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Predicting room-temperature multiferroic phase of NaLaFeMO6 (M = Ru, Re, Os) with strong magnetoelectric coupling
Journal of Alloys and Compounds 690 (2017) 923e929
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Predicting room-temperature multiferroic phase of NaLaFeMO6 (M ¼ Ru, Re, Os) with strong magnetoelectric coupling Guang Song a, b, *, Guannan Li a, c, Benling Gao a, Feng Liang a, Jun Zhang a a
Department of Physics, Huaiyin Institute of Technology, Huaian, 223003, China Jiangsu Provincial Key Laboratory of Palygorskite Science and Applied Technology, Huaiyin Institute of Technology, Huaian, 223003, China c National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing, 210093, China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 18 May 2016 Received in revised form 29 July 2016 Accepted 21 August 2016 Available online 23 August 2016
Discovering multiferroic materials is one of the most important questions for facilitating devices based on the electric field control of magnetism. The great challenge is to create room temperature multiferroic materials with strongly coupled ferroelectric and ferromagnetic (or ferrimagnetic) orderings. Here we present simple, chemically intuitive design rules to identify a class of bulk magnetoelectric materials based on the “bicolor” layering of P21 double ferrimagnetic perovskites, e.g., NaLaFeMO6 (M ¼ Ru, Re, Os). Using density functional theory calculations, we elucidated the origin of the ferroelectricity and show that it is a general consequence of the layering of any bicolor P21 double ferrimagnetic perovskites. Our calculations showed that the ferroelectric polarization is up to several mC/cm2 and the net magnetic moments are 3, 2, and 3 mB for NaLaFeRuO6, NaLaFeReO6, and NaLaFeOsO6, respectively in these proposed materials. More importantly, we highlighted the existence of a low-energy ferroelectric switching path, along which the magnetization is also likely reversed, evidencing the strong magnetoelectric coupling existing in this system. In addition, the critical temperature of polarization and magnetization are both well above room temperature. It is expected that this work can encourage the designing and experimental implementation of a large class of strong magneto-electric multiferroic materials with large magnetization and electric polarization above room temperature. © 2016 Elsevier B.V. All rights reserved.
Keywords: Ferroelectrics Magnetoelectric coupling Room temperature
1. Introduction Magneto-electric multiferroic materials have been widely studied due to their intriguing coupling between ferroelectricity and magnetism [1e4]. Such materials may, for example, overcome the drawbacks of ferroelectric memory (slow writing), magnetic random access memory (high power density), and open the possibility of four-state memory with reduced energy consumption [4e6]. Due to the antagonistic chemical requirements of the ferroelectricity and magnetism [7], it is particularly difficult to discover new single phase room temperature materials combining large electrical polarization P and large spontaneous magnetization M as well as strong coupling between them. To design such materials, one should address two crucially important issues: (i) the critical temperatures of electrical polarization and magnetization are above room temperature; (ii)
* Corresponding author. Department of Physics, Huaiyin Institute of Technology, Huaian, 223003, China. E-mail address: [email protected] (G. Song). http://dx.doi.org/10.1016/j.jallcom.2016.08.209 0925-8388/© 2016 Elsevier B.V. All rights reserved.
finding a new way to overcome the chemical incompatibility between ferroelectricity and magnetism. In present paper, we show that hybrid improper ferroelectricity (HIF) [8e11], a recently proposed ferroelectric mechanism, can be used to address these two issues. Good examples are that the ubiquitous polar P21 AA0 BB0 O6 double perovskites such as LaLnNiMnO6 (Ln is a rare-earth ion) superlattices [12], whereby the high temperature magnetic ordering originates from the magnetic coupling between different rock salt pattern B and B0 -site transition metal ions with strong super-exchange interaction, and the combination of rotations/tilts of the BO6 and B0 O6 octahedra and A-site cation layering ordering facilitate ferroelectric order. We emphasize that this mechanism discussed here is general to a wide range of materials and different realizations of HIF. In HIF, the large electrical polarization P, which is quite different from the classical ferroelectric materials (always driven by gamma point instability) [8,13], has been identified by specific zone-boundary octahedral tilts in an AA0 BB0 O6 double perovskite block. These tilts are coupled to translational symmetry breaking in layered perovskites [14] and can generate HIF without requiring classical
