Multiferroic and Magnetoelectric Oxides: The Emerging Scenario

Chemistry and Physics of Materials Unit, International Centre for Materials Science ... (7) Frustrated magnetism and spiral magnetic ordering induces ...
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Multiferroic and Magnetoelectric Oxides: The Emerging Scenario C. N. R. Rao,* A. Sundaresan, and Rana Saha Chemistry and Physics of Materials Unit, International Centre for Materials Science and CSIR Unit of Excellence in Chemistry, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India ABSTRACT: Multiferroics were considered to be rare because magnetism and ferroelectricity require entirely different criteria for the materials. Several multiferroic oxides have, however, been discovered in the past few years by virtue of novel operating mechanisms, the most effective one being ferroelectricity driven by magnetism itself. Many such oxides where the magnetic and electric order parameters interact also exhibit magnetoelectric or magnetodielectric properties. In this Perspective, properties of manganites, ferrites, and other monophasic multiferroic oxides with spin-induced electric polarization are described. Multiferroic properties arising from charge ordering are examined. The present status of BiMnO3, which is an unusual example of a ferromagnetic−ferroelectric, is presented. Recent findings suggest that it is likely that many more multiferroic and magnetoelectric oxide materials exhibiting magnetically induced ferroelectricity will be found in the future.

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ultiferroics are defined as those materials that exhibit both ferroelectricity and ferromagnetism. Ferroelctricity and magnetism, however, have contradicting requirements. While magnetism requires d electrons, ferroelectric distortion is suppressed by d electrons. Ferroelectricity also requires that the material crystallize in a noncentrosymmetric space group. It is, therefore, not surprising that this led to an article by Nicola Hill1 in J. Phys. Chem. (2000) entitled “Why Are There So Few Magnetic Ferroelectrics?”. Despite the limitations mentioned above, several multiferroics have been discovered wherein ferroelectricity is induced by ingeneous routes.2−5 Thus, in YMnO3 and related manganites, ferroelectricity results from polyhedral tilting.6 Lone pair (6s) electrons play a role in imparting ferroelectricity in bismuth-containing transition-metal oxides.7 Frustrated magnetism and spiral magnetic ordering induces ferroelectricity in manganese oxides of the type LnMn2O5 (Ln = rare earth) and Tb(Dy)MnO3.3−8 Magnetically induced ferroelectricity in oxides has become an intense area of investigation in the past few years.

In the past few years, several oxides exhibiting multiferroic behavior due to novel types of magnetic interactions, cation charge ordering, and other causes have been reported. A good example of multiferroic oxides based on charge ordering are rare earth ferrites of the type LnFe2O4.10,11 Especially noteworthy are the simple perovskite oxides that unexpectedly show spin-driven ferroelectricity. Some of the recent examples of magnetically induced ferroelctricity are TbMnO3,8 GdFeO3,12 SmFeO3,13 and LnMn2O5.3,14 In this Perspective, we briefly discuss the important features of monophasic multiferroic oxides exhibiting magnetically driven ferroelectricity. We then present the findings on chargeordered oxides including rare earth manganites (LnA1−xMnxO3; A = alkaline earth).15,16 We examine the curious case of BiMnO3, which is the only ferromagnetic oxide reported to be ferroelecric.17,18 Most of the multiferroic oxides reported are antiferromagnetic, with some of them exhibiting canted antiferromagnetism or ferrimagnetism. In this Perspective, we have attempted to present a fair picture of the recent developments in this exciting field. In doing so, we had to limit the number of references due to journal requirements, and we would like to be excused for any omission or error in judgement. Magnetically Induced Ferroelectricity in Manganites. Magnetically induced ferroelectricity arises from the coupling between magnetization and electric polarization. Many interesting aspects of magnetism and the relation of magnetism to ferroelectric polarization in oxides have emerged from recent studies. Thus, the overlap of the electronic wave functions of two atoms with canted spins appears to cause spontaneous electronic polarization.19 Unusual magnetic structures such as the spiral order in some of the rare earth manganites also give rise

