Multiferroic and magnetoelectric materials W.Eerenstein1,N.D.Mathur1&J.F.Scott2
A ferroelectric crystal exhibits a stable and switchable electrical polarization that is manifested in the form of cooperative atomic displacements.A ferromagnetic crystal exhibits a stable and switchable magnetization that aris through the quantum mechanical phenomenon of exchange.There are very few‘multiferroic’materials that exhibit both of the properties,but the‘magnetoelectric’coupling of magnetic and electrical properties is a more general and widespread phenomenon.Although work in this area can be traced back to pioneering rearch in the1950s and1960s, there has been a recent resurgence of interest driven by long-term technological aspirations.
S ince its discovery less than one century ago,the phenomenon of ferroelectricity1,like superconductivity,has been considered
in relation to the ancient phenomenon of magnetism.Just as
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recent work has shown that magnetic order can create super-conductivity2,it has also been shown that magnetic order can create (weak)ferroelectricity3and vice versa4,5.Single-pha materials in which ferromagnetism and ferroelectricity ari independently also exist,but are rare6.As this new century unfolds,the study of materials posssing coupled magnetic and electrical order parameters has been r
evitalized.In this Review we t recent developments in the context of the pioneering works of the1950s–1960s.
Thefield of rearch that we are describing has a tortuous taxonomy and typically involves terms such as‘multiferroic’and ‘magnetoelectric’,who overlap is incomplete(Fig.1).By the original definition,a single-pha multiferroic7material is one that posss two—or all three—of the so-called‘ferroic’properties: ferroelectricity,ferromagnetism and ferroelasticity(Fig.2and Table1;e Box1for a glossary of terms).However,the current trend is to exclude the requirement for ferroelasticity in practice,but to include the possibility of ferrotoroidic order(Box1)in principle. Moreover,the classification of a multiferroic has been broadened to include antiferroic order(Box1).Magnetoelectric coupling(Box1), on the other hand,may exist whatever the nature of magnetic and electrical order parameters,and can for example occur in para-magnetic ferroelectrics8(Fig.1).Magnetoelectric coupling may ari directly between the two order parameters,or indirectly via strain. We also consider here strain-mediated indirect magnetoelectric coupling in materials where the magnetic and electrical order parameters ari in parate but intimately connected phas(Fig.3).
A confluence of three factors explains the current high level of interest in magnetoelectrics and multif
erroics.First,in2000,Hill (now Spaldin)discusd the conditions required for ferroelectricity and ferromagnetism to be compatible in oxides,and declared them to be rarely met6.Her paper in effect issued a grand materials develop-ment challenge that was taken up becau empirically there are indeed few multiferroic materials,whatever the microscopic reasons. Second,the experimental machinery for the synthesis and study of various contenders was already in place when this happened.Third, the relentless drive towards ever better technology is aided by the study of novel materials.Aspirations here include transducers and magneticfield nsors,but tend to centre on the information storage industry.
It was initially suggested that both magnetization and polarization could independently encode information in a single multiferroic bit. Four-state memory has recently been demonstrated9,but in practice it is likely that the two order parameters are coupled10,11.Coupling could in principle permit data to be written electrically and read magnetically.This is attractive,given that it would exploit the best
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Figure1|The relationship between multiferroic and magnetoelectric materials.Ferromagnets(ferroelectrics)form a subt of magnetically (electrically)polarizable materials such as paramagnets and antiferromagnets(paraelectrics and antiferroelectrics).The interction (red hatching)reprents materials that are multiferroic.Magnetoelectric coupling(blue hatching)is an independent phenomenon that can,but need not,ari in any of the materials that are both magnetically and electrically polarizable.In practice,it is likely to ari in all such materials,either directly or via strain.
1Department of Materials Science,University of Cambridge,Pembroke Street,Cambridge CB23QZ,UK.2Centre for Ferroics,Earth Sciences Department,University of Cambridge,Downing Street,Cambridge CB23EQ,UK.
瑜伽教练培训aspects of ferroelectric random access memory (FeRAM)and mag-netic data storage,while avoiding the problems associated with reading FeRAM and generating the large local magnetic fields needed
to write.Unfortunately,significant materials developments will be required to generate magnetoelectric materials that could make a real contribution to the data storage industry.But given the paucity of rious competitors to contemporary memory technologies,the study of novel materials remains important if disruptive technologies are ultimately to emerge.In the shorter term,niche applications are more likely to emerge in strain coupled two-pha systems of the type that we describe later.
