Introduction to magnetoelectric coupling and multiferroic films

Home Search Collections Journals About Contact us My IOPscienceIntroduction to magnetoelectric coupling and multiferroic filmsThis article has been downloaded from IOPscience. Please scroll down to see the full text article.2011 J. Phys. D: Appl. Phys. 44 243001(/0022-3727/44/24/243001)View the table of contents for this issue, or go to the journal homepage for moreDownload details:IP Address: 202.38.78.154The article was downloaded on 13/08/2011 at 12:05Please note that terms and conditions apply.IOP P UBLISHING J OURNAL OF P HYSICS D:A PPLIED P HYSICS J.Phys.D:Appl.Phys.44(2011)243001(22pp)doi:10.1088/0022-3727/44/24/243001TOPICAL REVIEWIntroduction to magnetoelectric coupling and multiferroicfilmsG Lawes1and G Srinivasan21Department of Physics and Astronomy,Wayne State University,Detroit MI,USA2Department of Physics,Oakland University,Rochester MI,USAReceived10January2011,infinal form1April2011Published31May2011Online at /JPhysD/44/243001AbstractThere is an increasing understanding of the mechanisms underlying the development ofmagnetoelectric coupling and multiferroic order in both single-phase and composite materials.The investigations underlying this advance include a range of studies on thinfilms,which areexpected to play an important role in the development of novel magnetoelectric devices.Theproperties of both single-phase and composite systems are widely studied.While single-phasematerials can exhibit rich spin-charge coupling physics,the magnetizations,polarizations,andtransition temperatures are often too small to be innately useful for device design.Conversely,a number of ferromagnetic–piezoelectric composites can show strong magnetoelectriccoupling at ambient temperatures,which develops as a product-property mediated by elasticdeformation,making these systems more directly amenable to fabricating devices.In thisreview,we provide a short overview of the mechanisms for magnetoelectric coupling inmultiferroics,together with a discussion of how this magnetoelectric coupling is relevant fordesigning new multiferroic devices,including magneticfield sensors,dual electric andmagneticfield tunable microwave and millimetre wave devices and miniature antennas.Wepresent a brief summary of some of the significant results in studies on thin-film multiferroics,with an emphasis on single-phase materials,and covering systems where the magnetic andferroelectric transitions fall at the same temperature as well as systems where they fall atdifferent temperatures.(Somefigures in this article are in colour only in the electronic version)1.IntroductionThe broad and enthusiastic study of magnetoelectric multiferroics,materials developing simultaneous magnetic and ferroelectric structures,is motivated evenly by the rich physics underlying the spin-charge ordering in these materials and their potential application for pioneering new devices.Although a broad class of closely related materials has been studied theoretically since remarkably prescient work by Pierre Curie [1],receiving renewed theoretical and experimental interest in the1960s[2–6],and has been the subject of on-going investigations since throughout this period[7–9]there has been a strong resurgence of interest in magnetoelectrics,and particularly multiferroics,over the past decade[10–26].This current burst of activity was prompted by experimental studies highlighting the remarkably strong magnetoelectric coupling in certain multiferroics and potential for producing large magnetizations and polarizations simultaneously together with theoretical results concerning the development of co-existing magnetic and ferroelectric order.The contemporary sustained, world-wide research effort focusing on multiferroics has produced an explosion in the number of multiferroic materials identified with a similar increase in the number of open questions surrounding this class of systems.This review paper is intended to provide a pr´e cis of recent results,mainly experimental,on magnetoelectric multiferroic films.As such,this work complements the large number of excellent review papers written on magnetoelectrics,bulk multiferroics,composite multiferroics,and other reports on multiferroicfilms.There are a number of compelling reasons to explore thinfilm multiferroics in depth.As mentioned above,there is strong interest in exploiting multiferroic materials in developing new types of devices.The presence of coupled magnetic and electric moments offers the potentialfor designing new magnetoelectric elements.As the trend in device design moves towards building on thinfilms,it is crucial to develop an understanding of the properties of multiferroics in this specific geometry.The underlying magnetic and electrical properties of a bulk system can change significantly when confined to a thinfilm.One particularly striking example of this