It was believed that multiferroics can only be rare because magnetism cannot coexit with ferroelectricity in the same material. Magnetoelectric materials form a smaller subclass of multiferroics. In these materials, there is coupling between the electric and magnetic order parameters, and the application of a magnetic field induces electric polarization. In magnetodielectrics, the capacitance of a material is affected by an external magnetic field. A multiferroic may or may not be magnetoelectric but may exhibit magnetocapacitance. We must note that the magnetodielectric effect can also have a resistive origin arising from the Maxwell−Wagner effect and magnetoresistance.9 © 2012 American Chemical Society

Received: May 28, 2012 Accepted: July 26, 2012 Published: July 26, 2012 2237

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Figure 1. Magnetic-field-induced polarization switching in single crystals of TbMnO3. Variation of the dielectric constant at 10 kHz (a,b) and the electric polarization along the c and a axes (c,d) with temperature, at various magnetic fields applied along the b axis. Reprinted with permission from ref 23, copyright 2003, by the Nature Publishing Group.

magnetic field (≥8 T) along the c direction has a different effect than that along a or b. Application of a magnetic field results in the suppression of ferroelectricity at around 20 K, which is attributed to the magnetic transition from an incommensuarate antiferromagnetic structure to a canted A-type antiferromagnetic state of the Mn spins, which cannot support a lattice modulation with a nonzero wave vector.24,28 At lower temperatures and higher magnetic fields, ferroelectricity again manifests itself due to the development of incommensurate ordering of the Tb and Mn spins.28 Temperature variation of dielectric constant data shows a strong anomaly at the ferroelctric phase transition23 (Figure 1).

to ferroelectric polarization. Multiferroic manganites have been reviewed by a few workers.20−22 We shall briefly present some of the highlights of the multiferroic properties of some of the manganites. In the rare earth manganites of the type LnMnO3 with Ln = Tb or Dy, competition between the nearest-neighbor (NN) ferromagnetic and next-nearest-neighbor (NNN) antiferromagnetic interactions gives rise to complex magnetic structures, with the long-wavelength antiferromagnetic order generating ferroelectricity through lattice modulations induced by magnetoelasticity.23,24 Both ionic and electronic contributions, depending on the spiral plane and octahedral rotations, contribute to the ferroelectric polarization in these manganites.25 Neutron diffraction studies reveal that TbMnO3 undergoes successive magnetic phase transitions upon lowering the temperature.26 The Mn3+ moments exhibit incommensurate antiferromagnetic ordering with a collinear sinusoidal modulation along the b direction at TN (Mn, ∼46 K). Upon further reducing the temperature, transition to a noncollinear spiral spin structure occurs at Tlock (∼28 K). NNN spin exchange, which is enhanced by the orthorhombic GdFeO3-type distortion, causes spiral magnetic ordering, while the Dzyaloshinskii− Moriya interaction and single-ion anisotropy determine the spiral phase.27 Anomalies in heat capacity and magnetization have been observed at around 46 and 28 K, with an additional anomaly at ∼7 K due to sinusoidal ordering of the Tb spins. The spiral magnetic structure at the lock-in transition temperature (28 K) causes the spatial inversion symmetry to be broken and induces spontaneous electric polarization along the c direction of TbMnO3. Upon application of a magnetic field of 4−8 T along the a or b axis, the polarization switches from P∥c to P∥a, as shown in Figure 1. Such magnetic-field-induced ferroelctric polarization switching demonstrates the presence of strong coupling between magnetism and polarization. Application of a large