The purpo of this Review is to asss the current state of the field,to remind readers of the relevant work performed in the latter half of the twentieth century,and to discuss matters of scientific ‘hygiene’pertaining to accurate measurements and analys.For further details we refer the reader to three reviews written at different stages of this re-emerging field 12–14.
Magnetoelectric coupling
The magnetoelectric effect in a single-pha crystal is traditionally described 13,15in Landau theory by writing the free energy F of the system in terms of an applied magnetic field H who i th component is denoted H i ,and an applied electric field E who i th component is denoted E i .Note that this convention is unambiguous in free space,but that E i within a material encodes the resultant
field that a test particle would experience.Let us consider a non-ferroic material,where both the temperature-dependent electrical polarization P i (T )(m C cm 22)and the magnetization M i (T )(m B per formula unit,where m B is the Bohr magneton)are zero in the abnce of applied fields and there is no hysteresis.It may be reprented as an infinite,homogeneous and stress-free medium by writing F under the
ÞThe first term on the right hand side describes the contribution resulting from the electrical respon to an electric field,where the permittivity of free space is denoted 10,and the relative permittivity 1ij (T )is a cond-rank tensor that is typically independent of E i in non-ferroic materials.The cond term is the magnetic equivalent of the first term,where m ij (T )is the relative permeability and m 0is the permeability of free space.The third term describes linear magneto-electric coupling via a ij (T );the third-rank tensors b ijk (T )and g ijk (T )reprent higher-order (quadratic)magnetoelectric coefficients.In the prent scheme,all magnetoelectric coefficients incorporate the field independent material respon functions 1ij (T )and m ij (T ).The magnetoelectric effects can then easily be established in the form P i (H j )or M i (E j ).The former is obtained by differentiating F with respect to E i ,and then tting E i ¼0.A complementary operation involving H i establishes the latter.One obtains:
P i ¼a ij H j þb ijk
2
H j H k þ···
ð2Þand
M i ¼a ji E j þ
g ijk
2大学英语三级作文
E j E k þ···ð3ÞIn ferroic materials,the above analysis is less rigorous becau 1ij (T )and m ij (T )display field hysteresis.Moreover,ferroics are better parameterized in terms of resultant rather than applied fields 16.This is becau it is then possible to account for the potentially significant depolarizing/demagnetizing factors in finite media,and also becau the coupling constants would then be functions of tempera-ture alone,as in standard Landau theory.In practice,resultant electric and magnetic fields may sometimes be approximated 17by the polarization and magnetization respectively.
A multiferroic that is ferromagnetic and ferroelectric is liable to display large linear magnetoelectric effects.This follows becau ferroelectric and ferromagnetic materials often (but not always)posss a large permittivity and permeability respectively,and a ij is bounded by the geometric mean of the diagonalized tensors 1ii and m jj such that 18:
a 2ij #10m 01ii m jj
ð4Þ
Equation (4)is obtained from equation (1)by forcing the sum of the
first three terms to be greater than zero,that is,ignoring higher-order coupling terms.It reprents a stability condition on 1ij and m ij ,but if the coupling becomes so strong that it drives a pha transition to a more stable state,then a ij ,1ij and m ij take on new values in the new pha.Note that a large 1ij is not a prerequisite for a material to be ferroelectric (or vice versa);and similarly ferromagnets do not necessarily posss large m ij .For example,the ferroelectric KNO 3posss a small 1¼25near its Curie temperature of 1208C (ref.19),
manage
Figure 2|Time-reversal and spatial-inversion symmetry in ferroics.a ,Ferromagnets.The local magnetic moment m may be reprented
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classically by a charge that dynamically traces an orbit,as indicated by the arrowheads.A spatial inversion produces no change,but time reversal switches the orbit and thus m .b ,Ferroelectrics.The local dipole moment p
may be reprented by a positive point charge that lies asymmetrically within a crystallographic unit cell that has no net charge.There is no net time dependence,but spatial inversion revers p .c ,Multiferroics that are both ferromagnetic and ferroelectric posss neither symmetry.
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whereas paraelectric SrTiO 3exhibits 1.50,000at low tempera-tures 20.Therefore large magnetoelectric couplings need not ari in,or be restricted to,multiferroic materials.