effect is the suppression of the spin cycloid in epitaxially strained BiFeO3thinfilms[27],which has profound consequences on the magnetoelectric coupling in this system.From a practical experimental standpoint,it is generally easier to apply large electricfields to thinfilm samples rather than bulk crystal or ceramic samples,because these require relatively smaller bias voltages.This is relevant for fabricating devices,where the operating voltage is likely to be strictly limited,but also allows researchers to explore larger regions of phase space along the electricfield axis.A last justification for focusing on thinfilm materials is that this geometry can stabilize structures difficult to obtain in bulk samples,such as the hexagonal forms of some rare earth manganites,or,through judicious selection of the substrate,can produce uniaxial strain or stress.This review will not specifically touch on the important problem of preparing multiferroic thinfilms.A recent review paper by Martin et al[28]and references therein provide an appropriate overview of this topic.Briefly,the review is structured as follows.Section2 consists of a concise review of the most salient details of bulk magnetoelectric multiferroics,with an emphasis on experimental results.This background will serve to provide a more complete context for our discussion on multiferroic thin films.A great deal of the interest in multiferroic materials stems from possible device applications.Section3discusses some of the considerations for developing magnetoelectric multiferroics.Since the vast majority of room temperature multiferroics consists of composite materials,this discussion will focus on these systems.Section4surveys recent results on thinfilm multiferroics with separate magnetic and ferroelectric ordering temperatures,including a substantial discussion on BiFeO3but also covering a number of other systems.Section5will cover thinfilm multiferroics exhibiting coincident magnetic and ferroelectric ordering,while section6 will serve as a summary and conclusion.By providing a relatively broad but succinct overview of recent results concerning multiferroic thinfilms,we have attempted to make this review accessible to beginners in thefield,although the inclusion of some very recent results may also prove relevant to more established researchers.In discussing single-phase multiferroic systems,we have focused exclusively on oxide materials.This reflects that the preponderance of the literature on multiferroics is concerned with oxides,but it should be recognized that multiferroics can be found in other classes of compounds[29,30].2.BackgroundThe intimate connection between magnetism and electricity is elegantly expressed in the differential form of Maxwell’s equations.These coupled differential equations relate the time derivatives of electric and magneticfields to spatial gradients of magnetic and electricfields.Three decades after Maxwell’s equations werefirst published in their entirety,Pierre Curie proposed a linear coupling between electric and magnetic fields[1].This coupling presents an immediate challenge to respect the scalar transformation properties required of a free energy.While electricfields break spatial inversion symmetry and magneticfields break time reversal symmetry,they can be coupled tofirst order in Maxwell’s equations through the incorporation of time and spatial derivatives,which also have non-trivial transformation properties under time reversal and spatial inversion,respectively.The magnetoelectric effect is the induction of a magnetization with the application of an electricfield or the induction of a polarization with the application of a magneticfield.Some contemporary literature takes a more inclusive definition for magnetoelectric coupling and considers any coupling magnetic and electric order parameters to produce a effect,referring to the aforementioned coupling as a linear magnetoelectric effect. In many cases,it is convenient to express the magnetoelectric coupling,both linear and non-linear,as terms in the free energy expansion.Since the electricfield E and magneticfield H are vectors,the coupling parameters will,in the most general expression,be tensors.This leads to an expression for the magnetoelectric interaction energy[11],F ME,asF ME=αij E i H j+1/2b ijk E i H j H k+1/2γE i E j H k+1/6δijkl E i E j H k H l+ (1)When investigating the magnetoelectric coupling in multi-ferroics,equation(1)is often re-cast in terms of the electric polarization,P,and magnetization,M,or staggered magnetization,L.The fourth term in this expression,bilinear in both E and H,is a scalar,and can therefore appear in any free energy expansion.This term produces the magnetodielectric effect,a shift in the dielectric response in a system that varies quadratically with the appliedfield[31]. The other terms are not allowed in the most general case. Electricfields