Of the mechanisms responsible for multiferroicity in oxide materials, magnetism-induced ferroelectricity is of great interest. DyMnO3 also shows incommensurate to commensurate spin ordering below the Neel temperature (TN(Mn) = 38 K), which induces ferroelctricity and the associated dielctric anomaly. It exhibits magnetic-field-induced polarization switching and a large value of PS ≈ 0.2 μC/cm2 with a magnetocapacitance ratio of ∼500% at 18 K.29 The high value of polarization above the ordering temperature of Dy (6.5 K) arises because of the increased amplitude of the Mn spin spiral.30 Unlike TbMnO3 and DyMnO3, the ground state of GdMnO3 is paraelectric in the absence of a magnetic field. However, application of a low magnetic field of 1 T or more along the b axis induces ferroelectricity with spontaneous polarization along the a axis. The absence of ferroelectricity is attributed to the disappearance of lattice modulation with zero wave vectors below Tlock ≈ 23 K. 2238

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materials exhibit ferroelectricity due to magnetostriction induced by collinear spins in the frustrated magnetic structures. These manganites undergo four sequential magnetic phase transitions with different transition temperatures indicating competing exchange interactions among the Mn spins and interaction between the Mn spins and the Ln moments. Longrange incommensurate sinusoidal antiferromagnetic ordering of the Mn3+/Mn4+ spins (TN = 42−45 K) followed by a ferroelectric transition at a lower temperature (TN1 = 38−41 K) is observed due to the commensurate antiferromagnetic ordering that is almost collinear. One also observes a re-entrant transition into the incommensurate sinusoidal phase in the temperature range of 20−25 K and finally antiferromagnetic ordering of the rare earth ions below ∼10 K. Very strong coupling between magnetism and electric polarization is exhibited by TbMn2O5, which shows highly reversible flipping of the spontaneous ferroelectric polarization at 3 K with the periodic variation of the external magnetic field between 0 and 2 T.14 This magnetic-field-induced polarization switching phenomenon is also accompanied by a giant magnetocapacitance effect14 (Figure 3). DyMn2O5 also shows successive

Figure 2. Magnetoelectric phase diagram of TbMnO3 with the magnetic field along the a, b, and c axes. Circles, triangles, and diamonds indicate the dielectric constant, pyroelectric (or magnetoelectric) current, and magnetization data, respectively. Open and closed symbols indicate the data obtained with decreasing temperature (or increasing magnetic field) and increasing temperature (or decreasing magnetic field), respectively. Gray regions represent the ferroelectric states. Reprinted with permission from ref 24, copyright 2005, by the American Physical Society.

In Figure 2, we show a typical phase diagram,24 representing the magnetic-field-induced changes in the dielectric and ferroelectric properties of TbMnO3. Solid solutions of the type Ln1−xYxMnO3 (Ln = Eu, Gd) also exhibit remarkable multiferroic behavior accompanied by complex magnetic structures and ferroelctricity.31 Besides rare earth manganites of the type LnMnO3, there are other manganites showing ferroelectric polarization induced by magnetic interactions. LnMn2O5 (Ln = Tb, Dy, Ho, Y) type

Figure 3. Variation of (a) dielectric constant and (b) electric polarization of TbMn2O 5 as a function of magnetic field at 3 and 28 K; (c) highly reversible 180° polarization reversal at 3 K along the b axis induced by magnetic fields periodically varying between 0 and 2 T along the a axis. Reprinted with permission from ref 14, copyright 2004, by the Nature Publishing Group.

phase transitions associated with reordering of the spin state in the temperature range of 43−4 K, accompanied by three 2239