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Nonlinear coupling.Most materials have small values of either 1ij or m ij or both,so the linear magnetoelectric effect will also be small,given that permittivity and permeability appear as a product in equation (4).However,no such restriction applies to higher-order couplings,such as tho described by b ijk and g ijk .For example,in some materials terms such as b ijk H j H k can dominate
the linear term a ij H j in equation (2),as first shown experimentally at low tempera-tures in the piezoelectric paramagnet NiSO 4z 6H 2O (ref.21).In order to achieve large magnetoelectric effects at room temperature through higher-order terms,we suggest investigating magnetic materials with reduced dimensionality.Indeed,two-dimensional spin order associated with b (T )can persist to a temperature T 2D that exceeds the temperature T 3D at which three-dimensional spin order associ-ated with a (T )is destroyed.This scenario aris 22at low temperature in BaMnF 4.
Indirect coupling.So far,our discussion of linear and higher-order magnetoelectric coupling has ignored the effects of strain.Such effects could be significant or even dominant.For example,the inclusion of piezomagnetism (magnetostriction)would generate cross terms in equation (1)that are proportional to strain and vary linearly (quadratically)with H i .Analogous expressions would ari from piezoelectricity or electrostriction (e Box 1).Furthermore,mixed terms involving products of strain,H i and E j have been predicted 23.In two-pha materials,magnetic and electrical proper-ties are strain-coupled by design in the quest for large magneto-electric effects.The strength of this indirect coupling is not restricted by equation (4),and enhancements over single-pha systems of veral orders of magnitude have been achieved 24.鹦鹉科
Determination of coupling constants
The magnetoelectric behaviour of a material can only be fully understood if its magnetic point group symmetry is known.This is becau the magnetoelectric coefficients a ij ,b ijk and g ijk posss the symmetry of the material 12,13,15.For example,a ij can only be non-zero for materials that do not have a centre of symmetry and are time-asymmetric 12.Converly,information regarding the magneto-electric coefficients bad on electrical 25or optical 26experiments can aid the determination of magnetic point group symmetries.
Below we discuss experimental issues relating to magnetoelectric measurements.The major challenge is to make samples sufficiently insulating to prevent leakage currents contributing to the measured signal —a widespread problem undermining the measurement of ferroelectric polarization loops,as described in refs 16and 27.Another complication aris if ferroic domains are prent,and care should be taken to prepare single-domain states 11.
Magnetoelectric coupling can be measured indirectly by simply recording changes in either the magnetization near,say,a ferro-electric transition temperature or the dielectric constant near a magnetic transition temperature.The resulting effects are described using various terms such as ‘magnetocapacitance’or ‘magnetodi-electric respon’.Catalan has recently shown 28that the frequently reported effects could misleadingly ari owing to magnetoresistance effects alone,and th
at the signature of true magnetocapacitance effects is persistence to high frequencies and low loss.However,even true magnetocapacitance measurements do not provide mechanistic insight nor yield coupling constants.
Direct measurements are more challenging.They record either a magnetic respon to an applied electric field or an electrical respon to an applied magnetic field.The former scenario typically requires electrically addressing the sample in a magnetometer.In the latter scenario,the electrical respon can be measured in terms of either current or voltage.The time-integrated current per unit area directly reprents the magnetically induced change of polarization in equation (2),that is,a ¼›P /›H ,ignoring higher-order terms.Measurements of voltage,however,yield empirical coupling coeffi-cients commonly also denoted a ,which assuming linearity take the form ›E /›H .
Single-pha studies
Rearch into magnetoelectrics and multiferroics took off during the latter half of the twentieth century.In 1957,the linear magnetoelectric coupling coefficient a was predicted to occur in Cr 2O 3(ref.29).Then,in the 1960s,a was experimentally obrved 30,31to be non-zero below
the antiferromagnetic Ne
attendance´el temperature of 307K,near which it peaked to a value of a ¼›P /›H <4.1ps m 21.This work on Cr 2O 3and other antiferromagnetic crystals,such as Gd 2CuO 4,Sm 2CuO 4,KNiPO 4,LiCoPO 4and BiFeO 3,is well summarized in refs 13and 32.
1Ferroics
Ferroelectric materials posss a spontaneous polarization that is stable and can be switched hysteretically by an applied electric field;antiferroelectric materials posss ordered dipole moments that cancel each other completely within each crystallographic unit cell.Ferromagnetic materials posss a spontaneous magnetization that is stable and can be switched hysteretically by an applied magnetic field;antiferromagnetic materials posss ordered magnetic
moments that cancel each other completely within each magnetic unit cell.