break spatial inversion symmetry and magnetic fields break time reversal symmetry,so terms including an odd number of magnetic or electricfield terms breaks at least one of these two symmetries.However,it was recognized that these other magnetoelectric coupling terms can be non-zero in crystals having certain transformation properties.Schmid discusses the close connection between magnetoelectric coupling and crystal symmetries in depth in several papers[15,32].The beginning of the experimental study of magneto-electrics was marked by the observation of both the induction of a magnetization by an electricfield,and the converse effect,the induction of a polarization by a magneticfield,in Cr2O3,which had been previously proposed as a candidate magnetoelectric[2–5,33].Following these studies on Cr2O3,there were a number of investigations on other magnetoelectric systems,including studies on BaMnF4and Co doped BaMnF4[29,30]that illustrated the important role played by the magnetic symmetry,LiCoPO4[34,35], Gd2CuO4[36,37],Gd2(MoO4)3[38],Cr2BeO4[39]andNi3B7O13I,which exhibits simultaneous weak ferromagnetism and ferroelectricity[40–42].There were also a number of important results helping to build the conceptual theoretical framework required to understand these materials,including studies on the connection between magnetic symmetry and magnetoelectric coupling and discussions on polarization effects arising from inhomogeneous magnetizations[43–45].It was also recognized that composite materials offered the potential for engineering new multiferroic materials with desirable properties or characteristics that are absent in single-phase materials[10,11,16,46–53].In a composite consisting of magnetostrictive and piezoelectric phases,the magnetoelectric(ME)effect is the result of a‘product-property’,that is,the mechanical deformation due to magnetostriction results in a dielectric polarization due to the piezoelectric effect[54].Most attempts in the early1970s focused on bulk composites of magnetostrictive ferrites and piezoelectric barium titanate[55].However,the ME coupling in bulk composites was typically weak due to the presence of microcracks,defects,impurities and leakage currents in the sintered composites,limiting their potential applications for developing new devices[55–58].Despite a number of promising theoretical and experi-mental results concerning magnetoelectric coupling and multi-ferroic materials[29,39,40,44,59,60],thefield languished for a number of years.The study of multiferroics was re-energized by a number of studies appearing shortly after the turn of the millennium.One of these catalysing results was the observation of magnetically controlled ferroelectric order in TbMnO3[61].In this report,Kimura and co-workers found that a ferroelectric polarization developed simultaneously with an incommensurate magnetic structure in TbMnO3,and that the magnitude and direction of this polarization could be controlled using an applied magneticfield.This strong connection between the spin and charge degrees of freedom pointed to a new direction for investigations on multiferroic materials.Contemporaneously,it was reported by Wang and collaborators that epitaxial BiFeO3films could show a large polarization together with a weak ferromagnetic moment[62]. Although BiFeO3had been widely studied previously,the polarization in the antiferromagnetic samples had been judged too small for practical applications.These two results built on a number of significant studies in the preceding years,including an inquiry into the relative paucity of multiferroic materials [63],optical studies on antiferromagnetic and ferroelectric domains in YMnO3[64],and HoMnO3[65,66].In addition to this increasing interest in single-phase multiferroics,the development of new fabrication and characterization techniques for layered and nanostructured materials also fostered important advances in composite multiferroic materials[10,11,46–53].Harshe,Dougherty and Newnham,in their pioneering work on magnetoelectric composites proposed a theoretical model for multilayer hetrostructures with alternating layers of magnetostrictive and piezoelectric phases and fabricated such structures [67].A multilayer(ML)structure is expected to be far superior to bulk composites for the following reasons:(i)in bulk composites the leakage currentsdue Figure1.Schematic representation of the approximate magnitudes of the magnetization and polarization in composite multiferroics and type1and type2single phase multiferroics.While the properties of some materials fall outside these boundaries,thisfigure is intended to provide an illustration of the relative differences among the different classes of multiferroic materials.to low-resistivity ferromagnetic phases reduce the overall magnetoelectric coupling and(ii)the piezoelectric layer in a layered structure can easily be poled electrically to