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ferroelectric phases (TC = 40, 28, and 13 K) and the lowestlying re-entrant paraelectric phase.32 An interesting feature of this oxide is the induction of ferroelectric polarization in the paraelectric ground state upon application of a magnetic field of 1.5−2.5 T. This observation shows that the ferroelectric phases are strongly coupled to the antiferromagnetic Mn d electron spins with the large exchange striction affected by the f−d exchange interaction.32 The magnetic-field-induced ferroelectric polarization is the cause of the large magnetodielectric effect exhibited by DyMn2O5. DyMn2O5 exhibits a very large change in the dielectric constant of ∼109% (field-cooled, FC) and ∼90% (zero-field-cooled, ZFC) at 3 K by the application of 7 T, compared to the Tb and Ho analogues.33 The net P in these manganites is composed of two collinear components,34 one appearing below TC and another below TN1, where these two components are parallel to each other for HoMn2O5 and antiparallel for Tb(Dy)Mn2O5.34 The case of geometric ferroelectrics as exemplified by the hexagonal manganites YMnO3 and LuMnO3, wherein octahedral tilting gives rise to ferroelectricity, was mentioned earlier. These materials exhibit large magnetoelectric coupling accompanying the large atomic displacements. Among the other manganese oxides exhibiting ferroelectricity, CaMn7O12 is interesting. In this material, improper ferroelectricity is induced by the incommensurate helical magnetic structure below TN (90 K). One observes large polarization due to ferroaxial coupling.35 Magnetically Induced Ferroelectricity in Ferrites and Chromites. In the quest for magnetically induced multiferroics, rare earth orthoferrites and orthochromites would be expected to be good candidates for exploration. Among the rare earth orthoferrites, GdFeO3 is an example of a magnetic ferroelectric. The ferroelectric state is realized in the distorted orthorhombic perovskite, GdFeO3, at a low temperature (∼2.5 K) through a different mechanism.12 The polar state in GdFeO3 at the antiferromagnetic ordering temperature of Gd ions (TN = 2.5 K) is the result of spin-exchange striction between the Gd and Fe ions. The mutual controllability of the magnetization and polarization with the electric and magnetic fields shown in Figure 5

Figure 5. (a) Change in the electric polarization of GdFeO3 with the magnetic field at 2.2 K; the ferromagnetic component of magnetization is repeatedly reversed by changing the magnetic field between −1.5 and 1.5 kOe. (b) Change in the magnetization of GdFeO3 with the electric field at 2 K; the electric polarization is repeatedly reversed by changing the electric fields between −15 and 15 kV/cm. Reprinted with permission from ref 12, copyright 2009, by the Nature Publishing Group.

Dy3+ and Fe3+ layers with antiferromagnetic components gives rise to ferroelectric polarization in DyFeO3.36 SmFeO3 is reported to be a multiferroic at room temperature. Although SmFeO3 crystallizes in the centrosymmetric orthorhombic crystal structure, it exhibits improper ferroelctricity, with an onset temperature coinciding with TN (670 K).13 The magnetic structure of SmFeO3 consists of two nonequivalent Fe spin pairs, resulting in canted antiferromagnetism. Ferroelectricity in this ferrite was attributed to spin−orbit coupling driven inverse Dzyaloshinskii−Moriya-type antisymmetric mechanism, wherein the two nonequivalent canted AFM spin pairs are coupled, noncollinearly interacting with each other. It now appears that exchange striction is mainly responsible for the polarization in SmFeO3 as well.13 The appearance of the polar state shown in Figure 4 at the magnetic ordering temperature suggests that SmFeO3 is a magnetically driven ferroelectric. AlFeO3, GaFeO3, and their solid solutions crystallize in the noncentrosymmetric Pna21 structure, wherein there are four cationic sites Fe1, Fe2, Al(Ga)2, and Al(Ga)1, of which the first

Figure 4. Variation of the ferroelectric polarization along [010] with temperature in SmFeO3. Reprinted with permission from ref 13a, copyright 2011, by the American Physical Society.

is explained in light of the composite structure of the domain wall, which is a combination of ferroelectric as well as ferromagnetic domains.12 Exchange striction between adjacent 2240

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three are octahedral. They are collinear ferrimagnets with Néel temperatures in the 210−250 K range.37 Cationic disorder is prominent in these oxides. They exhibit the magnetodielectric effect.38 Studies based on pyroelectric current measurements indicate a maximum at around 100 K (below TN) due to possible appearance of ferroelectricity, as shown in Figure 6.39

