Ferroelectricity at the Néel Temperature of Chromium in Rare-earth. Orthochromites: Magnetic Jahn-Teller Effect

Transcription

1 Ferroelectricity at the Néel Temperature of Chromium in Rare-earth Orthochromites: Magnetic Jahn-Teller Effect B. Rajeswaran 1, D. I. Khomskii 2, A. Sundaresan 1 and C. N. R. Rao 1 1 Chemistry and Physics of Materials Unit and International Centre for Materials Science, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore , India 2 II. Physikalisches Institut, Universität zu Köln, Zülpicher Strasse 77, Köln, Germany sundaresan@jncasr.ac.in Abstract Rare-earth orthochromites RCrO 3 (R=rare-earth), with centrosymmetric orthorhombic structures (Pnma), exhibit antiferromagnetic ordering of the Cr 3+ moments (T N = K) with weak ferromagnetism. We demonstrate that below T N these perovskites become ferroelectric with fairly large spontaneous polarization ~ µc/cm 2 only when the rare-earth ion is magnetic (R = Sm, Gd, Tb and Tm), indicating the crucial role of magnetic interactions between R 3+ and Cr 3+ ions in inducing ferroelectric polarization. We suggest that ferroelectricity occurs in rare-earth orthochromites and orthoferrites containing magnetic rare-earths due to the instability of the symmetric position of rare earths ions in the exchange field of Cr(Fe) the magnetic analog of Jahn-Teller effect.

2 Magnetoelectric multiferroics constitute an emerging class of novel materials that combine coupled electric and magnetic dipole orders. 1-6 Interaction between the two order parameters leads to magnetoelectric effect, which gives rise to magnetization on application of an electric field or to electric polarization on applying a magnetic field. Coupling between magnetic and ferroelectric order is generally strong in the so-called type-ii materials where the ferroelectricity arises due to magnetic interactions. 4 Thus, a cycloidal spin structure below the spiral magnetic ordering of Mn 3+ ions in the centrosymmetric orthorhombic TbMnO 3, 5,6 and collinear magnetic ordering with E- type magnetic structure in HoMnO 3 7 break the inversion symmetry causing net electric polarization. In cycloidal-spin induced ferroelectricity, the antisymmetric spin-exchange (S i S j ) plays a key role in producing the electric polarization, the driving force to induce the polarization in these spiral magnets being the inverse Dzyaloshinskii-Moriya (DM) effect. 8 In other cases, including collinear structures, the mechanism of multiferroic behavior could be magnetostriction. 2,4,19 It has been shown recently that the canted antiferromagnet SmFeO 3 exhibits multiferroicity at the magnetic ordering temperature of iron (T N = 670 K). 11 This is surprising because the spin-current or the inverse DM interaction model for such a canted antiferromagnetic system suggests zero net polarization because local polarization cancels out due to the alternate arrangement of pairs of canted spins. 5,8 We believe that magnetic interaction between Sm 3+ and canted moments of Fe 3+ ions may play a crucial role in inducing net polarization in this oxide. The presence of such magnetic interactions is indicated by the occurrence of spin-reorientation in this, as well as in other rare-earth orthoferrites (RFeO 3 ), where anisotropic magnetic interactions between R 3+ and Fe 3+ ions induce rotation of the ordered Fe 3+ spins from

3 one crystallographic direction to another. 12,13 This is consistent with the fact that such spin reorientation does not occur in orthoferrites with nonmagnetic A-site cation as in YFeO 3. We, therefore, suggest that magnetic interactions between Sm 3+ and Fe 3+ ions may be responsible for inducing net ferroelectric polarization in SmFeO 3, and that ferroelectric polarization should also be observed in other rare-earth orthoferrites and orthochromites with magnetic R-ions. Accordingly, orthoferrites with a nonmagnetic R-ions should not show net polarization at the magnetic transition. Since the high Néel temperature of RFeO 3 (T N = K) makes it difficult to carry out polarization measurements due to the high leakage current, we have chosen isostructural rare-earth orthochromites (RCrO 3 ) which have similar magnetic properties with T N values of K. In the orthochromites with the orthorhombic structure (Pnma), 13* the following three types of G-type antiferromagnetic configuration are observed: Γ 1 (G x, C y, A z ), Γ 2 (C x, G y, F z ) and Γ 4 (A x, F y, G z ) following the Bertaut notation, 14 (or Γ 1 (A x, G y, C z ), Γ 2 (F x, C y, G z ) and Γ 4 (G x, A y, F z ) in Pbnm setting) 15. The first configuration does not allow weak ferromagnetism but the second and third have weak ferromagnetism along the z and y-directions, respectively. When the R-ion is nonmagnetic, the ground state magnetic structure of orthochromite is described by the configuration Γ 4 (A x, F y, G z ). If the R-ion is magnetic, then the spin configuration below T N can be Γ 2 or they undergo a temperature-induced spinreorientation from Γ 4 to Γ The spin configurations of Γ 4 and Γ 2 are shown in Fig. 1. We have investigated magnetic and electrical properties of the orthochromites containing magnetic rare-earth ions such as Sm 3+, Gd 3+, Tb 3+ and Tm 3+, and nonmagnetic Lu 3+ and Y 3+ in the A site. We have observed ferroelectric polarization