further enhance the magnetoelectric coupling[68].Several research groups in recent years have reported very strong magnetoelectric coupling in layered composites[69–80]. The use of Tb1−x Dy x Fe2(Terfanol-D),Fe x Ga1−x(Galfenol), Metglas,and ferrites in laminar composites led to dramatic increase in the magnetoelectric coupling in inhomogeneous multiferroics.A report on BaTiO3–CoFe2O4films consisting of spinel CoFe2O4nanopillars heteroepitaxially ordered in the perovskite BaTiO3matrix found significant magnetoelectric coupling and motivated further studies on self-assembled nanostructured multiferroics[81].An enormous collection of multiferroic materials have been identified in the past decade having an incredibly wide range of physical characteristics.Very broadly,these can be subdivided into single phase materials having widely separate ferroelectric and magnetic ordering temperatures(type1 multiferroics in the nomenclature introduced by Khomskii [82]),single phase materials manifesting a magnetic transition with collateral ferroelectric ordering(type2multiferroics),and composite multiferroics consistent of distinct ferromagnetic and ferroelectric components.Figure1gives a schematic representation of the relative magnitudes of the magnetization and polarization for different classes of multiferroic materials. The magnetization for some type2multiferroics is completely negligible,but can reach over103emu cm−3in composite systems.Similarly,the polarization for type2multiferroics is generally small,typically below1µC cm−2,but can reach over100µC cm−2in composites and some type1systems.The regions indicated infigure1are not sharp boundaries;some multiferroics have properties falling outside the demarcation lines;the boxes are intended only to provide a qualitative illustration of the approximate relative magnitudes of the physical properties of these materials.Composite multiferroics offer distinct benefits for engineering materials for device applications,as the propertiesof the ferromagnetic and ferroelectric constituents can beadjusted independently.Moreover,because of the largeintrinsic magnetizations and polarizations,the magnetoelectriccoupling in composite multiferroics can be very large.Conversely,the interplay between spin and charge degreesof freedom in some single phase system may allow somenovel magnetoelectric functionalities,such as rotating thepolarization with an applied magneticfield[83],but the verylow transition temperature typically observed precludes theincorporation of these materials into most devices.Despite thestrong qualitative differences among these different classes ofmultiferroics,there is pressing need to better understand theproperties of all these materials in thinfilm geometries.There are a wide variety of physical mechanismsunderlying the development of multiferroic order andmagnetoelectric coupling in these different materials,evenwithin the same class of systems.In compositemultiferroics,the magnetization and electric polarizationdevelop independently in separate materials,and can generallybe understood within the usual frameworks proposed forferromagnets and ferroelectrics.A composite of ferromagneticand ferroelectric materials is multiferroic and will allowcoupling between the two subsystems through mechanicalforces[55].A magneticfield applied to the composite willproduce a deformation due to magnetostriction,which will becoupled to the piezoelectric phase and result in an inducedpolarization.In a linear magnetoelectric,the polarization Pis related to H by P=αH,whereαis the second rankME-susceptibility tensor and is expressed in units of s/m inSI units(in Gaussian unitsα=4πP/H=4πM/E isdimensionless).A composite of piezomagnetic–piezoelectricphases is expected to be magnetoelectric sinceα=δP/δHis the product of the piezomagnetic deformationδz/δH andthe piezoelectric charge generationδQ/δz.For an acfieldδH applied to a magnetically biased sample,one measuresthe induced voltageδV.The ME voltage coefficient is thenαE=δV/tδH andα=εoεrαE where t is the composite thickness andεr is the relative permittivity.In order tomaximize the magnetoelectric coupling in these materials itis desirable to incorporate a ferromagnetic component havinga large piezomagnetic response,a ferroelectric componenthaving a large piezeoelectric response,and maximize themechanical coupling between the two phases.As mentioned previously,one of the great advantages ofcomposite multiferroic materials is that they offer the abilityto tune the properties of the ferroelectric and ferromagneticcomponents separately.Two components should exhibit largepiezoelectric and piezomagnetic coefficients,respectively.Ferromagnetic Terfanol-D,Metglas and spinel ferrites haveexcellent properties multiferroic applications,having amagnetostriction coefficient of30–2000ppm[10,11,46–53].There is also an enormous range of different ferroelectricsincorporated