Figure 7. (a) Temperature dependence of the FC magnetization data of SmCrO3 at 100 Oe. (b) Temperature dependence of the electric polarization (P) at +1.43 and −1.43 kV/cm. The inset in (b) shows the variation of the pyroelectric current with temperature at +ve and −ve poling fields. (From ref 42.)

earth ferrites, LnFeO3, with magnetic Ln (as in SmFeO3) to exhibit ferroelectricity at TN. Mandal et al.43 have observed magnetoelectric and magnetodielectric effects in YFe1−xMnxO3 (0.1 ≤ x ≤ 0.4). These oxides exhibit a spin-reorientation transition at a temperature TSR, which increases with x while the TN decreases. The magnetodielectric effect is found at TSR as well as TN (Figure 8a), but ferroelectricity occurs at a lower temperature (Figure 8b). Thus, when x = 0.4, TSR = 320 K, TN = 370 K, and the ferroelectric transition is at around 115 K. Recent studies of Sundaresan and Rajeswaran in this laboratory show that perovskite oxides of the type LnA1−xBxO3 (Ln = Y, La, Lu), where A and B are transition-metal ions (Fe, Cr, Mn), become ferroelectric at TN. The TN and hence the ferroelectric transition temperature can thus be varied depending on the A-site ion and the composition of the B-site. Ferroelectric polarization in these oxides is attributed to the nonequivalent disordered spins of these canted AFM oxides. It is noteworthy that adjacent atoms with canted antiferromagnetism coupled in a cycloidal spiral spin structure are expected to give rise to ferroelectric polarization22 (Figure 9). This finding enlarges the scope of finding more multiferroic and magnetoelectric oxides. Other Transition-Metal Oxides. Besides the above groups of oxides exhibiting spin-driven ferroelectricity, several other transition-metal oxides are found to exhibit multiferroic and magnetodielectric properties. Thus, CuO with a monoclinic C2/c structure is reported to become ferroelectric at 230 K.44 The delafossite CuFeO2 becomes ferroelectric upon partial substitution of Fe by Rh, with the dielectric maximum coinciding with the Néel temperature.45 In YBaCuFeO5, a dielectric anomaly is observed near the incommensurate to commensurate antiferromagnetic transition due to magnetically induced electric polarization.46 FeCr2O4 and CoCr2O4 spinels show polarization anomalies at the ferrimagnetic transition.47 There is a relation between the distortion due to Jahn−Teller Fe2+ and the large polarization value at low temperatures in the case of FeCr2O4. The CdV2O4 spinel with a collinear magnetic structure is also multiferroic.48 Magnetoelectric and magnetodielectric effects have been reported in FeVO4.49 A study of Ising chain magnetism and ferroelectricity in monoclinic Ca3CoMnO6 has shown the inequivalence of the Co−Mn distances to be responsible for

Figure 6. Temperature variation of the electric polarization (P) of AlFeO3 with +1 and −1 kV/cm poling along with the effect of a 4 T magnetic field. (Inset) The variation of the pyroelectric current (corrected for leakage current) with temperature, showing a maximum at around 100 K. (From ref 39.)

The unit cell parameters as well as some of the Raman bands of AlFeO3 do show anomalies around this temperature.37,40 The origin of ferroelectricity could be the noncentrosymmetric magnetic ordering arising from the inherent magnetic frustration. There are, however, some questions about the ferroelectric nature (below TN) of AlFeO3 and GaFeO3, suggested to occur on the basis of pyroelectric measurements, but then, we observe substantial polarization in addition to magnetoelectric and magnetodielectric properties. It is noteworthy that some of the hexaferrites have been recently found to exhibit the magnetoelectric effect because of magnetic frustration at room temperature and low magnetic fields.41 A typical example of such a hexaferrite is Sr3Co2Fe24O41. The hexaferrites may find practical applications.