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zone-center displacements. Here, the spontaneous electric polarization results as noncancellation of the antiferrodistortive displacements associated with the tilt at the interfaces between structural blocks. Because this mechanism relies on a ‘geometric’ effect (e.g. displacements of ions due to bond-coordination preferences and packing), in contrast to antagonistic chemical requirements there are many more potential routes for purposefully inducing and enhancing ferroelectricity by judicious selection of cation species [14,15]. In addition, HIF is no longer just theoretical ideas. For instance, in an exciting development, Oh and co-workers have authenticated polarization switching in Ca3Ti2O7 [11,16], one of the first predicted hybrid improper ferroelectrics. Weak ferromagnet Ca3Mn2O7 that has a similar structure with Ca3Ti2O7, was also predicted to be hybrid improper ferroelectrics [9,17]. Moreover, in this compound, the magnetization was predicted to be coupled with electric polarization when switching the direction of the polarization also results in a 180 deterministic switching of the magnetization. Very recently, Pitcher et al. have shown that the polar double perovskite (CaySr1y)1.15Tb1$85Fe2O7 is endowed with the polarization and magnetization at room temperature and that the polarization is induced by a hybrid improper mechanism [18]. The objective of this study is to looking for multiferroic materials combining both polarization and magnetization at room temperature. Polar P21 double perovskites, such as NaLaFeWO6 [19] and NaLaMnWO6 [20,21], in which the Na and La cation are layering ordering along the crystallographic c axis, while the Fe (Mn) and W cation are rock salt pattern, have been successfully synthesized under high temperature. These double perovskite compounds display the multiferroic behavior with a high ferroelectric transition temperature but a low antiferromagnetic transition temperature. It is suggest that one can enhanced the magnetic interaction in these polar compounds to achieve room temperature multiferroic materials [22]. Based on first-principles calculations, we predicted that polar P21 double perovskites NaLaFeMO6 (M ¼ Ru, Re, Os) are room temperature multiferroic materials. We showed that ferroelectric polarization was up to several mC/cm2 and the net magnetic moments are 3, 2, and 3 mB for NaLaFeRuO6, NaLaFeReO6, and NaLaFeOsO6, respectively. Moreover, there is a low-energy ferroelectric switching path, along which the magnetization is also likely reversed, evidencing the strong magnetoelectric coupling existing in this system. The critical temperature of the polarization and magnetization were both well above room temperature. Our results provide a new way to find strong magneto-electric multiferroic materials with large magnetization and electric polarization above room temperature. 2. Computational methods First-principles calculations were carried out using density functional theory [23] with projector augmented wave (PAW) potentials [24] as implemented in the Vienna ab initio simulation package (VASP) [25]. The PAW potentials explicitly include one valence electron for Na (3s1), 11 for La (4s24p64d15s2), for 14 for Fe (3p63d64s2), 8 for Ru (4d75s1), 13 for Re (5p65d56s2), 8 for Os (5d66s2) and six for O (2s22p4) atoms. The exchange-correlation part is approximated by the PBEsol functional [26], which improves the structural descriptions over standard LDA or GGA [27]. For transition-metal ions, we have included the on-site DMSO-d6 Coulomb interaction parameter U ¼ 5.0, 3.0, 3.0 and 2.5 eV for Fe3þ, Ru5þ, Re5þ, and Os5þ, respectively, and exchange interaction parameter J is fixed at 1.0 eV. To validate the parameter U in our approach, we first investigated the properties of G-type AFM bulk Ca2FeReO6 and Ca2FeOsO6. We correctly reproduced the lattice, electronic, and magnetic properties of ground-state structures of Ca2FeReO6 and Ca2FeOsO6, respectively (see Supplementary
material Table S1 and Fig. S3). The wave function is expanded in a plane wave basis with an energy cutoff of 600 eV. A 6 6 4 Gcentered k-points sampling is used for reciprocal space integrations. We have carefully checked convergence with these settings by testing higher energy cutoffs and larger k meshes. Each self-consistent electronic calculation is converged to 106 eV and the tolerance force is set to 0.005 eV/Å for ionic relaxation. Noncollinear magnetization calculations were performed with L-S coupling, and the electric polarization was calculated using the Berry phase method as implemented in VASP [28]. To calculate the phonon dispersion of NaLaFeMO6, the structures are firstly atomically relaxed with a higher accuracy using the 6 6 4 G-centered k-points sampling and the tolerance force of 0.0001 eV/Å. The phonon dispersion is then calculated using the Phonopy code with a 2 2 2 supercell [29]. The force constants are calculated by VASP using a 3 3 2 G-centered k-points sampling for the supercell. 3. Results and discussions We have used first-principles total energy calculations to consider the complete various structures generating by different plausible combinations of different A-site configures (rock salt, columnar and layered ordering, see Supplementary Material Fig. S4) and BO6 or B0 O6 octahedral rotations for double perovskites NaLaFeMO6 (M ¼ Ru, Re, Os) [30,31]. The lowest energy structure we found has a polar P21 symmetry and it is illustrated in Fig. 1(d) (see Supplementary material Table S2). These materials in this structure displayed both ferroelectricity and ferrimagnetism. Spontaneous ferroelectric polarizations of the NaLaFeMO6 are calculated by Berry phase method, and the calculated results are listed in Table 1. In addition, the direction of polarization is pointing nearly along [010] direction, it should note that there is a small component along [001] direction is found in our calculations (about two orders of magnitude smaller than the [010] direction). At the magnetic level, our collinear spin calculations for NaLaFeMO6 exhibit a G-type ferrimagnetic arrangement with magnetic moment on Fe, Ru, Re, and Os, respectively (as summarize in Table 1). From these results we can concluded that the Fe ion takes the high-spin