4 at T N in orthochromites containing magnetic R 3+ ions, but no ferroelectricity when the A-site cation is nonmagnetic. Polycrystalline samples of RCrO 3 (R=Sm, Gd, Tb, Tm, Lu and Y) were prepared by the solid state reaction of stoichiometric quantities of R 2 O 3 and Cr 2 O 3 at 1673K for 12 hours followed by several intermittent grinding and heating. Phase purity was confirmed by Rietveld refinement on the X-ray powder diffraction data collected with Bruker D8 Advance diffractometer. These compounds crystallize in a distorted orthorhombic structure with the space group Pnma. Magnetic measurements were carried out with a vibrating sample magnetometer (VSM) in the physical property measurement system (PPMS) of Quantum Design, USA. Pyroelectric measurements were carried out with 6517A Keithley electrometric resistance meter for measuring current. In this measurement, first the sample was poled by applying an electric field of kv/cm and kv/cm at a temperature (greater than T N ) and then the sample was cooled down to low temperatures under the applied field. After shorting the circuit for a reasonably long duration, the current was measured using the electrometer while warming the sample to a temperature higher than the T N at a rate of 4 K/min. Upon integrating the pyrocurrent with respect to time and dividing it by the area of the sample, we obtain electric polarization, which can be plotted as a function of temperature. In Figure 2(a), we show the temperature dependence of magnetization of SmCrO 3 under field-cooled conditions with an applied field of 100 Oe. The observed behaviour is characterisitic of canted antiferromagnetic ordering of Cr-moments (T N = 197 K). The drop in magnetization below 25 K is due to spin-reorientation where the

5 Cr-spin configuration changes from Γ 4 (A x, F y, G z ) to Γ 2 (C x, G y, F z ). Spinreorientation in orthoferrites and orthochromites is known to be brought about by anisotropic magnetic interactions between R 3+ and Fe/Cr ions Figure 2 (b) shows electric polarization of SmCrO 3 (P ~ ± 0.47 µc/cm 2 at T = 60 K for E = ±1.43 kv/cm) obtained from pyroelectric measurements. This figure clearly demonstrates the development of the spontaneous electric polarization in the vicinity of the magnetic ordering temperature of Cr and confirms that the polarization is switchable and induced by magnetism. It is important to note that the observed polarization values are relatively higher than those reported in most of the magnetically induced ferroelectric materials. 2,17,18 The inset in figure 2 (b) shows the pyroelectric current peaks around T N. We find ferroelectric polarization at T N = 167 K for GdCrO 3 (P ~ ±0.6 µc/cm 2 at T = 60 K for E = ±2.25 kv/cm) as shown in Fig. 3. We also find ferroelectric polarization at T N = 157 K for TbCrO 3 (P ~ ±0.21 µc/cm 2 at T = 60 K for E = ±1.43 kv/cm (see Fig. S1 in the Supplementary material)). In TmCrO 3, in addition to ferroelectric polarization at 127 K (P ~ ±0.04 µc/cm 2 at T = 127 K for E = ±1.43 kv/cm and P ~ ±0.20 µc/cm 2 at T = 60 K for E = ±1.43 kv/cm), we also observe a temperature-induced magnetization reversal with a compensation temperature (T * ) of 25 K indicating that the Tm and canted Cr moments are coupled antiferromagnetically, similar to SmFeO It should be noted that the rare-earth moments do not order magnetically down to the lowest temperature measured. We also observe dielectric anomalies near T N for SmCrO 3 as shown in Fig. S2. Figure 4 shows the magnetization data of orthochromites, LuCrO 3 and YCrO 3 with nonmagnetic A-site cation. It is important to note the insets of this figure where we do not observe pyroelectric current peaks near the magnetic ordering temperature thereby

