FIG.1:(a)Schematic diagram of the out-of-plane and in-plane structure of the gadolinium stearate Langmuir Blodgett film is shown with the scattering geometry employed for the polarized neutron reflectivity measurements.x−z plane is the scattering plane and the magneticfield is applied along the+y direction.λandαare the wavelength of the radiation and angle of incidence respectively.FIG.2:(a)In-plane Magnetization curves obtained as a func-tion of thefield(H)using neutron reflectivity measured at 4.2K(diamond)and1.75K(star)compared with conventional magnetization data[17]measured at2K(down-triangle)and 5K(up-triangle).Solid lines are thefits with a modified Bril-louin function[17].Magnetization measured at100mK and 500mK is shown for the1st(symbols)and2nd(line)cycle of the hysteresis loop.(b)Neutron reflectivity data(sym-bols)at H=13kOe and at T=2K for the neutron spin along(+)and opposite(-)to the magneticfield direction with the correspondingfit(line).In the left inset thefirst Bragg peak is shown in(+)and(-)channels in an expanded scale.Right inset:Transverse diffuse neutron scattering pro-files(symbols)measured at2K with unpolarized and polar-ized neutron beams.The solid line is afitted hypergeometric curve as described in the text.FIG.3:(a)Sub-Kelvin magnetization results with various appliedfields(symbols)fitted with Eq.(4)(Black line)and with Eq.(5)(wine coloured dashed lines).Dotted lines indi-cate the temperatures T m and T0(refer to text).Inset shows the magnetization obtained from neutron measurements as a function of temperature(symbols)andfit with Eq.(5)(line).(b)ZFC(green circles)and FC(blue stars)along with thefit (line)for FC measurements.2,1369(1990).[19]J.P.Goff,P.P.Deen,R.C.C.Ward,M.R.Wells,S.Langridge,R.Dalgleish,S.Foster,S.Gordeev,J.Mag.Mag.Mat.240,592(2002).[20]H.Zabel,Physica B198,156(1994).[21]V.Leiner,K.Westerholt, A.M.Blixt,H.Zabel, B.Hj¨o rvarsson,Phys.Rev.Lett.91,037202(2003). [22]H.Kepa,J.Kutner-Pielaszek,A.Twardowski,C.F.Ma-jkrzak,J.Sadowski,T.Story,and T.M.Giebultowicz, Phys.Rev.B64,121302(2001).[23]M.K.Sanyal,S.K.Sinha,K.G.Huang,and B.M.Ocko,Phys.Rev.Lett.66,628(1991);J.K.Basu,S.Hazra, and M.K.Sanyal,Phys.Rev.Lett.82,4675(1999). [24]The measured roughness and‘true’roughness[23]of theinterfaces are calculated to be2.3˚A and5.4˚A respec-tively and we get an effective surface tension equal to10 mN/m.[25]T.Sakakibara,H.Mitamura,T.Tayama,H.Amitsuka,Jpn.J.Appl.Phys.33,5067(1994).xyzOut-of-plane direction In-plane directionq zH49Å5Å(b)ααq z ()αλπsin 4=20 Å210203040024********X 1065 K2 K4.2 K1.75 K500 mK 100 mKM a g n e t i z a t i o n ( e m u / m m 2)Field ( kOe )0.10.20.30.410-510-410-310-210-1+ spin - spinR e f l e c t i v i t yq z ( Å -1)0.1200.1250.1300.1350.0020.004q z (Å-1)R e f l e c t i v i t y10-410-310-210-1100H = 0 kOe H = 20 kOeH = 2 kOe +spin H = 2 kOe - spinN o r m a l i z e d c o u n tq x ( Å -1)(a)(b)(b)(a)0.00.10.20.30.40.50.601234H=150 OeH=500 OeX 106Field CooledZero Field CooledM a g n e t i z a t i o n ( e m u / m m 2)Temperature ( K )0.00.30.60.9 1.2 1.5024681012T mT 05.0 kOe2.5 kOe1.0 kOe 0.5 kOe 0.25 kOex 106M a g n e t i z a t i o n ( e m u / m m 2)Temperature ( K )510152025300369x 106Temperature ( K )M a g n e t i z a t i o n( e m u / m m 2)。