Fe3þ (d5) valence state. It is also clear that the Ru, Re and Os ions take the high-spin Ru5þ (d3), Re5þ (d2), and Os5þ (d3) valence state, respectively. Thus the net magnetic moments calculated by PBEsol þ U method are 3, 2, and 3 mB for NaLaFeRuO6, NaLaFeReO6, and NaLaFeOsO6, respectively. The symmetry of this P21 can be established by two symmetrylowering structural distortions of P4/nmm double perovskite structure (AA0 BB0 O6) which is the highest symmetry structure compatible with the mentioned order of the A and B sites: an inplane rotation of the BO6 octahedral about the cubic [001] axis and an out-of-phase tilt of the BO6 octahedral about the cubic [110] axis, as shown in Fig. 1(a), (b), respectively. These symmetrybreaking distortions can be distinguished with symmetries labeled as Gþ5 and G1 (see Fig. 1(a), (b)). The Gþ5 and G1 distortion modes can be seen to be essentially two tilting modes of the octahedron framework. Together these two distortions produce the Glazer rotation pattern aacþ [32]. When described with respect to a Pm-3m perovskite (ABO3), their usual labels are Rþ4 and Mþ3 and would give rise to a distorted non-polar structure of Pnma symmetry. Here, the structure of the modes are same, but the cation orderings suggest that the reference parent structure in AA0 BB0 O6 double perovskite structure has a smaller tetragonal symmetry with a larger unit cell, so that they correspond to G modes in this larger tetragonal supercell. It should note that none of these distortions modes give rise to a polar subgroup. Nonetheless, in AA0 BB0 O6 double perovskite these two modes are
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Fig. 1. The monocline NaLaFeMO6 double perovskite, space group P21. The structure, Glazer pattern a-a-cþ, is describe by three symmetrize basis modes of P4/nmm: (a) QRot, in-phase rotation of FeO6 and MO6 octahedra about [001] (G1); (b) QTilt, tilt of FeO6 and MO6 octahedra about [110] (Gþ5); (c) QAFE, antiferroelectric Na and La displacements (G5); (d) the relaxed crystal structure of NaLaFeMO6; (e) The group subgroup tree connecting the paraelectric P4/nmm phase to ferroelectric P21 phase. Yellow, green, gold, grey, and red spheres indicate Na, La, Fe, M, and O atoms, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Table 1 Theoretical optimized atomic lattice parameters of NaLaFeMO6 with a P21 (#4) crystal structures calculated by PBEsol þ U method. The DNa and DLa represent the displace in NaLaFeMO6 for Na and La, respectively. The DFe-O and DM-O represent the bond difference of Fe-O and M-O along the [010] direction, respectively. The P represents the spontaneous polarizations. mFe and mM is the magnetic moment on Fe and M, respectively.
NaLaFeRuO6 NaLaFeReO6 NaLaFeOsO6
DNa (Å)
DLa (Å)
DFe-O (Å)
DM-O (Å)
P (mC cm2)
mFe (mB)
mM (mB)
0.117 0.105 0.115
0.171 0.172 0.175
0.080 0.085 0.085
0.023 0.050 0.025
11.79 2.40 10.99
4.13 4.08 4.12
1.83 1.33 1.95
sufficient to reduce the symmetry (P4/nmm) to P21 phase, which allows the presence of a secondary induced polar distortion. It can be seen that the intersection of the two mentioned isotropy subgroups is the observed P21 group, as it is their largest common subgroup. This means that the combination of these two tilting modes is able to induce a polar phase (although they do not produce a polarization by themselves). It must be stressed that the original Rþ4 and Mþ3 unstable modes in pure Pm-3m perovskites preserve in all cases a non-polar Pnma symmetry. It is only the fact that the cation ordering reduces the parent high symmetry (Pm3m) to P4/nmm, which permits, in the family of these compound, that two typical unstable non-polar perovskite tilting modes produce a polar structure, and, as a consequence, an improper ferroelectric. Let us move our focus another distortion mode in polar P21 phase labeled G5 (Xþ5 in Pm-3m perovskite). As shown in Fig. 1(c) it is a polar mode frozen, which is responsible for spontaneous ferroelectric polarization present in the family of these compounds [12,21,33,34]. The atomic displacements for this mode are mostly along the crystallographic [110] direction (polar axis). Na and La atoms displace in opposite directions (antipolar displacements)
and the calculated results of the displacements are listed in Table 1. It can be elucidated that the two rotation distortions QRot (Gþ5) and QTilt (G1) are break inversion symmetry at the A and A0 -site of the P4/nmm structure, whereas the A/A' cation layering ordering breaks B and B0 -site inversion symmetry. As a result, the A cation displacements are no longer equal in magnitude thus cause a macroscopic polarization (see Table 1). More interesting, these antipolar displacements are trilinearly coupled to the two rotation distortions in the free energy of the P4/nmm structure, F ¼ QAFEQRotQTilt, where QAFE (G5), QRot, and QTilt are the amplitudes of the antipolar distortions, rotation, and tilt, respectively. It indicates that reversing the sense of either rotation or tilt will affect the antipolar displacements QAFE. Another fact is that the magnetic properties are coupled with the QRot distortion in P21 double perovskites, and hence the sense of this particular rotation and the magnetism are naturally coupled in nontrivial way. If one of the rotations/tilts can be switched by the macroscopic polarization, then the magnetism can be tuned by the external electric-field. Thus it is expected that the polar P21 double perovskites AA0 BB0 O6 are the systems in which the magnetism and ferroelectricity can be naturally coupled by though tuning octahedral tilts.