6 confirming the absence of ferroelectric polarization in these materials. These results establish that the presence of a magnetic rare earth ion at the A-site is crucial for the occurence of ferroelectricity at the magnetic ordering of Cr 3+ in RCrO 3. Based on symmetry analysis of magnetoelectric interactions in rare-earth orthoferrites and orthochromites, it has been shown that the spontaneous electric polarization or magnetic-field-induced polarization appears at the magnetic ordering temperature of rare-earth ions, 15 and this effect was found experimentally in GdFeO Therefore, this mechanism may not directly account for the spontaneous electric polarization originating at the magnetic ordering of Cr 3+ ions. We suggest that an induced magnetization of the rare-earth ions by the local field produced by the ordering of Cr 3+ moments may lead to an effect similar to that due to spontaneous long-range ordering of R 3+ R ions below their transition temperatures (T N ~ 2.3, 5, 3, 5 K for Gd, Sm, Tb and Tm, respectively) As argued in 19, in the Pnma (or Pbnm) structure the molecular field produced on R ions by the strongest G- type ordering of transition metal (TM) ions (Fe, Cr) cancel, H exch =0. Consequently, RE ions remain paramagnetic, i.e. their spin states are degenerate (we ignore here weak induced polarization produced by the F- and C-ordering of TM). We propose that this degeneracy is lifted by the spontaneous distortion the shift of R ions, which would produce the disbalance of contributions to the exchange field on R from two TM G-sublattices. This would give a nonzero effective field acting on R ions H exch ~ gδ<s TM >, where δ is the shift of R ions e.g. in the z-direction, g ~ J/ r is the coupling constant, and <S TM > is the average magnetization of TM (here Cr). The corresponding Zeeman splitting or R spin states would give (at low temperatures) an energy gain E = - H exch S RE = - gδ<s TM > S RE. This energy gain is linear in

7 distortion δ, and it will overcome the elastic energy loss E el = Bδ 2 /2, giving rise to a finite displacement δ = g<s TM > S RE /B, and in effect producing polarization P ~ gδ. This effect is thus very similar to the usual Jahn-Teller effect in TM compounds (see e.g. 23 ) the lifting of the (here magnetic) degeneracy by lattice distortion reducing symmetry. Thus we have here the magnetic analogue of the Jahn-Teller effect, or simply magnetic Jahn-Teller effect (MJTE). 24 In effect this lattice distortion, giving rise to ferroelectric state, occurs not only in the presence of long-range magnetic ordering of both R and TM sublattices, but due to this MJTE also occurs spontaneously when only the TM subsystem (Cr, Fe) is ordered, i.e. at much higher temperatures, as found above. The mechanism producing electric polarization in this case is the magnetoelastic coupling (according to the arguments presented above P ~ J/ r), which can explain rather large values of polarization (the obtained values are ~ µc/cm 2 -- and that in polycrystalline samples; one could think that these values would be even bigger in single crystals). We believe that the same mechanism also operates in SmFeO 3, 11 although the authors of this work have proposed a different explanation. In conclusion, ferroelectricity is observed at the magnetic ordering temperatures of Cr 3+ ions in rare-earth orthochromites (RCrO 3, with R -- magnetic rare-earth ion), with relatively large electric polarization ~ µc/cm 2, starting at rather high temperatures (~ K) corresponding to the Néel temperatures of the Cr subsystem. We propose that the multiferroic behavior of these systems is caused by the interaction between magnetic rare earth and Cr ions, and can be explained by the magnetic Jahn-Teller effect the mechanism that is likely to hold in the case of other rare-earth orthoferrites and orthochromites as well. The same magnetic Jahn-Teller

8 effect could in principle be important also for many other magnetic systems and phenomena, not only for multiferroic behavior. The authors are grateful to P. Mandal for useful discussion and help. The work of D.Kh. was supported by the German programs SFB 608 and FOR 1346, and by the European project SOPRANO.