a r X i v :c o n d -m a t /9911014v 2 [c o n d -m a t .m e s -h a l l ] 20 J u l 2000A basic obstacle for electrical spin-injection from a ferromagnetic metal into adiffusive semiconductorG.Schmidt,D.Ferrand,L.W.MolenkampPhysikalisches Institut,Universit¨a t W¨u rzburg,Am Hubland,97074W¨u rzburg,GermanyA.T.Filip,B.J.van WeesDept.of Applied Physics and Materials Science Centre,University of Groningen,Nijenborgh 4,9747AG Groningen,the Netherlands(February 7,2008)(Accepted by PRB .)We have calculated the spin-polarization effects of a current in a two dimensional electron gas which is contacted by two ferromagnetic metals.In the purely diffusive regime,the current may indeed be spin-polarized.However,for a typical device geometry the degree of spin-polarization of the current is limited to less than 0.1%,only.The change in device resistance for parallel and antiparallel magnetization of the contacts is up to quadratically smaller,and will thus be difficult to detect.Spin-polarized electron injection into semiconductors has been a field of growing interest during the last years [1–4].The injection and detection of a spin-polarized cur-rent in a semiconducting material could combine mag-netic storage of information with electronic readout in a single semiconductor device,yielding many obvious advantages.However,up to now experiments for spin-injection from ferromagnetic metals into semiconductors have only shown effects of less than 1%[5,6],which some-times are difficult to separate from stray-field-induced Hall-or magnetoresistance-effects [2].In contrast,spin-injection from magnetic semiconductors has already been demonstrated successfully [7,8]using an optical detection method.Typically,the experiments on spin-injection from a fer-romagnetic contact are performed using a device with a simple injector-detector geometry,where a ferromag-netic metal contact is used to inject spin polarized car-riers into a two dimensional electron gas (2DEG)[5].A spin-polarization of the current is expected from the dif-ferent conductivities resulting from the different densities of states)for spin-up and spin-down electrons in the fer-romagnet.For the full device,this should result in a con-ductance which depends on the relative magnetization of the two contacts [1].A simple linear-response model for transport across a ferromagnetic/normal metal interface,which nonetheless incorporates the detailed behaviour of the electrochem-ical potentials for both spin directions was first intro-duced by van Son et al.[9].Based on a more detailed (Boltzmann)approach,the model was developed further by Valet and Fert for all metal multilayers and GMR [10].Furthermore,it was applied by Jedema et al.to superconductor-ferromagnet junctions [11].For the in-terface between a ferromagnetic and a normal metal,van Son et al.obtain a splitting of the electrochemical po-tentials for spinup and spindown electrons in the region of the interface.The model was applied only to a single contact and its boundary resistance [9].We now apply a similar model to a system in which the material proper-ties differ considerably.Our theory is based on the assumption that spin-scattering occurs on a much slower timescale than other electron scattering events [12].Under this assumption,two electrochemical potentials µ↑and µ↓,which need not be equal,can be defined for both spin directions at any point in the device [9].If the current flow is one dimen-sional in the x -direction,the electrochemical potentials are connected to the current via the conductivity σ,the diffusion constant D,and the spin-flip time constant τsf by Ohm’s law and the diffusion equation,as follows:∂µ↑,↓σ↑,↓(1a)µ↑−µ↓∂x 2(1b)where D is a weighted average of the different diffu-sion constants for both spin directions [9].Without loss of generality,we assume a perfect interface without spin scattering or interface resistance,in a way that the elec-trochemical potentials µ↑↓and the current densities j ↑↓are continuous.Starting from these equations,straightforward algebra leads to a splitting of the electrochemical potentials at the boundary of the two materials,which is proportional to the total current density at the interface.The dif-ference (µ↑−µ↓)between the electrochemical potentials1decays exponentially inside the materials,approaching zero difference at ±∞.(µ↑(±∞)=µ↓(±∞))(2)A typical lengthscale for the decay of (µ↑−µ↓)is thespin-flip length λ=j i ↑(x )+j i ↓(x )(3)where we set the bulk spin polarization in the ferro-magnets far from the interface α1,3(±∞)≡β1,3.The conductivities for the spin-up and spin-down channels in the ferromagnets can now be written as σ1,3↑=σ1,3(1+β1,3)/2and σ1,3↓=σ1,3(1−β1,3)/2.We as-sume that the physical properties of both ferromagnets are equal,but allow their magnetization to be either parallel (β1=β3and R 1↑,↓=R 3↑,↓)or antiparallel (β1=−β3and R 1↑,↓=R 3↓,↑).In the linear-response regime,the difference in conductivity for the spin-up and the spin-down channel in the ferromagnets caneasily be deduced from the Einstein relation with D i ↑=D i ↓[11]and ρi ↑(E F )=ρi ↑(E F ),where ρ(E F )is the density of states at the Fermi energy,and D the diffusion constant.To separate the spin-polarization effects from the nor-mal current flow,we now write the electrochemical po-tentials in the ferromagnets for both spin directions asµ↑,↓=µ0+µ∗↑,↓,(i =1,3),µ0being the electrochemi-cal potential without spin effects.For each part i of the device,Eqs.(1)apply separately.As solutions for the diffusion equation,we make the Ansatzµi ↑,↓=µ0i +µ∗i ↑,↓=µ0i +c i ↑,↓exp ±((x −x i )/λfm )(4)for i =1,3with x 1=0,x 3=x 0,and the +(-)sign referring to index 1(3),respectively.From the boundary conditions µ1↑(−∞)=µ1↓(−∞)and µ3↑(∞)=µ3↓(∞),we have that the slope of µ0is identical for both spin directions,and also equal in region 1and 3if the conductivity σis identical in both regions,as assumed above.In addition,these boundary condi-tions imply that the exponential part of µmust behave as c exp (x/λfm )in region 1and as c exp (−(x −x 0)/λfm )in region 3.In the semiconductor we set τsf =∞,based on the assumption that the spin-flip length λsc is several orders of magnitude longer than in the ferromagnet and much larger than the spacing between the two contacts.This is correct for several material systems,as semiconductor spin-flip lengths up to 100µm have already been demon-strated [13].In this limit,we thus can write the elec-trochemical potentials for spin-up and spin-down in the semiconductor asµ2↑,↓(x )=µ1↑,↓(0)+γ↑,↓x ,γ↑,↓=constant(5)While the conductivities of both spin-channels in the ferromagnet are different,they have to be equal in the two dimensional electron gas.This is because in the 2DEG,the density of states at the Fermi level is constant,and in the diffusive regime the conductivity is propor-tional to the density of states at the Fermi-energy.Each spin channel will thus exhibit half the total conductivity of the semiconductor (σ2↑,↓=σsc /2).If we combine equation 1and 4and solve in region 1at the boundary x =0and in region 3at x =x 0we are in a position to sketch the band bending in the overall device.From symmetry considerations and the fact that j 2↑and j 2↓remain constant through the semiconductor (no spin-flip)we haveµ1↑(0)−µ1↓(0)=±(µ3↓(x 0)−µ3↑(x 0))(6)where the +(-)sign refers to parallel (antiparallel)magnetization,respectively.This yields c 1↑=−c 3↑and c 1↓=−c 3↓in the expression for µ↑↓in Eq.4for the par-allel case,which is shown schematically in Fig.(1b).The antisymmetric splitting of the electrochemical potentials at the interfaces leads to a different slope and a crossing of the electrochemical potentials at x =x 0/2.We thus obtain a different voltage drop for the two spin directions over the semiconductor,which leads to a spin polariza-tion of the current.In the antiparallel case where the minority spins on the left couple to the majority spins on2the right the solution is c1↑=−c3↓and c1↓=−c3↑with j↑=j↓.A schematic drawing is shown in Fig.(1c).The splitting is symmetric and the current is unpolarized. The physics of this result may readily be understood from the resistor model(Fig.1a).For parallel(antipar-allel)magnetization we have R1↑+R3↑=R1↓+R3↓(R1↑+R3↑=R1↓+R3↓),respectively.Since the volt-age across the complete device is identical for both spin channels,this results either in a different(parallel)or an identical(antiparallel)voltage drop over R SC↑and R SC↓. For parallel magnetization(β1=β3=β)thefinite spin-polarization of the current density in the semicon-ductor can be calculated explicitly by using the continu-ity of j i↑,↓at the interfaces under the boundary condition of charge conservation for(j i↑+j i↓)and may be expressed as:α2=βλfmx02x0σfm+1)−β2(7)whereα2is evaluated at x=0and constant through-out the semiconductor,because above we have setτsf=∞in the semiconductor.For a typical ferromagnet,α2is dominated by (λfm/σfm)/(x0/σsc)where x0/σsc andλfm/σfm are the resistance of the semiconductor and the relevant part of the resistance of the ferromagnet,respectively.The max-imum obtainable value forα2isβ.However,this maximum can only be obtained in cer-tain limiting cases,i.e.,x0→0,σsc/σfm→∞,or λfm→∞,which are far away from a real-life situa-tion.If,e.g.,we insert some typical values for a spin injection device(β=60%,x0=1µm,λfm=10nm,and σfm=104σsc),we obtainα≈0.002%.The dependence ofα2on the various parameters is shown graphically in Figs.(2a)and(2b)whereα2is plotted over x0andλfm, respectively,for three different values ofβ.Apparently, even forβ>80%,λfm must be larger than100nm or x0well below10nm in order to obtain significant(i.e. >1%)current polarization.The dependence ofα2onβis shown in Fig.(3a)for three different ratiosσfm/σsc. Even for a ratio of10,α2is smaller than1%forβ<98%, where the other parameters correspond to a realistic de-vice.By calculating the electrochemical potential through-out the device we may also obtain R par and R anti which we define as the total resistance in the parallel or an-tiparallel configuration,respectively.The resistance is calculated for a device with ferromagnetic contacts of the thicknessλfm,because only this is the lengthscale on which spin dependent resistance changes will occur.In a typical experimental setup,the difference in resistance ∆R=(R anti−R par)between the antiparallel and the parallel configuration will be measured.To estimate the magnitude of the magnetoresistance effect,we calculate ∆R/R par and we readilyfind∆R1−β2λ2fmx204x0σfm+1)2−β2(8)Now,for metallic ferromagnets,∆R/R par is domi-nated by(λfm/σfm)2/(x0/σsc)2and is approx.α22.In the limit of x0→0,σsc/σfm→∞,orλfm→∞,we again obtain a maximum which is now given by∆R(β−1)(β+1)(9)Fig(3b)shows the dependence ofα2and∆R/R par onβ, for a realistic set of parameters.Obviously,the change in resistance will be difficult to detect in a standard ex-perimental setup.We have thus shown,that,in the diffusive transport regime,for typical ferromagnets only a current with small spin-polarization can be injected into a semiconductor 2DEG with long spin-flip length even if the conductiv-ities of semiconductor and ferromagnet are equal(Fig (3a)).This situation is dramatically exacerbated when ferromagnetic metals are used;in this case the spin-polarization in the semiconductor is negligible. Evidently,for efficient spin-injection one needs a con-tact where the spin-polarization is almost100%.One ex-ample of such a contact has already been demonstrated: the giant Zeeman-splitting in a semimagnetic semicon-ductor can be utilized to force all current-carrying elec-trons to align their spin to the lower Zeeman level[7]. Other promising routes are ferromagnetic semiconduc-tors[8]or the so called Heusler compounds[14]or other half-metallic ferromagnets[15,16].Experiments in the ballistic transport regime[17](whereσsc has to be re-placed by the Sharvin contact resistance)may circum-vent part of the problem outlined above.However,a splitting of the electrochemical potentials in the ferro-magnets,necessary to obtain spin-injection,will again only be possible if the resistance of the ferromagnet is of comparable magnitude to the contact resistance.ACKNOWLEDGMENTSThis work was supported by the European Commission (ESPRIT-MELARI consortium’SPIDER’),the German BMBF under grant#13N7313and the Dutch Founda-tion for Fundamental Research FOM.[3]A.G.Aronov,G.E.Pikus,Sov.Phys.Semicond.10(6),698(1976).15(3),1215,(1997)[4]G.A.Prinz,Physics Today,48(4),58-63,(1995)[5]W.Y.Lee,S.Gardelis,B.C.Choi,Y.B.Xu,C.G.Smith,C.H.W.Barnes,D.A.Ritchie,E.H.Linfield,J.A.C.Bland,J.Appl.Phys.85(9),6682(1999)[6]P.R.Hammar,B.R.Bennet,M.J.Yang,M.Johnson,Phys.Rev.Lett.83(1),203-206,(1999)[7]R.Fiederling,M.Keim,G.Reuscher,W.Ossau,G.Schmidt, A.Waag,L.W.Molenkamp,Nature,402, (1999),787[8]Y.Ohno,D.K.Young,B.Beschoten,F.Matsukura,H.Ohno,D.D.Awschalom,Nature,402,(1999),790 [9]P.C.van Son,H.van Kempen,P.Wyder,Phys.Rev.Lett.58(21),2271(1987)[10]T.Valet,A.Fert,Phys.Rev.B4810,7099(1993)[11]F.J.Jedema,B.J.van Wees,B.H.Hoving,A.T.Filip,T.M.Klapwijk,Phys.Rev.B60,16549(1999)[12]D.H¨a gele,M.Oestreich,W.W.R¨u hle,N.Nestle,K.Eberl,Appl.Phys.Lett.73(11),1580,(1998)[13]J.M.Kikkawa,D.D.Awschalom,Nature397,139-141,(1999)[14]R.A.de Groot,F.M.M¨u ller,P.G.van Engen,K.H.J.Buschow,Phys.Rev.Lett.50,2024(1983)[15]J.-H.Park,E.Vescovo,H.-J.Kim,C.Kwon,R.Ramesh,T.Venkatesan,Nature392,794(1998)[16]K.P.K¨a mper,W.Schmidt,G.G¨u ntherodt,R.J.Gam-bin,R.Ruf,Phys.Rev.Lett.59,2788(1988)[17]H.X.Tang,F.G.Monzon,R.Lifshitz,M.C.Cross,M.L.Roukes,Phys.Rev.B617,4437(1999)FIG.1.(a)Simplified resistor model for a device consisting of a semiconductor(SC)with two ferromagnetic contacts(FM) 1and3.The two independent spin channels are represented by the resistors R1↑,↓,R SC↑,↓,and R3↑,↓.(b)and(c)show the electrochemical potentials in the three different regions for parallel(b)and antiparallel(c)magnetization of the ferromagnets. The solid lines show the potentials for spin-up and spin-down electrons,the dotted line forµ0(undisturbed case).For parallel magnetization(b),the slopes of the electrochemical potentials in the semiconductor are different for both spin orientations. They cross in the middle between the contacts.Because the conductivity of both spin channels is equal,this results in a(small) spin-polarization of the current in the semiconductor.In the antiparallel case(c),the slopes of the electrochemical potentials in the semiconductor are equal for both spin orientations,resulting in unpolarized currentflow.(Note that the slope ofµin the metals is exaggerated).FIG.2.Dependence ofα2onλf m(a)and x0(b),respectively forσf m=100σsc and three different values ofβ.Infig.(a), x0is1µm.Note thatα2is only in the range of%forβ≈100%orλf m in theµm-range.Infig.(b)we haveλf m=10nm and again,we see that for a contact spacing of more than10nm,α2will be below1%if a standard ferromagnetic metal(β<80%) is used.FIG.3.Dependence ofα2and∆R/R onβ.In(a)α2is plotted overβfor different ratiosσf m/σsc.For a ratio of100,α2is well below0.1%forβ<99%.In(b),againα2is plotted versusβwithσf m/σsc=100,with the corresponding values for∆R/R on a logarithmic scale.Forβbetween0and90%,∆R/R is smaller than10−7and thus difficult to detect in the experiment.4µ 0µ ↑ µ ↓x = 0x = x0 F i g . 1 S c h m i d t e t a l .F MF MS Cc 1 ↑c 1 ↓µ 0µ ↑µ ↓c 1 ↑c 1 ↓p a r a l l e l a n t i p a r a l l e lbc R 1 ↑ R 1 ↓R s c ↑ R s c ↓R 3 ↑ R 3 ↓a1 011 02 1 0 31 01 01 0 1 0 1 0 α 2λ f m/ n m 0- 40 - 30 - 20 - 10 0F i g . 2 S c h m id te t a l .0 , 0 , 0 , 0 , 0 , 1 , α 2x 0/ n m , 0, 2 , 4 , 6 , 8 , 0F i g . 3 S c h m i d t e t a l .σ f m = σ s cσ f m = 1 0 σ s cσ f m = 1 0 0 σ s c- 1 , 0- 0 , 6 - 0 , 20 , 2 0 , 61 , 0- 0 , 2- 0 , 1 0 , 00 , 1 0 , 2 βα 2a- 0 , 2- 0 , 1 0 , 00 , 1 0 , 21 E - 1 E - 1 E - 0 , α βE - 1 3E - 1 1 E - 9E - 7 E - 5E - 3 , 1∆ R / R2。