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Now let us clarify how the magnetic properties will be switched by an external electric-field in this system. We expect to determine the switching path. Unfortunately, finding the precise switching path is still a challenging problem, because it is a complex dynamic, also strongly influenced by defects, and certainly beyond the scope of density functional theory at 0 K. Nevertheless, Zanolli et al. have demonstrated that the switching path does depend on the energy barriers DEi ¼ Ei EP21 between the ground state and the intermediate state such as the P21/m, P4/n, and P4/nmm phases [34]. The energy barriers can be estimated from the full relaxation of the intermediate phases which are DEP4/nmm, DEP4/n, and DEP21/m. The calculated results are summarized in Fig. 2. We found that the DEP21/m was the smallest barrier among the calculated results. From these results we can conclude that it is more likely that the QRot would be switched when the polarization switches in all these compounds. Since the QRot switching will switch the magnetic properties (see Table 2), thus the NaLaFeMO6 systems do appear to be likely candidates to pursue the external electric-field control the magnetization [33,34]. Previous theoretical researches have shown that in Pmc21 or Pnma phase, the spins are nevertheless not forced be symmetry to stay exactly antiparallel but can rotate to give rise to a weak magnetic moment [34]. The octahedral rotations/tilts in P21 phase are same with the Pmc21 or Pnma phase as describe above (in Glazer natation: aacþ). Thus it is expect that similar switching properties will take place in the P21 phase. To quantify this effect in NaLaFeMO6 double perovskite compounds, we included spinorbital interaction and performed noncollinear spin calculations. The calculated results listed in Fig. 3(a), (b) revealed that the easy axis for the spins are along the [010] and [001] direction for the P21 and P21/m phase, respectively. It should note that in the P21 the easy axis is in-plane and parallel to the polarization direction. Moreover, letting the spin relax produces a net spin-canted moment and the magnitude of the components of the magnetization resulting from a spin canting are summarized in Table 2. From the knowledge of the magnetic space group, group theory analysis shows that the QTilt/QRot will control the sign of the magnetization. Previous studies have shown that switching Pxy together with QTilt switches the direction of the weak magnetization from [001] to [001] [34], and switching Pxy together with QRot leaves the net magnetic moment unchanged, instead. From Table 2, we can see that the magnitude and direction of magnetization will be switched by the switching of QRot. It is indicate that electric switching of the magnetization is a priori achievable in P21 AA0 BB0 O6 double perovskite system, as long as the switching of the polarization is accompanied by the switching of QRot. Now let us discuss the electric structure of NaLaFeMO6. As shown in Fig. 4, we report the density of states (DOS) on the d levels of Fe and M sites. For these three compounds, we can clearly see that the spin-up Fe-3d states are fully occupied while the spindown states are nearly empty. It should note that there are spin down states for Fe3þ (d5), it mainly because the spin down states of Fe3þ (d5) will hybridize with the O2 (p6) ions around it (see Supplementary Material Fig. S7). Therefore, the electronic configure of Fe-3d state is t32ge2g . For the NaLaFeRuO6 and NaLaFeOsO6 (see Fig. 4(a), (c)), the valence band is formed by the spin-down Ru-4dt2g and Os-5d-t2g states, while the spin up Ru-4d-t2g and Os-5d-t2g states are completely empty and form the conduction band. The band gaps are 0.85 and 0.77 eV for the NaLaFeRuO6 and NaLaFeOsO6, respectively. For the NaLaFeReO6, however the electric structure is quite different from NaLaFeRuO6 and NaLaFeOsO6, the valence band is formed by the spin-down Re-5d-t2g states, while the conduction band is also formed by the spin-down Re-5d-t2g states. The band gap is 0.14 eV for NaLaFeReO6. As shown in Fig. 4(b), we can see that the band of NaLaFeReO6 originate from the
Fig. 2. Intrinsic energy barriers (meV/f.u.) associated with various ferroelectric switching paths in the P21 phase of NaLaFeMO6.