into composite multiferroics.Pb(ZrTi)O3(PZT),lead magnesium niobate-lead titanate(PMN-PT)withpiezoelectric coupling coefficients of200–2000pm V−1arecommonly used as a standard ferroelectric,although as withmany applications,there is particular interest in identifyinglead-free materials.BaTiO3has been used in a number of multiferroics,while polymer ferroelectrics may also offerdesirable properties[10,11,46–53].There is considerableinterest in understanding the limiting length scales forcomposite multiferroics.Recent experimental and theoreticalwork on ultrathin BaTiO3grown on Fe(001)find ferroelectricorder developing at only two unit cells thickness,suggestingatomic scale multiferroic order in this composite[84].While the magnetoelectric coupling in compositemultiferroics can largely be understood using elasticitytheory,the mechanisms underlying the development ofmultiferroic order and spin-charge coupling in many single-phase systems are exceedingly diverse and often remainambiguous.Type1multiferroics have distinct magneticand ferroelectric transition temperatures allowing for differentmechanisms to be responsible for eachflavour of ordering.Despite this apparent freedom in tuning the spin-chargeproperties,even this class of multiferroics is relatively sparse[63].This is typically attributed to the observation thatfor many conventional ferroelectrics the development of aspontaneous polarization involves the off-centre displacementof transition metal ions having empty d shells(a d0electronicconfiguration).Conversely,magnetism requires partiallyfilledd shells,meaning that the same ions are unlikely to produce theferroelectric distortions and magnetic ordering[63].Hill andSeshadri have proposed one specific mechanism for producingmultiferroic order in certain perovskites,based on a6s26p nelectronic configuration on the A site cation.In this‘lonepair’model,the6s2electrons are stereochemically active andcan produce a structural distortion and resultant polarization[85].This scenario is believed to arise in BiMnO3,wherethe lone pair electrons on the Bi3+site cause a structuraldistortion,while the Mn3+ions order ferromagnetically onthis distorted perovskite lattice.Different mechanisms havebeen proposed for other type1multiferroics,includingferroelectricity produced by the tilting of the MnO5bipyramidsin hexagonal YMnO3[86].The coupling between charge and spin degrees of freedomin type1multiferroics is strictly restricted by symmetryconsiderations.Terms involving a biquadratic couplingbetween E and H are always allowed by symmetry,hencemagnetodielectric effects can generally be observed in type1multiferroics.This is often associated with dielectricanomalies at magnetic transitions,or a quadratic dependence ofthe dielectric constant on an applied magneticfield[31].Thiscoupling can be strongly enhanced by controlling the magneticsymmetry[87],with the magnetodielectric response increasingby two orders of magnitude in Ga substituted YMnO3ascompared with pure YMnO3[88].In type2multiferroics,where ferroelectric orderingcoincides with a magnetic transition,typically at lowtemperatures,the ferroelectricity is produced by the magneticstructure.One of the best-known examples of thisbehaviour is TbMnO3,an insulating perovskite that ordersantiferromagnetically at T N=41K and then undergoes a second magnetic transition at T C=28K(this lower magnetic transition temperature is also referred to as‘T lock’in some of the earlier literature).A polarization on the orderof800µC m−2develops in this low-temperature magneticphase,and this polarization can be controlled by an externalmagneticfield[61].Since this observation of multiferroicityin TbMnO3,simultaneous ferroelectric and magnetic orderinghas appeared in a large number of insulating magnets havingspiral spin structures,including Ni3V2O8[89],CoCr2O4[90],MnWO4[91]and FeVO4[92,93],as well as other systems,such as TbMn2O5[94,95],have been identified.A morecomplete discussion of spin spiral multiferroics can be foundin reviews by Kimura[96,97].The net magnetization is oftennegligibly small,on account of the spiral magnetic structure,and the transition temperatures are typically well below roomtemperature.Experimentally,these type2multiferroics alsohave relatively small polarizations.The simultaneous development of magnetic and ferro-electric order can be explained on a meanfield level usingGinzburg–Landau formalism including terms in the free energythat couple magnetic and ferroelectric order parameters[42],asdiscussed in depth by Harris and coworkers[20,89,98–100].Because magnetic order parameters are antisymmetric undertime reversal,while ferroelectric order parameters change signunder spatial inversion,a linear coupling between the twois normally forbidden.However,it was recognized that incertain crystal systems,including TbMnO3[99]and Ni3V2O8[89],a trilinear coupling,consisting of two