a rXiv:h ep-ph/4317v11Mar24Particle and spin motion in polarized media A.J.Silenko Institute of Nuclear Problems,Belarusian State University,Minsk,Belarus E-mail:silenko@inp.minsk.by Abstract Quantum mechanical equations of motion are obtained for particles and spin in media with polarized electrons in the presence of external fields.The motion of elec-trons and their spins is governed by the exchange interaction,while the motion of positrons and their spins is governed by the annihilation interaction.The equations obtained describe the motion of particles and spin in both magnetic and nonmag-netic media.The evolution of positronium spin in polarized media is investigated.Media with polarized electrons can be used for polarization of positronium beams.1IntroductionThe quantum mechanical description of the motion of particles and spin in matter is a very important problem.The classical theory of motion of particles and spin has been developed in great detail (see [1,2])).A quantum mechanical equation of motion of relativistic particles in an electromagnetic field was derived by Derbenev and Kondratenko[3].The motion of the spin of relativistic particles in an electromagnetic field is described by the Bargmann–Michel–Telegdi (BMT)equation [4].The Lagrangian with an allowance for terms quadratic in spin was obtained in [5,6].The corresponding equation of spin motion was presented in [7].The interaction between polarized particles and polarized matter was analyzed in [8,9].In the present paper,we find quantum mechanical equations of motion of particles and spin for relativistic particles with arbitrary spin that move in media with polarized electrons in the presence of external fields.The system of units ¯h =c =1is used.2Hamiltonian for particles in polarized mediaFor particles with arbitrary spin,the Hamiltonian can be derived with the use of the interaction Lagrangian L ,obtained in [5,6].This Lagrangian contains terms that are linear (L 1)and quadratic (L 2)in spin:L =L 1+L 2,L 1=eγ (S ·B )−(g −2)γγ+1(S ·[E ×v ]) ,L 2=Qγ+1(S ·v )(v ·∇) (S ·E )−γ2m 2γγ (S ·B )−(g −1)γγ+1 (S ·[E ×v ]) ,γ=11−v 2,(1)where g =2µm/(eS ),v is the velocity operator,γis the Lorentz factor,Q is the quadrupole moment,and S is the spin operator.The Hermitian form of formula (1)is obtained by the substitution L →(L +L †)/2.The total Hamiltonian is given byH =√1)Recall that the exchange interaction is responsible for the ferromagnetism.field for electrons should be replaced in (2)by the effective quasimagnetic field [8]B →G e =B +H c eff +H m eff ,H c eff =−4π|e |Nm (P ·n )n ,(3)where N and P =<σ′>are the polarization density and vector (average spin),respec-tively,of polarized matter electrons and n =v /v .The main contribution to the effective quasimagnetic field,H c eff ,is made by the Coulomb exchange interaction,or the Coulomb scattering.The exchange magnetic scattering yields the lesser contribution,H m eff .For nonrelativistic positrons in polarized media,the effective field with an allowance for the annihilation interaction,H a eff ,is determined byG p =B +H a eff =B −π|e |Nv 2M −4π(M ·n )n ,G p =B +2πM ,M =−|e |Nµm v 2B −µm −12µm B .(6)An appropriate expression for the Hamiltonian is expressed as (G =G e ,G p )[9]H =√2m g (S ·G )+(g −1)(S ·[E ×v ]) .(7)3Equations of motion of particles and spinThe equation of particle motion in both polarized and unpolarized media is the same if the Hamiltonian remains unchanged.For electrons and positrons,the equation of particle motion is given by [9]d π2m ∇ g (S ·G )+(g −1)(S ·[E ×v ]) .(8)For particles with arbitrary spin,the equation of spin motion with regard to the terms quadratic in spin is given in [7].For nonrelativistic electrons and positrons,the equation of the spin motion takes the form [9]d S2m g [S ×G ]+(g −1)[S ×[E ×v ]] .(9)The effect of the exchange interaction on the spin motion is stronger than that on the particle motion.The equations can be used for dia-,para-,and ferromagnetic media.4Polarization of positronium beams by polarized mediaPositronium beams can be polarized under passing through the polarized medium. Such a possibility takes place due to a dependence of the ortho-para-conversion(spin-conversion)rate on the polarization of the positronium.Positronium atoms have spin0(para-positronium,p-Ps)or1(ortho-positronium,o-Ps).Only o-Ps atoms pass through the medium because p-Ps atoms annihilate very quickly.As a rule,the positronium energy does not exceed several eV.In the matter,the o-Ps lifetime can be shortened by several processes,namely,the pick-offannihilation,the ortho-para-conversion that is the spin-conversion,and chemical reactions[10].The spin-conversion takes place in para-and ferromagnetic media,whose molecules contain unpaired electrons.In these media,the spin-conversion rate is generally much more than the rates of the pick-offannihilation and other processes.As particular,in the oxygen gas the spin-conversion rate is dozens of times larger than the pick-offannihilation one[11].The same conclusion can be made from an analysis of experimental data on the spin-conversion in solutions of HTMPO[12].We consider the simplified description of the positronium polarization process.For a more detailed description,the method and results obtained in Ref.[13]can be used.Let all the unpaired electrons of the matter be polarized along the z-axis(Fig.1). The spin exchange interaction can cause changing the o-Ps spin or its projection.This process can result in both the ortho-para-conversion and the prompt annihilation of the o-Ps.However,the simple analysis shows that the ortho-para-conversion is only possible when the o-Ps spin projection onto the z-axis equals either−1or0(see Figs.1a,b). When it equals1,flipping the spin is forbidden(see Fig.1c).The operator of the spin exchange interaction has the formP=−J(1+4s·s′)/2,(10) where s and s′are the spin operators of the o-Ps electron and the matter electron,re-spectively,and J is the exchange integral that determines splitting energy levels.The operator P mixes the states of the o-Ps and p-Ps.The o-Ps with S z=−1interacting with a matter electron(s z=1/2)is described by the spin wave function|1,−1;1/2,1/2 .As a result of simultaneousflipping the spins of the o-Ps electron and the matter one,the o-Ps can convert into the p-Ps with the spin wave function|0,0;1/2,−1/2 .This process is characterized by the matrix element2)0,0;1/2,−1/2|P|1,−1;1/2,1/2 =−J/√2.Analogous processes take place for the o-Ps with S z=0.The spin exchange interaction between the o-Ps electron and the matter one with and without the ortho-para-conversion is described by the matrix elements0,0;1/2,1/2|P|1,0;1/2,1/2 =−J/2and 1,1;1/2,−1/2|P|1,0;1/2,1/2 =−J/√2)All the matrix elements of the operator s·s′are given,e.g.,in Ref.[14].respectively.Coupled electrons do not contribute to the spin-conversion because matrixelements characterizing the exchange interaction between the o-Ps and the pair of coupledelectrons are zero.For the o-Ps with S z=1,all the corresponding matrix elements are zero.Therefore,the majority of o-Ps atoms passes through the medium without the annihilation.Thepick-offannihilation is possible for the o-Ps atoms with any spin projection.The o-Ps lifetime is changed by a magneticfield into the medium.Thisfield can bestrong enough.As is known,such afield does not change the lifetime of the o-Ps with S z=±1and shortens the lifetime of the o-Ps with S z=0(see Ref.[10]).This circumstance accelerates the process of polarization of the o-Ps beam.However,the evaluation showssuch an acceleration is not very significant.For example,the pick-offannihilation shortens the o-Ps lifetime more greatly than the magneticfield in ferromagnetic media.5Discussion and conclusionsMagnetic crystals can be effectively used for the rotation of the polarization vectorof particles.Even for neutrons,whose magnetic moment is relatively small,for B∼1T,the angle of rotation of the polarization vector per unit length is of the order of ∆Φ/∆l∼(c/v)×10−3rad/cm.The rotation of the polarization vector in magnetic crystals reaches especially large values for nonrelativistic electrons.It follows from(6)and(7)that the angular velocity of the spin precession of nonrelativistic electrons is increased by the factor of(c/v)2due to the exchange interaction.For B∼1T,we have∆Φ/∆l∼(c/v)3×1rad/cm in order of magnitude.In particular,when v/c∼0.1,we have∆Φ/∆l∼103rad/cm.The use of magnetic crystals may also be sufficiently effective for the rotation of the polarization vector of relativistic electrons.The Stern–Gerlach force,which splits beams according to the polarization of particles,is considerably increased.However,the use of polarized media for splitting electron beams according to the polarization is seriously hampered by the small value of the energy of interaction between the spin of electrons and a quasimagneticfield W(s)(of the order of 1eV or less)and a multiple scattering that increases the transverse energy of electrons. If the transverse energy of electrons is greater than|W(s)|,splitting the beam according to the polarization becomes impossible.The formulas obtained in this work are also valid for beams of polarized nuclei.Media with polarized electrons can be used for the polarization of positronium beams.The spin direction of positroniums coincides with the spin direction of polarized electrons.The considered effect of the polarization of positronium beams is more importantfor para-and ferromagnetic media without conductivity electrons,e.g.,ferrites.The spinexchange interaction of o-Ps atoms with conductivity electrons leads to the spin-conversion that does not depend on the o-Ps polarization.As a result,a presence of conductivity electrons can cause a strong background making the effect unobservable.It is important that the intensity of the positronium beam passing through two samplesmagnetized in different directions,depends on the angleφbetween the magnetization axes.This effect is similar to passing the unpolarized light through two polarizers when their axes do not coincide.Polarized positronium beams can be used for an investigation of magnetic media.Theinvestigation can include monitoring the process of magnetization and determining the magnetic structure of materials.The work is supported by the grant of the Belarusian Republican Foundation for Fundamental Research No.Φ03-242.References[1]I.M.Ternov and V.A.Bordovitzyn,Usp.Fiz.Nauk132,345(1980)[p. 23,679(1980)].[2]K.Yee,M.Bander,Phys.Rev.D48,2797(1993).[3]Ya.S.Derbenev and A.M.Kondratenko,Zh.Eksp.Teor.Fiz.64,1918(1973)[Sov. Phys.JETP37,968(1973)].[4]V.Bargmann,L.Michel,and V.L.Telegdi,Phys.Rev.Lett.2,435(1959).[5]A.A.Pomeransky and I.B.Khriplovich,Zh.Eksp.Teor.Fiz.113,1537(1998)[JETP 86,839(1998)].[6]A.A.Pomeransky and R.A.Sen’kov,Phys.Lett.B468,251(1999).[7]A.J.Silenko,Yader.Fiz.64,1054(2001)[Phys.At.Nucl.64,983(2001)].[8]V.G.Baryshevsky,Nuclear Optics of Polarized Media,Evergoatomizdat,Moscow, 1995.[9]A.J.Silenko,Zs.Eksp.Teor.Fiz.123,688(2003)[JETP96,610(2003)].[10]V.I.Goldanskii,Chemical Reactions of Positronium,Univ.of Newcastle upon Tyne, Newcastle-upon-Tyne(1968).[11]N.Shinohara,N.Suzuki,T.Chang,and T.Hyodo,Phys.Rev.A64,042702(2001); arXiv:physics/0011054.[12]J.Major,H.Schneider,A.Seeger et al.,J.Radioanal.Nucl.Chem.190,481(1995).[13]M.Senba,Can.J.Phys.74,385(1996);75,117(1997).[14]ndau and E.M.Lifshitz,Quantum Mechanics:Non-relativistic Theory,3rd ed.,Pergamon Press,Oxford(1977).。