Table 2 The components of the magnetization for the P21/m and P21 phase NaLaFeMO6 calculated by PBEsol þ U þ SOC method. The Mx, My, and Mz represent the x, y, and z components, respectively. The units are all in mB.
NaLaFeRuO6 NaLaFeReO6 NaLaFeOsO6
P21/m P21 P21/m P21 P21/m P21
Mx
My
Mz
0.179 0.011 0.059 0.011 0.401 0.018
0.004 4.014 0.004 6.158 0.007 4.324
4.031 0.374 6.183 0.596 4.372 0.406
splitting of the spin-down Re-5d-t2g. It should be noted that only when we adopt a large value Ueff of 3.0 eV both Fe and Re does a finite energy gap appear which is consistent with previous LSDA þ U study [35]. In addition, we can conclude that the electronic configures of Ru-4d, Re-5d and Os-5d states are t32ge0g , t22ge0g , and t32ge0g , respectively. According the electronic configure we can conclude that only antiferromagnetic super-exchange interactions between Fe3þ and M5þ via single O-2p orbitals are allowed. From previous work, the robustness and universality of the electric control the magnetic properties are clear. However, we must address the issue whether the spontaneous polarizations and magnetic ordering can be persisted above room temperature. To study the critical temperature (Tc) of the polar distortions in NaLaFeMO6, we can calculate the energy difference between the para-electric phase (P21/m) and ferroelectric phase (P21), and then compare it with the NaLaFeWO6 that has been synthesized experimentally, and may exhibit a polar P21 ground state at room temperature. The energy differences are 202, 126, and 130 meV for NaLaFeRuO6, NaLaFeReO6, and NaLaFeOsO6, respectively, while in NaLaFeWO6, the energy difference is 112 meV. Therefore, it is implied that the Tc will be well above room temperature in NaLaFeMO6. Next let us discuss the Curie temperature (Tcr) for the ferrimagnetic orderings in NaLaFeMO6. A relatively straightforward mean field approach to calculate the Tcr involves mapping total energy calculations onto a Heisenberg model, from which the magnetic exchange interaction could be extracted. However, it is well known that the results gained through this approach depend sensitively on the particular value of Hubbard Ueff. Here, we can also take the advantage of the fact that the experimental values of Tcr are known for the double perovskite
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Fig. 3. The magnetocrystalline anisotropy energy of P21 and P21/m phase of NaLaFeMO6. We take the energy of [010] and [001] as the reference for the P21 and P21/m, respectively. The black, red, and blue columns indicate the magnetocrystalline anisotropy energy for NaLaFeRuO6, NaLaFeReO6, and NaLaFeOsO6, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
Fig. 4. Calculated density of states for (a) NaLaFeRuO6, (b) NaLaFeReO6, and (c) NaLaFeOsO6 in P21 symmetry with PBEsol þ U method. The Fermi level is located at 0 eV.
that have same magnetic ions such as Ca2FeReO6 (540 K) and Ca2FeOsO6 (320 K) [35e37]. Table 3 shows the calculated values of Tcr for NaLaFeMO6 at a fixed value Ueff, considering up to the second nearest neighbors exchange interactions, and we found that the dominant interaction is only between nearest neighbors (NNs) spins and the calculated average NNs exchange interaction (Jnn avg) of the NaLaFeReO6 and NaLaFeOsO6 is almost equal in value to that of Ca2FeReO6 and Ca2FeOsO6 (see Table 3) [35e37]. In addition, when compared with the experimental values, our results generally overestimated Tcr. To obtain authentic values for the NaLaFeMO6, we rescale the calculate values with the measured values. Given in this, the Tcr is expected to be 317, 397, and 464 K for NaLaFeRuO6, NaLaFeReO6, and NaLaFeOsO6. This leads us to propose that these compounds are expected to order magnetically above room temperature. The high magnetic transition temperature is driven by the strong superexchange between Fe3þ and M5þ, as we discuss above. It remains to be verified that the structure of ferroelectric and ferrimagnetic NaLaFeMO6 insulators are robust structures and can be prepared by the usual laboratory method. Therefore, the phonon dispersion spectra are calculated using the frozen-phonon method. The calculated phonon dispersions are plotted in Fig. 5 for the compounds NaLaFeMO6. It is clear that the soft-phonon modes are absent in the entire Brillouin Zone which indicate that the P21 NaLaFeMO6 structure do correspond to stable structures.