Several manganites, ferrites, and chromites have been found to exhibit magnetically driven ferroelectricity. Rare earth orthochromites, LnCrO3, have been investigated for possible ferroelectricity. 42 These chromites with a centrosymmetric orthorhombic structure exhibit antiferromagnetic ordering with weak ferromagnetism in the 120−300 K range. Interestingly, the chromites with a magnetic rare earth Ln (Ln = Sm, Gd, Tb, Tm) become ferroelectric at the TN(Cr) as shown in Figure 7. The cause of the ferroelectricity is considered to lie in the interaction between the magnetic Ln ion and the ferromagnetic moment of the Cr ion. The underlying mechanism could, however, be complex. On the basis of the results of LnCrO3, we would expect all of the rare 2241

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Figure 9. Schematic representation of spin-canting-induced changes in the local electric polarization in (a) counterclockwise (CCW) cycloidal spiral, (b) clockwise (CW) cycloidal spiral, and (c) normal canted antiferromagnetic66 structures. The difference between the dark green and the light green dots represents the shift of oxygen ions due to the spin canting between the two neighboring spins. The resultant change of the local electric polarization is shown by blue arrows (ΔP). Reprinted with permission from ref 22, copyright 2007 by Annual Reviews. Figure 8. (a) Temperature dependence of (a) FC magnetization data of YFe0.6Mn0.4O3 at 100 Oe and 50 kOe, exhibiting a change in the spin-reorientation temperature (TSR) and (b) the dielectric constant at 0 Oe and 50 kOe, exhibiting a magnetocapacitance effect in YFe0.6Mn0.4O3. The insets show dielectric constant anomalies near TSR and TN. (b) Variation of ferroelectric polarization (P) in YFe0.6Mn0.4O3 with temperature at positive and negative poling fields. (Inset) The effect of the magnetic field on the ferroelectric polarization. Reprinted with permission from ref 43, copyright 2011, by the American Physical Society.

ordering and also electrical polarization at the ferrimagnetic transition (Figure 10a); these oxides also show a magnetodielectric effect10,11 (Figure 10b). An interesting charge-ordered oxide system that has been investigated is that of rare earth manganites. Efremov et al.16 have proposed that charge-ordered manganites can be classified into bond-centered (BCO) and site-centered (SCO) systems (Figure 11). For certain compositions, for example, Pr0.6Ca0.4MnO3, the ground state is ferroelectric. These manganites show dielectric anomalies around the charge-ordering temperature.57 Magnetic fields markedly affect the dielctric properties of Pr0.6Ca0.4MnO3, suggesting coupling between magnetization and polarization. In order to see whether magnetoresistance has any effect on the magnetocapacitance, investigations have been carried out on the highly insulating Y1−xCaxMnO3 (x = 0.4, 0.45, 0.5), where the charge-ordered state is very robust and is not affected even by high magnetic fields (>10 T). These oxides also show dielectric constant maxima at around the charge-ordering temperature as well as magnetocapacitance (Figure 12).58 Application of an electric field is known to melt the charge-ordered state of manganites into the metallic magnetic state.5,15 Upon applying an electric field, charge-ordered manganites are found to emanate a magnetic flux. These manganites exhibit secondharmonic generation as well. Occurrence of ferroelectricity in charge-ordered half-doped manganites has been discussed on the basis of theoretical simulations.59 Curious Case of BiMnO3. Among the bismuth compounds, BiFeO3 is well-known as a multiferroic with a ferroelectric transition at 1100 K and antiferromagnetic transition at 643 K. There have been extensive studies on BiFeO3 and compounds