Name _______________ C lass _______________ Score ____________Biochemistry (I) Final Exam (fall, 2004)NOTE: You must write your answer on the answer sheet!Part I: For the following multiple choice questions, one answer is most appropriate (2.5x18 = 45 points).1.With regard to amino acids, which statement is false?A)Amino acids can act as proton donors and acceptors.B)All amino acids discovered in organism are L enantiomers・C)An L amino acid can be Dextrorotary.D)A conjugate acid/base pair is at its greatest buffering capacity when thepH equals its pK.E)Non-standard amino acids can be found in the hydrolysis product of aprotein.2.A mixture of Ala, Arg, and Asp in a pH 5.5 buffer was placed on a cationexchange column (the column is negatively charged) and eluted with the same buffer. What is the order of elution from the column? Use these pK a values: terminal COOH ・ 2, terminal NH3+- 9, R-amino ・ 10, R-COOH ・ 3A)Arg, Ala then AspB)Arg, Asp then AlaC)Asp, Ala then ArgD)Asp, Arg then AspE)Ala, Asp then Arg3.Proteins can be chromatographically separated by their differentA)Charge.B)Molecular weight.C)Hydrophobicity.D)Affinity for other molecules.E)All of above.4.A peptide was found to have a molecular mass of about 650 and uponhydrolysis produced Ala，Cys，Lys, Phe，and Vai in a 1:1:1:1:1 ratio.The peptide upon treatment with Sanger*s reagent (FDNB) produced NP・Cys and exposure to carboxypeptidase produced valine. Chymotrypsintreatment of the peptide produced a dipeptide that contained sulfur and has a UV absorbance, and a tripeptide. Exposure of the peptide to trypsinproduced a dipeptide and a tripeptide. The sequence of the peptide isA)val-ala-lys-phe-cysB)cys-lys-phe-ala-valC)cys-ala-lys-phe-valD)cys-phe-lys-ala-valE)val-phe-lys-ala-cys5.With regard to protein structure, which statement is false?A)The dominant force that drives a water-soluble protein to fold ishydrophobic interaction.B)The number of hydrogen bonds within a protein intends to beminimized.C)The conformations of a native protein are possibly the lowest energystate.D)The conformations of a native protein are countless.E)Disulfde bridges can increase the stability of a protein.6.Which structure is unique to collagen?A)The alpha helix.B)The double helix.C)The triple helix.D)The beta structure・E)The beta barrel・7.Which protein has quaternary structure?A)Insulin.B)A natural antibody.C)Chymotrypsin.D)Aspartate transcarbamoylase (ATCase)・E)Myoglobin.8.Which of the following are "broad themes used in discussing enzymereaction mechanisms11?A)Proximity stabilizationB)Transition state stabilizationC)Acid-base catalysisD)Covalent catalysisE)All of the above9.Under physiological conditions, which of the following processes is not animportant method for regulating the activity of enzymes?A)PhosphorylationB)Temperature changesC)AdenylationD)Allosteric regulationE)Protein processing10.The conversion of glucose to pyruvate is a multistep process requiring tenenzymes・ If a mutation occurs resulting in a lack of activity for one of these enzymes, which of the following happens?A)The concentration of the metabolic intermediate which is the substrateof the missing enzyme is likely to increase and accumulateB)The concentration of pyruvate will increaseC)The cell will produce more of the other nine enzymes to maintain steadystateD)The concentration of the metabolic intermediate which is the product ofthe missing enzyme will decreaseE)A and D11.Indicate which is true about enzymes.A)Enzymes are permanently changed during the conversion of substrateinto product.B)Enzymes interact irreversibly with their substrates.C)Enzymes change the energy difference between substrates andproducts.D)Enzymes reduce the energy of activation for the conversion of reactantinto product.E)Enzymes increase the energy content of the products.12.Consider a reaction as follows:A +B <==>C + D, AG'。