Table 3 Computed super-exchange constants (Jij) and magnetic transition temperatures nn calculated by mean field approach. Jnn p and Jap represent nearest neighbor Fe-M interaction mediated via planner and apical oxygen, respectively. The average nn nn interaction is calculated by Jnn avg ¼ (4 Jp þ 2 Jap )/6. System
Jnn p
Jnn ap
Jnn avg
Tcr Computed
Experiment
Ca2FeReO6 Ca2FeOsO6 NaLaFeRuO6 NaLaFeReO6 NaLaFeOsO6
15.1 8.0 6.9 10.2 10.1
15.3 7.7 9.5 13.1 14.0
15.2 7.8 7.8 11.2 11.4
704 547 541 517 793
540 [35] 320 [37]
The reason why we practically proposed NaLaFeMO6 as a possible multiferroic is threefold. First, in NaLaFeMO6, the Na and La cations are ordered in layers along the crystallographic c axis. Combining with the common aacþ octahedral rotations pattern, this structure is capable of lifting inversion symmetry through a hybrid improper mechanism. Second, it was experimentally showed that Ca2FeReO6 and Ca2FeOsO6 crystallize into a rock salt ordered double-perovskite structure with a space group of P21/c under high pressure and high temperature, and Ca2FeReO6 and Ca2FeOsO6 presents a long-range ferrimagnetic transition above room temperature [35,37]. Third, a number of A-site layer and Bsite rock salt ordered members of this family, such as NaLaFeWO6
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Fig. 5. Phonon dispersion of P21 NaLaFeMO6 calculated by PBEsol þ U method. (a) NaLaFeRuO6. (b) NaLaFeReO6. (c) NaLaFeOsO6. The wave vector takes a path along the high symmetrical points of the Brillouin Zone: G (0, 0, 0) / X (1/2, 0, 0) / M (1/2, 1/2, 0) / R (1/2, 1/2, 1/2) / G (1/2, 1/2, 0).
and NaLaMnWO6 [19e21], and so on, have been synthesized experimentally, and many exhibit a polar P21 ground state at room temperature. 4. Conclusion In conclusion, based on first-principles calculations we have shown that the NaLaFeMO6 (M ¼ Ru, Re, and Os) exhibits a multiferroic P21 ground state combing ferroelectricity and ferrimagnetism. The calculated ferroelectric polarization is up to several mC/ cm2 in these proposed materials and the net magnetic moments are 3, 2, and 3 mB for NaLaFeRuO6, NaLaFeReO6, and NaLaFeOsO6, respectively. More importantly, we found a low-energy ferroelectric switching path, along which the magnetization is also likely switched, evidencing the strong magnetoelectric coupling existing in this system. By mean field approach and compared with the experimental values, we have proved that the critical temperatures for both electric polarization and magnetization are well above room temperature. The presented results imply that such system is a promising candidate to achieve electric controlling of the magnetization at room temperature. Acknowledgements We are grateful to the High Performance Computing Center (HPCC) of Nanjing University for doing the numerical calculations in this paper on its IBM Blade cluster system. Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.jallcom.2016.08.209. References [1] S.-W. Cheong, M. Mostovoy, Multiferroics: a magnetic twist for ferroelectricity, Nat. Mater. 6 (2007) 13e20. [2] W. Eerenstein, N.D. Mathur, J.F. Scott, Multiferroic and magnetoelectric materials, Nature 442 (2006) 759e765. [3] R. Ramesh, N.A. Spaldin, Multiferroics: progress and prospects in thin films, Nat. Mater. 6 (2007) 21e29.
[4] X. Yang, Z. Zhou, T. Nan, Y. Gao, G.M. Yang, M. Liu, N.X. Sun, Recent advances in multiferroic oxide heterostructures and devices, J. Mater. Chem. C 4 (2016) 234e243. [5] M. Bibes, A. Barthelemy, Multiferroics: towards a magnetoelectric memory, Nat. Mater. 