Ferroelastic materials display a spontaneous deformation that is stable and can be switched hysteretically by an applied stress.Ferrotoroidic materials posss a stable and spontaneous order parameter that is taken to be the curl of a magnetization or
polarization.By analogy with the above examples,it is anticipated that this order parameter may be switchable.Ferrotoroidic materials have evaded unambiguous obrvation.
Ferrimagnetic materials differ from antiferromagnets becau the magnetic moment cancellation is incomplete in such a way that there is a net magnetization that can be switched by an applied magnetic field.
Order parameter coupling
Magnetoelectric coupling describes the influence of a magnetic (electric)field on the polarization (magnetization)of a material.Piezoelectricity describes a change in strain as a linear function of applied electric field,or a change in polarization as a linear function of applied stress.
Piezomagnetism describes a change in strain as a linear function of applied magnetic field,or a change in magnetization as a linear function of applied stress.
Electrostriction describes a change in strain as a quadratic function of applied electric field.
Magnetostriction describes a change in strain as a quadratic function of applied magnetic
field.
Figure 3|Strain-mediated magnetoelectric coupling in two-pha systems.Magnetic materials in which the magnetic order parameter
couples to strain may be electrically addresd via an intimately connected material that develops a strain in respon to an electrical stimulus.Equally,a magnetic stimulus may produce an electrical respon.Suitable structures include mixtures of grains (a )and thin-film heterostructures (b ).Note that in a but not b the magnetic material must be electrically insulating in order to avoid the possibility of short-circuits.
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Magnetoelectric switching.The application potential for multi-ferroic materials in data storage lies in the possibility of reversing the magnetization by applying an electric field (or vice versa).Magneto-electric switching was first demonstrated 1140years ago in the boracite Ni 3B 7O 13I.The weak magnetic and electrical order t in simultaneously 11below 60K,and a magnetic-field-induced reversal of the magnetization was found to flip the polarization (0.076m C cm 22).This hysteretic respon is shown in Fig.4a.Alternatively,in the paramagnetic ferroelectric Tb 2(MoO 4)3,a mag-netically induced persistent polarization can ari in large applied magnetic fields 8(Fig.4b).Recently,magnetoelectric switching has been obrved in orthorhombic manganites,REMnO 3or REMn 2O 5,where RE is a rare earth element.The are antiferromagnets that display improper (weak)ferroelectricity.A small polarization
appears at the magnetic Ne
´el temperature (,30K)becau the magnetic transition gives ri to crystalline distortions.The polarization of 0.04m C cm 22in TbMn 2O 5has been magnetically reverd 33,and the polarization of 0.08m C cm 22in TbMnO 3has been magnetically rotated 3by 908.Similarly,in the hexaferrite 34Ba 0.5Sr 1.5Zn 2Fe 12O 22,a polarization of 0.015m C cm 22may be magnetically induced and subquently rotated 3608about the c axis.Unfortunately,the changes in polarization are not persis
tent,and ari at low temperatures only.
Role of magnetic and crystallographic structure.As magneto-electric coupling is determined by the structure and magnetic symmetry of a crystal,small modifications might alter,eliminate or allow magnetoelectric effects.Here we discuss key examples.Spontaneous magnetoelectric coupling in BaMnF 4permits the ferroelectric order to cant the spins of the two anti-aligned magnetic sub-lattices along the a axis of the crystal,giving a small net ferromagnetic magnetization 5.The periodicity of this magnetization
is commensurate with the crystal lattice,but the periodicity of the ferroelectricity is incommensurate,and therefore the spatial average of the magnetoelectric coupling is nearly zero and difficult to measure directly.Instead,evidence for coupling comes from changes in the dielectric constant 22obrved at magnetic transition tempera-tures.The magnetization of BaMnF 4orders two dimensionally below T 2D ,where a change in the b -axis dielectric constant is obrved (Fig.5).This has been quantified in terms of the magnetic correlation energy 22,35.A 1%replacement of Mn with Co destroys the spin canting,and strongly influences the changes in the dielectric constant near the magnetic pha transition,clearly highlighting the key role of magnetic symmetry 36.