用第一原理计算软件开展的工作，分析结果主要是从以下三个方面进行定性/定量的讨论：1、电荷密度图（charge density）；2、能带结构（Energy Band Structure）；3、态密度（Density of States，简称DOS）。

电荷密度图是以图的形式出现在文章中，非常直观，因此对于一般的入门级研究人员来讲不会有任何的疑问。

唯一需要注意的就是这种分析的种种衍生形式，比如差分电荷密图（def-ormation charge density）和二次差分图difference charge density）等等，加自旋极化的工作还可能有自旋极化电荷密度图（spin-polarized charge density）。

所谓"差分"是指原子组成体系（团簇）之后电荷的重新分布，"二次"是指同一个体系化学成分或者几何构型改变之后电荷的重新分布，因此通过这种差分图可以很直观地看出体系中个原子的成键情况。

通过电荷聚集（accumulation）/损失（depletion）的具体空间分布，看成键的极性强弱；通过某格点附近的电荷分布形状判断成键的轨道（这个主要是对d轨道的分析，对于s或者p轨道的形状分析我还没有见过）。

分析总电荷密度图的方法类似，不过相对而言，这种图所携带的信息量较小。

能带结构分析现在在各个领域的第一原理计算工作中用得非常普遍了。

但是因为能带这个概念本身的抽象性，对于能带的分析是让初学者最感头痛的地方。

关于能带理论本身，我在这篇文章中不想涉及，这里只考虑已得到的能带，如何能从里面看出有用的信息。

首先当然可以看出这个体系是金属、半导体还是绝缘体。

判断的标准是看费米能级和导带（也即在高对称点附近近似成开口向上的抛物线形状的能带）是否相交，若相交，则为金属，否则为半导体或者绝缘体。

对于本征半导体，还可以看出是直接能隙还是间接能隙：如果导带的最低点和价带的最高点在同一个k点处，则为直接能隙，否则为间接能隙。

（完整版）量子力学英语词汇1、microscopic world 微观世界2、macroscopic world 宏观世界3、quantum theory 量子[理]论4、quantum mechanics 量子力学5、wave mechanics 波动力学6、matrix mechanics 矩阵力学7、Planck constant 普朗克常数8、wave-particle duality 波粒二象性9、state 态10、state function 态函数11、state vector 态矢量12、superposition principle of state 态叠加原理13、orthogonal states 正交态14、antisymmetrical state 正交定理15、stationary state 对称态16、antisymmetrical state 反对称态17、stationary state 定态18、ground state 基态19、excited state 受激态20、binding state 束缚态21、unbound state 非束缚态22、degenerate state 简并态23、degenerate system 简并系24、non-deenerate state 非简并态25、non-degenerate system 非简并系26、de Broglie wave 德布罗意波27、wave function 波函数28、time-dependent wave function 含时波函数29、wave packet 波包30、probability 几率31、probability amplitude 几率幅32、probability density 几率密度33、quantum ensemble 量子系综34、wave equation 波动方程35、Schrodinger equation 薛定谔方程36、Potential well 势阱37、Potential barrien 势垒38、potential barrier penetration 势垒贯穿39、tunnel effect 隧道效应40、linear harmonic oscillator 线性谐振子41、zero proint energy 零点能42、central field 辏力场43、Coulomb field 库仑场44、δ-function δ-函数45、operator 算符46、commuting operators 对易算符47、anticommuting operators 反对易算符48、complex conjugate operator 复共轭算符49、Hermitian conjugate operator 厄米共轭算符50、Hermitian operator 厄米算符51、momentum operator 动量算符52、energy operator 能量算符53、Hamiltonian operator 哈密顿算符54、angular momentum operator 角动量算符55、spin operator 自旋算符56、eigen value 本征值57、secular equation 久期方程58、observable 可观察量59、orthogonality 正交性60、completeness 完全性61、closure property 封闭性62、normalization 归一化63、orthonormalized functions 正交归一化函数64、quantum number 量子数65、principal quantum number 主量子数66、radial quantum number 径向量子数67、angular quantum number 角量子数68、magnetic quantum number 磁量子数69、uncertainty relation 测不准关系70、principle of complementarity 并协原理71、quantum Poisson bracket 量子泊松括号72、representation 表象73、coordinate representation 坐标表象74、momentum representation 动量表象75、energy representation 能量表象76、Schrodinger representation 薛定谔表象77、Heisenberg representation 海森伯表象78、interaction representation 相互作用表象79、occupation number representation 粒子数表象80、Dirac symbol 狄拉克符号81、ket vector 右矢量82、bra vector 左矢量83、basis vector 基矢量84、basis ket 基右矢85、basis bra 基左矢86、orthogonal kets 正交右矢87、orthogonal bras 正交左矢88、symmetrical kets 对称右矢89、antisymmetrical kets 反对称右矢90、Hilbert space 希耳伯空间91、perturbation theory 微扰理论92、stationary perturbation theory 定态微扰论93、time-dependent perturbation theory 含时微扰论94、Wentzel-Kramers-Brillouin method W. K. B.近似法95、elastic scattering 弹性散射96、inelastic scattering 非弹性散射97、scattering cross-section 散射截面98、partial wave method 分波法99、Born approximation 玻恩近似法100、centre-of-mass coordinates 质心坐标系101、laboratory coordinates 实验室坐标系102、transition 跃迁103、dipole transition 偶极子跃迁104、selection rule 选择定则105、spin 自旋106、electron spin 电子自旋107、spin quantum number 自旋量子数108、spin wave function 自旋波函数109、coupling 耦合110、vector-coupling coefficient 矢量耦合系数111、many-particle system 多子体系112、exchange forece 交换力113、exchange energy 交换能114、Heitler-London approximation 海特勒-伦敦近似法115、Hartree-Fock equation 哈特里-福克方程116、self-consistent field 自洽场117、Thomas-Fermi equation 托马斯-费米方程118、second quantization 二次量子化119、identical particles 全同粒子120、Pauli matrices 泡利矩阵121、Pauli equation 泡利方程122、Pauli’s exclusion principle泡利不相容原理123、Relativistic wave equation 相对论性波动方程124、Klein-Gordon equation 克莱因-戈登方程125、Dirac equation 狄拉克方程126、Dirac hole theory 狄拉克空穴理论127、negative energy state 负能态128、negative probability 负几率129、microscopic causality 微观因果性本征矢量eigenvector本征态eigenstate本征值eigenvalue本征值方程eigenvalue equation本征子空间eigensubspace (可以理解为本征矢空间)变分法variatinial method标量scalar算符operator表象representation表象变换transformation of representation表象理论theory of representation波函数wave function波恩近似Born approximation玻色子boson费米子fermion不确定关系uncertainty relation狄拉克方程Dirac equation狄拉克记号Dirac symbol定态stationary state定态微扰法time-independent perturbation定态薛定谔方程time-independent Schro(此处上面有两点)dinger equation 动量表象momentum representation 角动量表象angular mommentum representation占有数表象occupation number representation坐标（位置）表象position representation角动量算符angular mommentum operator角动量耦合coupling of angular mommentum对称性symmetry对易关系commutator厄米算符hermitian operator厄米多项式Hermite polynomial分量component光的发射emission of light光的吸收absorption of light受激发射excited emission自发发射spontaneous emission轨道角动量orbital angular momentum自旋角动量spin angular momentum轨道磁矩orbital magnetic moment归一化normalization哈密顿hamiltonion黑体辐射black body radiation康普顿散射Compton scattering基矢basis vector基态ground state基右矢basis ket ‘右矢’ket基左矢basis bra简并度degenerancy精细结构fine structure径向方程radial equation久期方程secular equation量子化quantization矩阵matrix模module模方square of module内积inner product逆算符inverse operator欧拉角Eular angles泡利矩阵Pauli matrix平均值expectation value （期望值）泡利不相容原理Pauli exclusion principle氢原子hydrogen atom球鞋函数spherical harmonics全同粒子identical particles塞曼效应Zeeman effect上升下降算符raising and lowering operator 消灭算符destruction operator产生算符creation operator矢量空间vector space守恒定律conservation law守恒量conservation quantity投影projection投影算符projection operator微扰法pertubation method希尔伯特空间Hilbert space线性算符linear operator线性无关linear independence谐振子harmonic oscillator选择定则selection rule幺正变换unitary transformation幺正算符unitary operator宇称parity跃迁transition运动方程equation of motion正交归一性orthonormalization正交性orthogonality转动rotation自旋磁矩spin magnetic monent(以上是量子力学中的主要英语词汇，有些未涉及到的可以自由组合。