7 (2008) 425e426. [6] C.A.F. Vaz, Electric field control of magnetism in multiferroic heterostructures, J. Phys. Conden. Matter 24 (2012) 333201. [7] N.A. Hill, Why are there so few magnetic ferroelectrics? J. Phys. Chem. B 104 (2000) 6694e6709. [8] E. Bousquet, M. Dawber, N. Stucki, C. Lichtensteiger, P. Hermet, S. Gariglio, J.M. Triscone, P. Ghosez, Improper ferroelectricity in perovskite oxide artificial superlattices, Nature 452 (2008) 732e736. [9] N.A. Benedek, C.J. Fennie, Hybrid improper ferroelectricity: a mechanism for controllable polarization-magnetization coupling, Phys. Rev. Lett. 106 (2011) 107204. [10] J.M. Rondinelli, C.J. Fennie, Octahedral rotation-induced ferroelectricity in cation ordered perovskites, Adv. Mater. 24 (2012) 1961e1968. [11] Y.S. Oh, X. Luo, F.-T. Huang, Y. Wang, S.-W. Cheong, Experimental demonstration of hybrid improper ferroelectricity and the presence of abundant charged walls in (Ca,Sr)3Ti2O7 crystals, Nat. Mater. 14 (2015) 407e413. ~ iguez, X.M. Chen, L. Bellaiche, Near room[12] H.J. Zhao, W. Ren, Y. Yang, J. In temperature multiferroic materials with tunable ferromagnetic and electrical properties, Nat. Commun. 5 (2014). [13] R.E. Cohen, Origin of ferroelectricity in perovskite oxides, Nature 358 (1992) 136e138. [14] S.J. Patwe, V. Katari, N.P. Salke, S.K. Deshpande, R. Rao, M.K. Gupta, R. Mittal, S.N. Achary, A.K. Tyagi, Structural and electrical properties of layered perovskite type Pr2Ti2O7: experimental and theoretical investigations, J. Mater. Chem. C 3 (2015) 4570e4584. [15] J. Young, A. Stroppa, S. Picozzi, J.M. Rondinelli, Tuning the ferroelectric polarization in AA0 MnWO6 double perovskites through A cation substitution, Dalton. Trans. 44 (2015) 10644e10653. [16] X.Q. Liu, J.W. Wu, X.X. Shi, H.J. Zhao, H.Y. Zhou, R.H. Qiu, W.Q. Zhang, X.M. Chen, Hybrid improper ferroelectricity in Ruddlesden-Popper Ca3(Ti,Mn)2O7 ceramics, Appl. Phys. Lett. 106 (2015). [17] W. Zhu, L. Pi, Y. Huang, S. Tan, Y. Zhang, Electrically induced decrease of magnetization in Ca3Mn2O7, Appl. Phys. Lett. 101 (2012). [18] M.J. Pitcher, P. Mandal, M.S. Dyer, J. Alaria, P. Borisov, H. Niu, J.B. Claridge, M.J. Rosseinsky, Tilt engineering of spontaneous polarization and magnetization above 300 K in a bulk layered perovskite, Science 347 (2015) 420e424. [19] M. Retuerto, M.R. Li, A. Ignatov, M. Croft, K.V. Ramanujachary, S. Chi, J.P. Hodges, W. Dachraoui, J. Hadermann, T. Thao Tran, P.S. Halasyamani, C.P. Grams, J. Hemberger, M. Greenblatt, Polar and magnetic layered A-site and rock salt B-site-ordered NaLnFeWO6 (Ln ¼ La, Nd) perovskites, Inorg. Chem. 52 (2013) 12482e12491. [20] G. King, A.S. Wills, P.M. Woodward, Magnetic structures of NaLMnWO6 perovskites (L ¼ La,Nd,Tb), Phys. Rev. B 79 (2009). [21] T. Fukushima, A. Stroppa, S. Picozzi, J.M. Perez-Mato, Large ferroelectric polarization in the new double perovskite NaLaMnWO6 induced by non-polar instabilities, Phys. Chem. Chem. Phys. 13 (2011) 12186e12190.
G. Song et al. / Journal of Alloys and Compounds 690 (2017) 923e929 [22] P.S. Wang, W. Ren, L. Bellaiche, H.J. Xiang, Predicting a ferrimagnetic phase of Zn2FeOsO6 with strong magnetoelectric coupling, Phys. Rev. Lett. 114 (2015) 147204. [23] W. Kohn, L.J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140 (1965) A1133eA1138. €chl, Projector augmented-wave method, Phys. Rev. B 50 (1994) [24] P.E. Blo 17953e17979. [25] G. Kresse, J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B 47 (1993) 558e561. [26] J.P. Perdew, A. Ruzsinszky, G.I. Csonka, O.A. Vydrov, G.E. Scuseria, L.A. Constantin, X. Zhou, K. Burke, Restoring the density-gradient expansion for exchange in solids and surfaces, Phys. Rev. Lett. 100 (2008) 136406. [27] R. Wahl, D. Vogtenhuber, G. Kresse, SrTiO3 and BaTiO3 revisited using the projector augmented wave method: performance of hybrid and semilocal functionals, Phys. Rev. B 78 (2008) 104116. [28] R.D. King-Smith, D. Vanderbilt, First-principles investigation of ferroelectricity in perovskite compounds, Phys. Rev. B 49 (1994) 5828e5844. [29] A. Togo, F. Oba, I. Tanaka, First-principles calculations of the ferroelastic transition between rutile-type and CaCl2-type SiO2 at high pressures, Phys. Rev. B 78 (2008) 134106.