BiFeO 3is a commensurate ferroelectric 37and an incommensurate antiferromagnet at room temperature 38.The spins are not collinear,but instead take the form of a long-wavelength (62nm)spiral 38.Conquently,the linear magnetoelectric effect also averages to zero here,and indeed only the quadratic effect has been obrved 39.However,the linear effect may be recovered if the spiral is ‘unwound’by applying 40large magnetic fields of 20T,by chemical substi-tutions 41,or by attempting to introduce thin-film epitaxial con-straints 42.Note that the concept of unwinding has been successfully employed in the ca of smectic liquid crystals by confinement within treated glass plates.This surface-stabilized ferroelectric liquid crystal technology (SSFLC)has become the basis for the flat-screen television industry and display screens in cameras.
The linear magnetoelectric effect is also symmetry-forbidden in hexagonal manganites 43of the form REMnO 3.The materials are ferroelectric,and posss antiferromagnetically aligned Mn 3þions (Ne
´el temperature 70–130K).RE-site magnetic ordering is en below ,5K,but large moments may only be achieved in large
magnetic fields 44.Large Ne
´el temperature dielectric anomalies of 42%and 60%are obrved in YMnO 3and HoMnO 3(ref.45),respectively.In a landmark experiment,ferroelectric and antiferro-magnetic domain walls were en 43to be coincident in YMnO 3.Coupling via such walls could then ari becau the local magnetiza-tion in an antiferromagnetic domain wall either posss reduced magnetic symmetry 46,or el interacts with the strain from the coincident ferroelectric wall 43.In HoMnO 3,an electrically driven magnetic pha transition is obrved 17.This is a dramatic form of switching that suggests a new approach for magnetoelectric switching.Circular or toroidal ordering of domains in magnetic or magneto-electric materials can ari from two unrelated effects.Non-ferroelectric magnetic nanodots typically show vortex (circular)domains 47that may be treated as topological defects 48.In the bulk,ordered magnetic or ferroelectric moments are usually collinear,but toroidal magnetoelectric phenomena have been propod in ferro-electric ferromagnetic systems 49,50.Experimental arches for toroidal ordering 51became unpopular following irreproducible reports 52
in
Figure 4|Examples of magnetoelectric coupling.a ,Ni 3B 7O 13I at 46K (after ref.11,with permission).The magnetoelectric (ME)H voltage signal,and therefore the polarization via equation (2),may be reverd in magnetic fields (20:6T ,m 0H ,0:6T)that are much lower than the switching fields of recently studied materials 5,55.b ,Tb 2(MoO 4)3at 78K (after ref.9,with permission).A persistent polarization (P )of ,0.5m C cm 22develops after exposure to magnetic fields in excess of 8
T.Figure 5|Link between the magnetic and electrical properties of BaMnF 4.The temperature dependence of the (7%)change in b -axis dielectric anomaly D 1b at T 2D ¼70K cloly follows the temperature dependence of the normalized magnetic correlation function S z i S z i þ1 =S 2.Here S z
i is the z component of spin S at site i .(After ref.22,with permission.)
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1974,but there is now fresh hope that its existence will be experimen-tally established 53,54.The symmetry requirements for toroidal ordering and their relationship with magnetoelectric coupling are reviewed in refs 13and 14.The area is not well explored,and the possibility of large magnetoelectric coupling exists;however,other possible phenomena,such as ferromagnetism inside antiferromagnetic domain walls,complicate measurements.
Ferromagnetic ferroelectric multiferroics.In 1958,Smolensky’s group studied weakly ferromagnetic mixed perovskites,such as (12x )Pb(Fe 2/3W 1/3)O 3-x Pb(Mg 1/2W 1/2)O 3(ref.55).The were doped to increa resistivity,but the boracite discusd above was the first highly insulating ferromagnetic ferroelectric to be studied 11.The perovskite BiMnO 3is a promising low-temperature multi-ferroic that has been considered for quite some time 56,57.Ferromag-netic ordering below 105K is attributed to orbital ordering of the Mn 3þions (3d 4)and a large magnetization of 3.6m B per formula unit has been measured for polycrystalline samples 57.The samples tend to be electrically conducting,restricting evidence of ferroelec-tricity to low temperatures and precluding definitive measurements of polarization.Multiferroic behaviour was en 58at ,80K (,1m B per Mn,,0.15m C cm 22),and a peak change of 20.6%in the dielectric constant in 8T was recorded at T C (ref.59).This inspires investigations into less-conducting samples.We have recently shown 60that epitaxial films can be highly insulating,even at room temperature (107Q cm).