different magneticorder parameters and a ferroelectric electric order parameter,could transform as a scalar and appear in the free energy.The direction of the electric polarization is restricted by thesymmetry transformations of the magnetic order parameters.This model proved to be extremely successful in understandingthe multiferroic behaviour qualitatively in a number of spinspiral magnets having multiple magnetic transitions,includingNi3V2O8[89],TbMnO3[99]and FeVO4[101]and has alsobeen applied to systems having a single magnetic transition,such as RbFe(MoO4)2[102].Mostovoy proposed another phenomenological modelfor multiferroic ordering in cycloidal spin spirals basedon the symmetry of the magnetic structures[103].Thisspin spiral model predicts that the electric polarization Pshould be given by P∼r ij×(S i×S j),where r ij is the propagation direction of the spin spiral and S i and S jare the moments on neighbouring spins.While this spinspiral model provides helpful insight into the developmentof multiferroic order in a range of systems,there are somecases where the simple application of this model can beinsufficient to capture the essential physics.This issueis discussed in depth for RbFe(MoO4)2,which consistsof stacked layers of antiferromagnetic triangular lattices[102,104,105].The magnetoelectric coupling in this class ofsystems has also been discussed theoretically in the contextof an electricfield selecting the spin chirality for stackedtriangular antiferromagnets[106].There are a number of proposals for different microscopicmechanisms that could be relevant for the strong spin-charge coupling found in type II parisonsbetweenfirst principle LDA+U calculations and inelasticneutron scattering and polarized IR measurements suggestthat coupling between a specific phonon mode and thespin structure may be responsible for the development of ferroelectric order in Ni3V2O8[107,108]and significant spin-phonon coupling has been observed in multiferroic TbMn2O5 [109],TbMnO3[110]and FeVO4[93].The spin current model proposed by Katsura et al[111]is closely related to the phenomenological model of Mostovoy.In this spin current model the spin–orbit coupling and electron hopping between neighbouring spins can distort the electron density leading to an electron dipole moment having the same form proposed by Mostovoy,P∼r ij×(S i×S j)[111].Sergienko and Dagotto have also discussed in detail how the Dzyaloshinskii–Moriya term,D•(S i×S j),can result in magneticallyinduced ferroelectric order[112].Picozzi et al have described a theoretical overview of the microscopic mechanisms associated with magnetically induced ferroelectricity in these materials[113],and Kaplan and Mahanti discuss the local symmetry considerations involved with canted spins producing a ferroelectric polarization[114].More recently,multiferroic behaviour has been observed in conjunction with Ising chain collinear up–up–down–down spin structure,as in Ca3CoMnO6[115].In this class of systems,the development of ferroelectric order can be associated with the difference in exchange striction between parallel and antiparallel pairs of spin producing a structural distortion and polarization along the chain direction.Although showing similar properties to other type2multiferroics,the origin of the magnetoelectric coupling is distinctly different from the spin spiral multiferroics,arising from symmetric rather than antisymmetric superexchange.As there are few studies on this fascinating class of multiferroics in thinfilm geometries,we will not discuss these systems in more detail.3.Device considerations for magnetoelectric coupling3.1.BackgroundThe multiferroic composites of interest in the1970s were sintered ferrites-BaTiO3for whichαE were2–3orders of magnitude smaller than predicted values[10,11,46–55,58]. The bulk composites had extensive microcracks leading to poor mechanical coupling.The piezoelectric phase is susceptible to electrical shunting and loss of induced charges due to low resistivity ferrites.In addition,possible presence of Fe2+in the ferrite phase will increase the leakage current.Studies in recent years,however,have been primarily on layered composites[47,50,52,53].Such a configuration has several advantages over bulk sintered composites.In particular, leakage currents due to low resistivity of ferromagnetic phases in bulk composites can easily be overcome in laminates[67].Efforts to date have focused mainly on ME interactions in composites of ferrites,manganites,or transition metals/alloys for the ferromagnetic phase,and lead zirconate titanate(PZT), lead magnesium niobate–lead titanate(PMN–PT),or lead zinc niobate–lead titanate(PZN–PT)for the piezoelectric yered samples are synthesized by a variety of techniques such as bonding ferromagnetic and piezoelectric samples,sintering thickfilms made by tape-casting,and MBE,PLD or MOCVD growth of thinfilms[47,50,52,53].。