9 References: [1] W. Eerenstein, N.D. Mathur and J.F.Scott, Nature 442, (2006) [2] S.-W.Cheong and M.V.Mostovoy, Nature Mater. 6, 13 (2007) [3] C.N.R. Rao and C.R. Serrao, J. Mater. Chem. 17, 4931 (2007) [4] D.Khomskii, J.Magn.Magn. Mater. 306, 1 (2006); Physics 2, 20 (2009) [5] T.Kimura, Ann. Revs. of Mater. Res. 37, (2007) [6] Y. Tokura and S. Seki, Adv. Mater. 22, (2010) [7] J. Huang, Y. Cao, Y.Y. Sun, Y.Y. Xue and C.W. Chu, Phys. Rev. B 56, (1997) [8] H. Katsura, N. Nagaosa and A.V. Balatsky. Phys. Rev. Lett. 95, (2005) [9] A. Malashevich and D. Vanderbilt. Phys. Rev. Lett. 101, (2008) [10] H.J. Xiang, S.H. Wei, M.H. Whangbo and J.L.F.D. Silva. Phys. Rev. Lett. 101, (2008) [11] J-H. Lee, Y.K. Jeong, J.H. Park, M-A. Oak, H.M. Jang, J.Y. Son, J.F. Scott. Phys. Rev. Lett. 107, (2011) [12] T.Yamaguchi. J.Phys. Chem. Solids. 35, (1974) [13] G. Gorodetsky and Lionel M. Levinson. Solid State Comm. 7, (1969) [13*] We use in this paper the group Pnma; the transformation of coordinates from Pnma to Pbnm is (x 1 y 2, y 1 z 2, z 1 x 2 ) [14] G. Gorodetsky, S. Shaft, A. Shanlof, B.M. Wanklyn, B. Sharon and I. Yaegar. AIP Conf. Proc. 29 (1976) [15] A.K. Zvezdin and A.A. Mukhin. JETP Letters. 88 (2008) [16] J.B. Goodenough. Rep. Pro. Phys. 67, (2004) [17] M. Kenzelmann et al. Phys. Rev. Lett. 95, (2005) [18] M. Mostovoy. Phys. Rev. Lett. 96, (2006)

10 [19] Y. Tokunaga, N. Furukawa, H. Sakai, Y. Taguchi, T. Arima and Y. Tokura. Nature Mater. 8, (2009) [20] A.H. Cooke, D.M.Martin and M.R.Wells. J.Phys. C. Solid State Phys. 7, (1974) [21] N. Shamir, H. Shaked and S. Shtrikman. Phys. Rev. B 24 (1981) [22] J.B. Gordon, R.M. Hornreich and S. Shtrikman. Phys. Rev. B 3 (1976) [23] K.I.Kugel and D.I. Khomskii, Sov. Phys Uspekhi, 25, 231 (1982) [24] The degeneracy of magnetic subsystem can in principle be lifted not only by lattice distortion, but also by modification of magnetic structure itself (A.K.Zvezdin, A.A.Mukhin and A.I.Popov, JETP Lett. 23, 240 (1976)). Apparently in orthochromites the first mechanism is realized.

11 Figure captions Fig. 1. (Color online) Schematic of Γ 2 and Γ 4 spin structures. As can be seen from the scheme, Γ 2 and Γ 4 structure allow spin canting along the y and z directions respectively. The location of rare earth ions is marked by spheres without spin. Fig. 2. (Color online) (a) Field-cooled magnetization of SmCrO 3 at 100 Oe with respect to temperature. (b) Electric polarization as a function of temperature. Poling is done at two different fields kv/cm(black) and kv/cm( blue). Inset in (b) shows the pyroelectric current as a function of temperature at two different poling fields. Fig. 3. (Color online) (a) Field-cooled magnetization of GdCrO 3 at 100 Oe with respect to temperature. (b) Electric polarization as a function of temperature. Poling is done at two different fields kv/cm(black) and kv/cm( blue). Inset in (b) shows the pyroelectric current as a function of temperature at two different poling fields. Fig. 4. (Color online) (a). Field-cooled magnetization of LuCrO 3 at 100 Oe with respect to temperature. Inset shows the absence of peak in pyroelectric current. (b) Field-cooled magnetization of YCrO 3 at 100 Oe with respect to temperature. Inset shows the absence of peak in pyroelectric current.

12 Fig. 1

13 0.2 SmCrO 3 M(emu/g) (a) 100 Oe T N = 197 K P(µC/cm 2 ) (b) I(pA) kv/cm kv/cm Fig. 2

14 M (emu/g) P(µC/cm 2 ) (a) 100 Oe I(pA) (b) GdCrO 3 T N = 167 K kv/cm kv/cm Fig. 3

15 M(emu/g) M(emu/g) (a) kv/cm kv/cm T (K) I (pa) (b) I (pa) kv/cm kv/cm T (K) LuCrO 3 T N = 120 K YCrO 3 T N = 140 K 100 Oe 100 Oe Fig. 4

16 Supporting Information 2 (a) TbCrO 3 M(emu/g) P(µC/cm 2 ) T N = 157 K Oe (b) kv/cm I(pA) kv/cm S1 (Color online) (a) Field-cooled magnetization of TbCrO 3 at 100 Oe with respect to temperature. (b) Electric polarization as a function of temperature. Poling is done at two different fields kv/cm(black) and kv/cm( blue). Inset in (b) shows the pyroelectric current as a function of temperature at two different poling fields.

17 80 SmCrO ε r tan δ khz S2 (Color online): Temperature dependence of dielectric constant in SmCrO 3. Inset shows the loss as a function of temperature. A small anomaly both in dielectric constant and loss indicate the magnetodielectric effect near T N.