ferroelectricity.50 A dielectric anomaly has been found at the magnetic ordering temperature of CoV2O6 as well.51 In monoclinic MnWO4 with a spiral magnetic order, the multiferroic state occurs at low temperatures.52 Charge-Ordered Oxides. One of the most well-known chargeordered materials is magnetite, Fe3O4. This oxide itself is magnetoelectric at 4.2 K, as shown by Rado et al. several years ago.53 There is some evidence for the occurrence of ferroelectricity in the low-temperature noncentrosymmetric triclinic phase of Fe3O4.54 According to the model of Brink and Khomskii,55 alternate arrangement of Fe2+ and Fe3+ ions along with alternating long and short Fe−Fe bonds along the b direction of the monoclinic cell results in polarization. A mechanism of ferroelectricity in the Verwey structure of magnetite in terms of three-site distortions, “trimerons”, where the localized electrons are distributed over linear three-Fe-site units, has also been proposed.56 The trimerons together with off-center atomic displacements in the charge-ordered phase give rise to electrical polarization, which couples with magnetization. Oxides derived from Fe3O4 such as LnFe2O4 (Ln = Y, Yb, Lu) show charge 2242

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Figure 12. (a) Variation of the dielectric constant data of Y0.5Ca0.5MnO3 with temperature at different frequencies. (b) Effect of magnetic fields on the temperature dependence of dielectric constant of Y0.5Ca0.5MnO3 at 10 kHz. Reprinted with permission from ref 58, copyright 2009, by Elsevier.

antiferromagnetic along with weak ferromagnetic order at 114 K and is antiferroelectric at room temperature.61 Because of the influence of the stereochemically active 6s lone pair, BiMnO3 was predicted to be ferroelectric.7 BiMnO3 would be one of the very few multiferroics that is ferromagnetic (TC = 450 K). EuTiO3 is reported to become a ferromagnetic multiferroic at very low temperature upon application of stress. Ferroelectricity in BiMnO3 was reported some time ago, but the observed polarization was small.17 The magnetoelectric nature of BiMnO3 has also been demonstrated.18 Doubts about the ferroelectricity of BiMnO3 arose because the experimentally observed and theoretically predicted space group is centrosymmetric, C2/c. Pair distribution function analysis, however, showed that BiMnO3 contains domains corresponding to P21 and P2 space groups, whose atomic shifts break the symmetry of the C-center.62 Because BiMnO3 is prepared under high pressures, the sample generally contains some impurity phases. A careful synthesis paying attention to stoichiometry carried out by Sundaresan et al.63 showed that the structure as well as magnetic and dielectric properties were dependent on the oxygen stoichiometry. Recently, Midgley and co-workers64 have carried out a convergent beam electron diffraction (CBED) study of BiMnO3 with differing oxygen stoichiometries. From the CBED patterns, they found that BiMnO2.99 and BiMnO2.94 both belong to the noncentrosymmetric space groups of Pmn21 and Cmc21, respectively, as shown in Figure 13. It appears that the BiMnO3 compositions with oxygen deficiency crystallize in noncentrosymmetric space groups, consistent with the

Figure 10. (a) Temperature dependence of the ferroelectric polarization of LuFe2O4. Reprinted with permission from ref 10, copyright 2005, by the Nature Publishing Group. (b) Temperature dependence of dielectric constant data of YFe2O4 measured at 0, 1, and 2 T at a frequency of 1 kHz. (Inset) The dielectric data measured at 100 kHz. Reprinted with permission from ref 11, copyright 2008, by the American Institute of Physics.

Figure 11. Different types of charge ordering: (a) site-centered charge order; (b) bond-centered charge order; and (c) a ferroelectric state. Green arrows indicate the dipole moments of horizontal and vertical dimers, and the diagonal arrow is the net spontaneous polarization. Reprinted with permission from ref 16, copyright 2004, by the Nature Publishing Group.

where Bi and Fe have been substituted partly by other cations. BiFeO3 has an incommensurately modulated spin structure. Room-temperature electronic conductivity has been found at the ferroelectric domain walls of BiFeO3.60 BiCrO3 becomes 2243