The spinel CdCr 2S 4is reported to be a low-temperature multi-ferroic.In 1965it was known 61to be ferromagnetic (6m B per formula unit)and insulating below 97K,but only recently was it reported to display 62relaxor ferroelectricity (0.5m C cm 22)below 135K.A colossal magnetocapacitance of 450%in 5T was also reported,but magnetoresistance effects 28could be responsible.
Reports of room temperature multiferroic materials have centred on BiFeO 3and its derivatives.Promising multiferroic behaviour (1m B per formula unit,,50–60m C cm 22)was reported in thin epitaxial films 63,triggering widespread activity.However,subquent works 64–66did not reproduce the findings.The large magnetization only aris in deoxygenated films that are too electrically conducting for valid ferroelectric measurements to be made 64.Moreover,the prence of impurity phas could play a role 65,66.Preliminary reports of multiferroicity in chemically doped BiFeO 3(ref.67)and PbTiO 3(ref.68)remain unconfirmed.
英语四级网Two-pha systems
checking
An alternative strategy for engineering enhanced magnetoelectric effects is to introduce indirect coupling,via strain 69,between two materials such as a ferromagnet and a ferroelectric.Each pha may then be independently optimized for room temperature perform-ance,and the coupling limit of e
quation (4)is lifted.Strain coupling requires intimate contact (Fig.3)between a piezomagnetic (or magnetostrictive)material and a piezoelectric (or electrostrictive)material.This can be achieved in the form of composites 69,70,laminates 24,71,72or epitaxial multilayers 73(Table 2).The coupling constant depends on the frequency of applied magnetic field 74,and such multiferroic structures could thus find applications in,for example,microwave frequency transducers.
Epitaxial thin-film heterostructures could permit preci magne-
toelectric studies,becau crystallographic orientation,layer thick-ness and interfacial roughness may be controlled accurately,but direct measurements of a in epitaxial systems have not been forth-coming.However,ferroelectric layers can generate strains of the order of 1%in magnetic epilayers owing to structural pha tran-sitions.For example,the tetragonal to monoclinic structural pha transition in a BaTiO 3substrate at 278K produces 73a 70%change in the magnetization of an epitaxial film of the ferromagnetic manga-nite La 0.67Sr 0.33MnO 3(Fig.6).Alternatively,one may attempt to alter the magnetic structure of a film by applying a voltage to the underlying piezoelectric material 75,76,77.Promising results 78were found for a thin film heterostructure of CoPd and Pb(Zr,Ti)O 3(PZT),where the application of an electric field to the PZT layer rotated the magnetization of the CoPd film by 908.
The ferromagnetic and ferroelectric phas may be distributed laterally in a film while prerving an epitaxial relationship with one another and the substrate.This has been achieved for nanopillars of CoFe 2O 4in a BaTiO 3matrix,grown on a SrRuO 3electrode with a SrTiO 3substrate.However,the obrved change in magnetization of the CoFe 2O 4pillars at the ferroelectric Curie temperature was 79just 5%,possibly due to either clamping from the underlying epitaxial structure which is not piezoelectric,or electric field effects associated with the ferroelectric.Nevertheless,when the matrix was changed to BiFeO 3,an electrically induced magnetization reversal in the CoFe 2O 4nanopillars was reported 80.
Devices.Ferroelectrics may be ud to address magnetic materials in devices for two reasons that in practice are not easy to parate 81–83.First,their superlative piezoelectric properties permit them to strain intimately connected layers as discusd above.Second,the large
Table 2|Magnetoelectric coupling constants in two-pha systems
Morphology
Materials
Coupling constant (mV cm 21Oe 21)
Ref.
Composite BaTiO 3and CoFe 2O 4
5069Composite
Terfenol-D and PZT in polymer matrix
4270Laminated composites Terfenol-D in polymer matrix/PZT in polymer matrix
3,00071Laminate Terfenol-D/PZT 4,80024Laminate La 0.7Sr 0.3MnO 3/PZT 6072Laminate NiFe 2O 4/PZT 1,40072
PZT (Pb(Zr,Ti)O 3)and BaTiO 3are piezoelectric,and terfenol-D (Tb x Dy 12x Fe 2),the manganite and the ferrites are
magnetostrictive.
Figure 6|Magnetoelectric coupling in two-pha systems.Main figure,the magnetization M of an epitaxial La 0.67Sr 0.33MnO 3film measured in a small applied field H (top int)shows sharp chang
es due to structural pha transitions in the underlying BaTiO 3substrate.Lower int,the hard and easy axes are reverd between temperatures T1and T2.(After ref.73,with permission.)
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