S TATE OF THE A RT:C ONCISE R EVIEWInternational Association for the Study of LungCancer/American Thoracic Society/European Respiratory Society International Multidisciplinary Classification of Lung AdenocarcinomaWilliam D.Travis,MD,Elisabeth Brambilla,MD,Masayuki Noguchi,MD,Andrew G.Nicholson,MD, Kim R.Geisinger,MD,Yasushi Yatabe,MD,David G.Beer,PhD,Charles A.Powell,MD,Gregory J.Riely,MD,Paul E.Van Schil,MD,Kavita Garg,MD,John H.M.Austin,MD,Hisao Asamura,MD,Valerie W.Rusch,MD,Fred R.Hirsch,MD,Giorgio Scagliotti,MD,Tetsuya Mitsudomi,MD,Rudolf M.Huber,MD,Yuichi Ishikawa,MD,James Jett,MD,Montserrat Sanchez-Cespedes,PhD,Jean-Paul Sculier,MD,Takashi Takahashi,MD, Masahiro Tsuboi,MD,Johan Vansteenkiste,MD,Ignacio Wistuba,MD,Pan-Chyr Yang,MD, Denise Aberle,MD,Christian Brambilla,MD,Douglas Flieder,MD,Wilbur Franklin,MD,Adi Gazdar,MD,Michael Gould,MD,MS,Philip Hasleton,MD,Douglas Henderson,MD, Bruce Johnson,MD,David Johnson,MD,Keith Kerr,MD,Keiko Kuriyama,MD,Jin Soo Lee,MD, Vincent ler,MD,Iver Petersen,MD,PhD,Victor Roggli,MD,Rafael Rosell,MD,Nagahiro Saijo,MD,Erik Thunnissen,MD,Ming Tsao,MD,and David Yankelewitz,MDIntroduction:Adenocarcinoma is the most common histologic type of lung cancer.To address advances in oncology,molecular biology, pathology,radiology,and surgery of lung adenocarcinoma,an in-ternational multidisciplinary classification was sponsored by the International Association for the Study of Lung Cancer,American Thoracic Society,and European Respiratory Society.This new adenocarcinoma classification is needed to provide uniform termi-nology and diagnostic criteria,especially for bronchioloalveolar carcinoma(BAC),the overall approach to small nonresection cancer specimens,and for multidisciplinary strategic management of tissue for molecular and immunohistochemical studies.Methods:An international core panel of experts representing all three societies was formed with oncologists/pulmonologists,pathol-ogists,radiologists,molecular biologists,and thoracic surgeons.A systematic review was performed under the guidance of the American Thoracic Society Documents Development and Implementation Commit-tee.The search strategy identified11,368citations of which312articles met specified eligibility criteria and were retrieved for full text review.A series of meetings were held to discuss the development of the new classification, to develop the recommendations,and to write the current document. Recommendations for key questions were graded by strength and quality of the evidence according to the Grades of Recommendation,Assessment, Development,and Evaluation approach.Results:The classification addresses both resection specimens,and small biopsies and cytology.The terms BAC and mixed subtype adenocarcinoma are no longer used.For resection specimens,new concepts are introduced such as adenocarcinoma in situ(AIS)and minimally invasive adenocarcinoma(MIA)for small solitary adenocar-cinomas with either pure lepidic growth(AIS)or predominant lepidic growth withՅ5mm invasion(MIA)to define patients who,if they undergo complete resection,will have100%or near100%disease-specific survival,respectively.AIS and MIA are usually nonmucinous but rarely may be mucinous.Invasive adenocarcinomas are classified by predominant pattern after using comprehensive histologic subtyping with lepidic(formerly most mixed subtype tumors with nonmucinous BAC),acinar,papillary,and solid patterns;micropapillary is added as a new histologic subtype.Variants include invasive mucinous adeno-carcinoma(formerly mucinous BAC),colloid,fetal,and enteric adeno-carcinoma.This classification provides guidance for small biopsies and cytology specimens,as approximately70%of lung cancers are diag-nosed in such samples.Non-small cell lung carcinomas(NSCLCs),in patients with advanced-stage disease,are to be classified into more specific types such as adenocarcinoma or squamous cell carcinoma,Affiliations are listed in the appendix.Disclosure:Valerie W.Rusch,MD,is an active member of the IASLCStaging Committee.Georgio Scagliotti,MD,has received honoraria fromSanofiAventis,Roche,Eli Lilly,and Astrozeneca.David Yankelevitz,MD,is a named inventor on a number of patents and patent applicationsrelating to the evaluation of diseases of the chest,including measurementof nodules.Some of these,which are owned by Cornell ResearchFoundation(CRF)are non-exclusively licensed to General Electric.Asan inventor of these patents,Dr.Yankelevitz is entitled to a share of anycompensation which CRF may receive from its commercialization ofthese patents.The other authors declare no conflicts of interest.Address for correspondence:William Travis,MD,Department of Pathology,Memorial Sloan Kettering Cancer Center,1275York Avenue,NewYork,NY10065.E-mail:travisw@Copyright©2011by the International Association for the Study of LungCancerISSN:1556-0864/11/0602-0244Journal of Thoracic Oncology•Volume6,Number2,February2011 244whenever possible for several reasons:(1)adenocarcinoma or NSCLC not otherwise specified should be tested for epidermal growth factor receptor(EGFR)mutations as the presence of these mutations is predictive of responsiveness to EGFR tyrosine kinase inhibitors,(2) adenocarcinoma histology is a strong predictor for improved outcome with pemetrexed therapy compared with squamous cell carcinoma,and (3)potential life-threatening hemorrhage may occur in patients with squamous cell carcinoma who receive bevacizumab.If the tumor cannot be classified based on light microscopy alone,special studies such as immunohistochemistry and/or mucin stains should be applied to classify the tumor e of the term NSCLC not otherwise specified should be minimized.Conclusions:This new classification strategy is based on a multidis-ciplinary approach to diagnosis of lung adenocarcinoma that incorpo-rates clinical,molecular,radiologic,and surgical issues,but it is pri-marily based on histology.This classification is intended to support clinical practice,and research investigation and clinical trials.As EGFR mutation is a validated predictive marker for response and progression-free survival with EGFR tyrosine kinase inhibitors in advanced lung adenocarcinoma,we recommend that patients with advanced adenocar-cinomas be tested for EGFR mutation.This has implications for strategic management of tissue,particularly for small biopsies and cytology samples,to maximize high-quality tissue available for molecular studies. Potential impact for tumor,node,and metastasis staging include adjustment of the size T factor according to only the invasive component(1)patho-logically in invasive tumors with lepidic areas or(2)radiologically by measuring the solid component of part-solid nodules.Key Words:Lung,Adenocarcinoma,Classification,Histologic, Pathology,Oncology,Pulmonary,Radiology,Computed tomogra-phy,Molecular,EGFR,KRAS,EML4-ALK,Gene profiling,Gene amplification,Surgery,Limited resection,Bronchioloalveolar carci-noma,Lepidic,Acinar,Papillary,Micropapillary,Solid,Adenocar-cinoma in situ,Minimally invasive adenocarcinoma,Colloid,Mu-cinous cystadenocarcinoma,Enteric,Fetal,Signet ring,Clear cell, Frozen section,TTF-1,p63.(J Thorac Oncol.2011;6:244–285)RATIONALE FOR A CHANGE IN THE APPROACH TO CLASSIFICATION OF LUNGADENOCARCINOMALung cancer is the most frequent cause of major cancer incidence and mortality worldwide.1,2Adenocarcinoma is the most common histologic subtype of lung cancer in most coun-tries,accounting for almost half of all lung cancers.3A widely divergent clinical,radiologic,molecular,and pathologic spec-trum exists within lung adenocarcinoma.As a result,confusion exists,and studies are difficult to compare.Despite remarkable advances in understanding of this tumor in the past decade,there remains a need for universally accepted criteria for adenocarci-noma subtypes,in particular tumors formerly classified as bron-chioloalveolar carcinoma(BAC).4,5As enormous resources are being spent on trials involving molecular and therapeutic aspects of adenocarcinoma of the lung,the development of standardized criteria is of great importance and should help advance thefield, increasing the impact of research,and improving patient care. This classification is needed to assist in determining patient therapy and predicting outcome.NEED FOR A MULTIDISCIPLINARY APPROACH TO DIAGNOSIS OF LUNG ADENOCARCINOMA One of the major outcomes of this project is the recognition that the diagnosis of lung adenocarcinoma re-quires a multidisciplinary approach.The classifications of lung cancer published by the World Health Organization (WHO)in1967,1981,and1999were written primarily by pathologists for pathologists.5–7Only in the2004revision, relevant genetics and clinical information were introduced.4 Nevertheless,because of remarkable advances over the last6 years in our understanding of lung adenocarcinoma,particu-larly in area of medical oncology,molecular biology,and radiology,there is a pressing need for a revised classification, based not on pathology alone,but rather on an integrated multidisciplinary platform.In particular,there are two major areas of interaction between specialties that are driving the need for our multidisciplinary approach to classification of lung adenocarcinoma:(1)in patients with advanced non-small cell lung cancer,recent progress in molecular biology and oncology has led to(a)discovery of epidermal growth factor receptor(EGFR)mutation and its prediction of re-sponse to EGFR tyrosine kinase inhibitors(TKIs)in adeno-carcinoma patients8–11and(b)the requirement to exclude a diagnosis of squamous cell carcinoma to determine eligibility patients for treatment with pemetrexed,(because of improved efficacy)12–15or bevacizumab(because of toxicity)16,17and (2)the emergence of radiologic-pathologic correlations be-tween ground-glass versus solid or mixed opacities seen by computed tomography(CT)and