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magnetically driven ferroelectricity, is quite impressive. It is indeed likely that many transition-metal oxides with fascinating polar and magnetic properties will be discovered in the future, as exemplified by the high-pressure polar corundum phase of ScFeO3, which exhibits weak ferromagnetism.66 Interestingly, hexagonal LuFeO3 is a high-temperature ferroelectric just like YMnO3.67 It appears that there is yet need to unravel the origin of ferroelectricity in many of the oxides such as LuFe2O4.68,69 Oxide materials such as the hexaferrites, which exhibit multiferroic properties at room temperature, would be of great value in terms of applications.70 It would be worthwhile to look for ferromagnetic multiferroics, which are rare. Because the magnetic transition temperature and hence the ferroelectric transition temperature in some of the perovskite oxides can be varied by tuning the constituent rare earth or transition-metal ions, it may be possible to generate multiferroics operating over a wide range of temperatures. In terms of theory, it would be important to know whether the multiferroic properties of rare earth orthochromites, manganites, and ferrites have some commonality. Other mechanisms of inducing ferroelectricity such as charge ordering and the lone pair effect can also be exploited to design multiferroics. A noteworthy aspect relates to the multiferroic properties of nanoparticles of BaTiO3.71 Nanoparticles of BaTiO3 exhibit room-temperature ferromagnetism just like all other inorganic nanostructures. It appears that magnetism in these nanoparticles couples with ferroelectricity. It would be worth exploring nanomultiferroics.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: (+91) 80-2208-2760. Webpage: http://www.jncasr.ac.in/cnrrao/. Notes

The authors declare no competing financial interest. Biographies C. N. R. Rao is National Research Professor and Linus Pauling Research Professor at Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR). His main interests are in materials chemistry. He is a member of several science academies including the U.S. National Academy of Sciences. He is the recipient of the Royal Medal of the Royal Society of London, the Dan David Prize for materials research, and the August Wilhelm von Hoffmann medal of the German Chemical Society. http://www.jncasr.ac.in/cnrrao/

Figure 13. (a) Precession electron diffraction patterns from the orthorhombic phase of BiMnO2.94, recorded parallel to a) [001], b) [01−1], c) [010], and d) [10−1] zone axes. (b) Convergent beam electron diffraction (CBED) patterns of BiMnO2.99 recorded parallel to the a) [010] and b) [100] zone axes. Reprinted with permission from ref 64, copyright 2011, by the Royal Society of Chemistry.

A. Sundaresan obtained his Ph.D. degree from the Indian Institute of Technology Bombay and did postdoctoral work in Tsukuba, Caen, and Grenoble before joining JNCASR. He is an associate professor at JNCASR, where he works on oxide materials and magnetism. He is the recipient of medals of the Materials and Chemical Research Societies of India.

occurrence of ferroelectricity. These phases are also ferromagnetic. BiMn7O12, which is antiferromagnetic, is found to show a magnetodielectric effect.65

Rana Saha obtained his B.Sc. degree in chemistry from the University of Calcutta and his M.S. degree in materials science from JNCASR. He is carrying out his Ph.D. studies on multiferroics at JNCASR.

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A good room-temperature ferromagnetic magnetoelectric would find many uses.

REFERENCES

(1) Hill, N. A. Why Are There So Few Magnetic Ferroelectrics? J. Phys. Chem. B 2000, 104, 6694−6709. (2) Ramesh, R.; Spaldin, N. A. Multiferroics: Progress and Prospects in Thin Films. Nat. Mater. 2007, 6, 21−29. (3) Cheong, S.-W.; Mostovoy, M. Multiferroics: A Magnetic Twist for Ferroelectricity. Nat. Mater. 2007, 6, 13−20. (4) Eerenstein, W.; Mathur, N. D.; Scott, J. F. Multiferroic and Magnetoelectric Materials. Nature 2006, 442, 759−765.

Outlook. The preceding discussion should clearly indicate that multiferroics are not as few and far between as expected a decade ago. The discovery of several monophasic multiferroic and magnetoelectric oxides in the past few years, exhibiting 2244

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