BAC versus invasive growth by pathology have opened new opportunities for imaging studies to be used by radiologists,pulmonologists,and sur-geons for predicting the histologic subtype of adenocarcino-mas,18–21patient prognosis,18–23and improve preoperative assessment for choice of timing and type of surgical inter-vention.18–26Although histologic criteria remain the foundation of this new classification,this document has been developed by pathologists in collaboration with clinical,radiology,molec-ular,and surgical colleagues.This effort has led to the development of terminology and criteria that not only define pathologic entities but also communicate critical information that is relevant to patient management(Tables1and2).The classification also provides recommendations on strategic handling of specimens to optimize the amount of information to be gleaned.The goal is not only longer to solely provide the most accurate diagnosis but also to manage the tissue in a way that immunohistochemical and/or molecular studies can be performed to obtain predictive and prognostic data that will lead to improvement in patient outcomes.For thefirst time,this classification addresses an ap-proach to small biopsies and cytology in lung cancer diag-nosis(Table2).Recent data regarding EGFR mutation pre-dicting responsiveness to EGFR-TKIs,8–11toxicities,16and therapeutic efficacy12–15have established the importance of distinguishing squamous cell carcinoma from adenocarci-noma and non-small cell lung carcinoma(NSCLC)not oth-erwise specified(NOS)in patients with advanced lung can-cer.Approximately70%of lung cancers are diagnosed andJournal of Thoracic Oncology•Volume6,Number2,February2011Lung Adenocarcinoma Classificationstaged by small biopsies or cytology rather than surgical resection specimens,with increasing use of transbronchial needle aspiration(TBNA),endobronchial ultrasound-guided TBNA and esophageal ultrasound-guided needle aspiration.27 Within the NSCLC group,most pathologists can identify well-or moderately differentiated squamous cell carcinomas or adenocarcinomas,but specific diagnoses are more difficult with poorly differentiated tumors.Nevertheless,in small biopsies and/or cytology specimens,10to30%of specimens continue to be diagnosed as NSCLC-NOS.13,28,29Proposed terminology to be used in small biopsies is summarized in Table2.Pathologists need to minimize the use of the term NSCLC or NSCLC-NOS on small samples and aspiration and exfoliative cytology,providing as specific a histologic classification as possible to facilitate the treatment approach of medical oncologists.30Unlike previous WHO classifications where the pri-mary diagnostic criteria for as many tumor types as possible were based on hematoxylin and eosin(H&E)examination, this classification emphasizes the use and integration of immunohistochemical(i.e.,thyroid transcription factor[TTF-1]/p63staining),histochemical(i.e.,mucin staining),and molecular studies,as specific therapies are driven histologic subtyping.Although these techniques should be used when-ever possible,it is recognized that this may not always be possible,and thus,a simpler approach is also provided when only H&E-stained slides are available,so this classification may be applicable even in a low resource setting.METHODOLOGYObjectivesThis international multidisciplinary classification has been produced as a collaborative effort by the International Associa-tion for the Study of Lung Cancer(IASLC),the American Thoracic Society(ATS),and the European Respiratory Society. The purpose is to provide an integrated clinical,radiologic, molecular,and pathologic approach to classification of the var-ious types of lung adenocarcinoma that will help to define categories that have distinct clinical,radiologic,molecular,and pathologic characteristics.The goal is to identify prognostic and predictive factors and therapeutic targets.ParticipantsPanel members included thoracic medical oncologists, pulmonologists,radiologists,molecular biologists,thoracic surgeons,and pathologists.The supporting associations nom-inated panel members.The cochairs were selected by the IASLC.Panel members were selected because of special interest and expertise in lung adenocarcinoma and to provide an international and multidisciplinary representation.The panel consisted of a core group(author list)and a reviewer group(Appendix1,see Supplemental Digital Content1 available at /JTO/A59,affiliations for coauthors are listed in appendix).EvidenceThe panel performed a systematic review with guidance by members of the ATS Documents Development and Im-plementation Committee.Key questions for this project were generated by each specialty group,and a search strategy was developed(Appendix2,see Supplemental Digital Content 2available at /JTO/A60).Searches were performed in June2008with an update in June2009resulting in11,368citations.These were reviewed to exclude articles that did not have any relevance to the topic of lung adeno-carcinoma classification.The remaining articles were evalu-ated by two observers who rated them by a predetermined set of eligibility criteria using an electronic web-based survey program()to collect responses.31This process narrowed the total number of articles to312that were reviewed in detail for a total of141specific features,including 17study characteristics,35clinical,48pathologic,16radio-logic,16molecular,and nine surgical(Appendix2).These141 features were summarized in an electronic database that was distributed to members of the core panel,including the writing committee.Articles chosen for specific data summaries were reviewed,and based on analysis of tables from this systematic review,recommendations were made according to the Grades of Recommendation,Assessment,Development,and Evaluation (GRADE).32–37Throughout the rest of the document,the term GRADE(spelled in capital letters)must be distinguished from histologic grade,which is a measure of pathologic tumor differ-entiation.The GRADE system has two major components:(1) grading the strength of the recommendation and(2)evaluating the quality of the evidence.32The strength of recommendations is based on weighing estimates of benefits versus downsides. Evidence was rated as high,moderate,or low or very low.32TheTABLE1.IASLC/ATS/ERS Classification of LungAdenocarcinoma in Resection SpecimensPreinvasive lesionsAtypical adenomatous hyperplasiaAdenocarcinoma in situ(Յ3cm formerly BAC)NonmucinousMucinousMixed mucinous/nonmucinousMinimally invasive adenocarcinoma(Յ3cm lepidic predominant tumorwithՅ5mm invasion)NonmucinousMucinousMixed mucinous/nonmucinousInvasive adenocarcinomaLepidic predominant(formerly nonmucinous BAC pattern,withϾ5mminvasion)Acinar predominantPapillary predominantMicropapillary predominantSolid predominant with mucin productionVariants of invasive adenocarcinomaInvasive mucinous adenocarcinoma(formerly mucinous BAC)ColloidFetal(low and high grade)EntericBAC,bronchioloalveolar carcinoma;IASLC,International Association for theStudy of Lung Cancer;ATS,American Thoracic Society;ERS,European RespiratorySociety.Travis et al.Journal of Thoracic Oncology•Volume6,Number2,February2011quality of the evidence expresses the confidence in an estimate of effect or an association and whether it is adequate to support a recommendation.After review of all articles,a writing com-mittee met to develop the recommendations with each specialty group proposing the recommendations,votes for or against the recommendation,and modifications were conducted after mul-tidisciplinary discussion.If randomized trials were available,we started by assuming high quality but down-graded the quality when there were serious methodological limitations,indirectness in population,inconsistency in results,imprecision in estimates,or a strong suspicion of publication bias.If well-done observa-tional studies were available,low-quality evidence was as-sumed,but the quality was upgraded when there was a large treatment effect or a large association,all plausibleresidual confounders would diminish the effects,or if there was a dose-response gradient.36We developed considerations for good practice related to interventions that usually represent necessary and standard procedures of health care system—such as history taking and physical examination helping patients to make informed decisions,obtaining written consent,or the importance of good communication—when we considered them helpful.In that case,we did not perform a grading of the quality of evidence or strength of the recommendations.38MeetingsBetween March 2008and December 2009,a series of meetings were held,mostly at Memorial Sloan Kettering Cancer Center,in New York,NY,to discuss issues related toTABLE 2.Proposed IASLC/ATS/ERS Classification for SmallBiopsies/CytologyIASLC,International Association for the Study of Lung Cancer;ATS,American Thoracic Society;ERS,European Respiratory Society;WHO,World Health Organization;NSCLC,non-small cell lung cancer;IHC,immunohistochemistry;TTF,thyroid transcription factor.Journal of Thoracic Oncology •Volume 6,Number 2,February 2011Lung Adenocarcinoma Classificationlung adenocarcinoma classification and to formulate this document.The core group established a uniform and consis-tent approach to the proposed types of lung adenocarcinoma. ValidationSeparate projects were initiated by individuals involved with this classification effort in an attempt to develop data to test the proposed system.These included projects on small biopsies,39,40histologic grading,41–43stage I adenocarcino-mas,44small adenocarcinomas from Japan,international mul-tiple pathologist project on reproducibility of recognizing major histologic patterns of lung adenocarcinoma,45molecu-lar-histologic correlations,and radiologic-pathologic correla-tion focused on adenocarcinoma in situ(AIS),and minimally invasive adenocarcinoma(MIA).The new proposals in this classification are based on the best available evidence at the time of writing this document. Nevertheless,because of the lack of universal diagnostic criteria in the literature,there is a need for future validation studies based on these standardized pathologic criteria with clinical,molecular,radiologic,and surgical correlations.PATHOLOGIC CLASSIFICATIONHistopathology is the backbone of this classification,but lung cancer diagnosis is a multidisciplinary process requiring correlation with clinical,radiologic,molecular,and surgical information.Because of the multidisciplinary approach in de-veloping this classification,we are recommending significant changes that should improve the diagnosis and classification of lung adenocarcinoma,resulting in therapeutic benefits.Even after publication of the1999and2004WHO clas-sifications,4,5the former term BAC continues to be used for a broad spectrum of tumors including(1)solitary small noninva-sive peripheral lung tumors with a100%5-year survival,46(2) invasive adenocarcinomas with minimal invasion that have ap-proximately100%5-year survival,47,48(3)mixed subtype in-vasive adenocarcinomas,49–53(4)mucinous and nonmuci-nous subtypes of tumors formerly known as BAC,50–52,54,55 and(5)widespread advanced disease with a very low survival rate.4,5The consequences of confusion from the multiple uses of the former BAC term in the clinical and research arenas have been the subject of many reviews and editorials and are addressed throughout this document.55–61 Pathology Recommendation1We recommend discontinuing the use of the term “BAC.”Strong recommendation,low-quality evidence.Throughout this article,the term BAC(applicable to multiple places in the new classification,Table3),will be referred to as“former BAC.”We understand this will be a major adjustment and suggest initially that when the new proposed terms are used,it will be accompanied in parenthe-ses by“(formerly BAC).”This transition will impact not only clinical practice and research but also cancer registries future analyses of registry data.CLASSIFICATION FOR RESECTION SPECIMENS Multiple studies have shown that patients with small solitary peripheral adenocarcinomas with pure lepidic growth may have100%5-year disease-free survival.46,62–68In addi-tion,a growing number of articles suggest that patients with lepidic predominant adenocarcinomas(LPAs)with minimal invasion may also have excellent survival.47,48Recent work has demonstrated that more than90%of lung adenocarcino-mas fall into the mixed subtype according to the2004WHO classification,so it has been proposed to use comprehensive histologic subtyping to make a semiquantitative assessment of the percentages of the various histologic components: acinar,papillary,micropapillary,lepidic,and solid and to classify tumors according to the predominant histologic sub-type.69This has demonstrated an improved ability to address the complex histologic heterogeneity of lung adenocarcino-mas and to improve molecular and prognostic correlations.69 The new proposed lung adenocarcinoma classification for resected tumors is summarized in Table1. Preinvasive LesionsIn the1999and2004WHO classifications,atypical adenomatous hyperplasia(AAH)was recognized as a prein-vasive lesion for lung adenocarcinoma.This is based on multiple studies documenting these lesions as incidentalfind-ings in the adjacent lung parenchyma in5to23%of resected lung adenocarcinomas70–74and a variety of molecularfind-ings that demonstrate a relationship to lung adenocarcinoma including clonality,75,76KRAS mutation,77,78KRAS polymor-phism,79EGFR mutation,80p53expression,81loss of het-erozygosity,82methylation,83telomerase overexpression,84 eukaryotic initiation factor4E expression,85epigenetic alter-ations in the Wnt pathway,86and FHIT expression.87Depend-ing on the extensiveness of the search,AAH may be multiple in up to7%of resected lung adenocarcinomas.71,88A major change in this classification is the official recognition of AIS,as a second preinvasive lesion for lung adenocarcinoma in addition to AAH.In the category of preinvasive lesions,AAH is the counterpart to squamous dysplasia and AIS the counterpart to squamous cell carci-noma in situ.Atypical Adenomatous HyperplasiaAAH is a localized,small(usually0.5cm or less) proliferation of mildly to moderately atypical type II pneu-mocytes and/or Clara cells lining alveolar walls and some-times,respiratory bronchioles(Figures1A,B).4,89,90Gaps are TABLE3.Categories of New Adenocarcinoma Classification Where Former BAC Concept was Used1.Adenocarcinoma in situ(AIS),which can be nonmucinous and rarelymucinous2.Minimally invasive adenocarcinoma(MIA),which can be nonmucinousand rarely mucinous3.Lepidic predominant adenocarcinoma(nonmucinous)4.Adenocarcinoma,predominantly invasive with some nonmucinouslepidic component(includes some resected tumors,formerly classified as mixed subtype,and some clinically advanced adenocarcinomasformerly classified as nonmucinous BAC)5.Invasive mucinous adenocarcinoma(formerly mucinous BAC)BAC,bronchioloalveolar carcinoma.Travis et al.Journal of Thoracic Oncology•Volume6,Number2,February2011usually seen between the cells,which consist of rounded,cuboidal,low columnar,or “peg”cells with round to oval nuclei (Figure 1B ).Intranuclear inclusions are frequent.There is a continuum of morphologic changes between AAH and AIS.4,89,90A spectrum of cellularity and atypia occurs in AAH.Although some have classified AAH into low-and high-grade types,84,91grading is not recommended.4Distinc-tion between more cellular and atypical AAH and AIS can be difficult histologically and impossible cytologically.AIS,Nonmucinous,and/or MucinousAIS (one of the lesions formerly known as BAC)is a localized small (Յ3cm)adenocarcinoma with growth re-stricted to neoplastic cells along preexisting alveolar struc-tures (lepidic growth),lacking stromal,vascular,or pleural invasion.Papillary or micropapillary patterns and intraalveo-lar tumor cells are absent.AIS is subdivided into nonmuci-nous and mucinous variants.Virtually,all cases of AIS are nonmucinous,consisting of type II pneumocytes and/or Clara cells (Figures 2A,B ).There is no recognized clinical signif-icance to the distinction between type II or Clara cells,so this morphologic separation is not recommended.The rare cases of mucinous AIS consist of tall columnar cells with basal nuclei and abundant cytoplasmic mucin;sometimes they resemble goblet cells (Figures 3A ,B ).Nuclear atypia is absent or inconspicuous in both nonmucinous and mucinousAIS (Figures 2B and 3B ).Septal widening with sclerosis is common in AIS,particularly the nonmucinous variant.Tumors that meet criteria for AIS have formerly been classified as BAC according to the strict definition of the 1999and 2004WHO classifications and type A and type B adenocarcinoma according to the 1995Noguchi classifica-tion.4,46Multiple observational studies on solitary lung ade-nocarcinomas with pure lepidic growth,smaller than either 2or 3cm have documented 100%disease-free survival.46,62–68Although most of these tumors are nonmucinous,2of the 28tumors reported by Noguchi as types A and B in the 1995study were mucinous.46Small size (Յ3cm)and a discrete circumscribed border are important to exclude cases with miliary spread into adjacent lung parenchyma and/or lobar consolidation,particularly for mucinous AIS.Pathology Recommendation 2For small (Յ3cm),solitary adenocarcinomas with pure lepidic growth,we recommend the term “Adenocarcinoma in situ”that defines patients who should have 100%disease-specific survival,if the lesion is completely resected (strong recommendation,moderate quality evidence).Remark:Most AIS are nonmucinous,rarely are they mucinous.MIA,Nonmucinous,and/or MucinousMIA is a small,solitary adenocarcinoma (Յ3cm),with a predominantly lepidic pattern and Յ5mm invasion in greatest dimension in any one focus.47,48,92MIA is usually nonmucinous (Figures 4A –C )but rarely may be mucinous (Figures 5A,B ).44MIA is,by definition,solitary and discrete.The criteria for MIA can be applied in the setting of multiple tumors only if the other tumors are regarded as synchronous primaries rather than intrapulmonary metastases.The invasive component to be measured in MIA is de-fined as follows:(1)histological subtypes other than a lepidic pattern (i.e.,acinar,papillary,micropapillary,and/or solid)or (2)tumor cells infiltrating myofibroblastic stroma.MIA is excluded if the tumor (1)invades lymphatics,blood vessels,or pleura or (2)contains tumor necrosis.If multiple microinvasive areas are found in one tumor,the size of the largest invasive area should be measured in the largest dimension,and it should be Յ5mmFIGURE 1.Atypical adenomatous hyperplasia.A ,This3-mm nodular lesion consists of atypical pneumocytes prolif-erating along preexisting alveolar walls.There is no invasive component.B ,The slightly atypical pneumocytes are cuboi-dal and show gaps between the cells.Nuclei are hyperchro-matic,and a few show nuclear enlargement and multinucle-ation.FIGURE 2.Nonmucinous adenocarcinoma in situ.A ,This circumscribed nonmucinous tumor grows purely with a lepi-dic pattern.No foci of invasion or scarring are seen.B ,The tumor shows atypical pneumocytes proliferating along the slightly thickened,but preserved,alveolarwalls.FIGURE 3.Mucinous adenocarcinoma in situ.A ,This muci-nous AIS consists of a nodular proliferation of mucinous co-lumnar cells growing in a purely lepidic pattern.Although there is a small central scar,no stromal or vascular invasion is seen.B,The tumor cells consist of cuboidal to columnar cells with abundant apical mucin and small basally oriented nuclei.AIS,adenocarcinoma in situ.Journal of Thoracic Oncology •Volume 6,Number 2,February 2011Lung Adenocarcinoma Classification。