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[30] G. King, P.M. Woodward, Cation ordering in perovskites, J. Mater. Chem. 20 (2010) 5785e5796. [31] J. Young, P. Lalkiya, J.M. Rondinelli, Design of noncentrosymmetric perovskites from centric and acentric basic building units, J. Mater. Chem. C 4 (2016) 4016e4027. [32] A.M. Glazer, The classification of tilted octahedra in perovskites, Acta Crystallogr. Sect. B 28 (1972) 3384e3392. [33] S. Ghosh, H. Das, C.J. Fennie, Linear magnetoelectricity at room temperature in perovskite superlattices by design, Phys. Rev. B 92 (2015) 184112. ~ iguez, P. Ghosez, Electric control of the magneti[34] Z. Zanolli, J.C. Wojdeł, J. In zation in BiFeO3/LaFeO3 superlattices, Phys. Rev. B 88 (2013) 060102. [35] H. Iwasawa, T. Saitoh, Y. Yamashita, D. Ishii, H. Kato, N. Hamada, Y. Tokura, D.D. Sarma, Strong correlation effects of the Re-5d electrons on the metalinsulator transition in Ca2FeReO6, Phys. Rev. B 71 (2005) 075106. [36] W. Westerburg, O. Lang, C. Ritter, C. Felser, W. Tremel, G. Jakob, Magnetic and structural properties of the double-perovskite Ca2FeReO6, Solid State Commun. 122 (2002) 201e206. [37] H.L. Feng, M. Arai, Y. Matsushita, Y. Tsujimoto, Y. Guo, C.I. Sathish, X. Wang, Y.H. Yuan, M. Tanaka, K. Yamaura, High-temperature ferrimagnetism driven by lattice distortion in double perovskite Ca2FeOsO6, J. Am. Chem. Soc. 136 (2014) 3326e3329.
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Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
Predicting room-temperature multiferroic phase of NaLaFeMO6 (M ¼ Ru, Re, Os) with strong magnetoelectric coupling Guang Song a, b, *, Guannan Li a, c, Benling Gao a, Feng Liang a, Jun Zhang a a
Department of Physics, Huaiyin Institute of Technology, Huaian, 223003, China Jiangsu Provincial Key Laboratory of Palygorskite Science and Applied Technology, Huaiyin Institute of Technology, Huaian, 223003, China c National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing, 210093, China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 18 May 2016 Received in revised form 29 July 2016 Accepted 21 August 2016 Available online 23 August 2016
Discovering multiferroic materials is one of the most important questions for facilitating devices based on the electric field control of magnetism. The great challenge is to create room temperature multiferroic materials with strongly coupled ferroelectric and ferromagnetic (or ferrimagnetic) orderings. Here we present simple, chemically intuitive design rules to identify a class of bulk magnetoelectric materials based on the “bicolor” layering of P21 double ferrimagnetic perovskites, e.g., NaLaFeMO6 (M ¼ Ru, Re, Os). Using density functional theory calculations, we elucidated the origin of the ferroelectricity and show that it is a general consequence of the layering of any bicolor P21 double ferrimagnetic perovskites. Our calculations showed that the ferroelectric polarization is up to several mC/cm2 and the net magnetic moments are 3, 2, and 3 mB for NaLaFeRuO6, NaLaFeReO6, and NaLaFeOsO6, respectively in these proposed materials. More importantly, we highlighted the existence of a low-energy ferroelectric switching path, along which the magnetization is also likely reversed, evidencing the strong magnetoelectric coupling existing in this system. In addition, the critical temperature of polarization and magnetization are both well above room temperature. It is expected that this work can encourage the designing and experimental implementation of a large class of strong magneto-electric multiferroic materials with large magnetization and electric polarization above room temperature. © 2016 Elsevier B.V. All rights reserved.
Keywords: Ferroelectrics Magnetoelectric coupling Room temperature
1. Introduction Magneto-electric multiferroic materials have been widely studied due to their intriguing coupling between ferroelectricity and magnetism [1e4]. Such materials may, for example, overcome the drawbacks of ferroelectric memory (slow writing), magnetic random access memory (high power density), and open the possibility of four-state memory with reduced energy consumption [4e6]. Due to the antagonistic chemical requirements of the ferroelectricity and magnetism [7], it is particularly difficult to discover new single phase room temperature materials combining large electrical polarization P and large spontaneous magnetization M as well as strong coupling between them. To design such materials, one should address two crucially important issues: (i) the critical temperatures of electrical polarization and magnetization are above room temperature; (ii)
* Corresponding author. Department of Physics, Huaiyin Institute of Technology, Huaian, 223003, China. E-mail address: [email protected] (G. Song). http://dx.doi.org/10.1016/j.jallcom.2016.08.209 0925-8388/© 2016 Elsevier B.V. All rights reserved.
finding a new way to overcome the chemical incompatibility between ferroelectricity and magnetism. In present paper, we show that hybrid improper ferroelectricity (HIF) [8e11], a recently proposed ferroelectric mechanism, can be used to address these two issues. Good examples are that the ubiquitous polar P21 AA0 BB0 O6 double perovskites such as LaLnNiMnO6 (Ln is a rare-earth ion) superlattices [12], whereby the high temperature magnetic ordering originates from the magnetic coupling between different rock salt pattern B and B0 -site transition metal ions with strong super-exchange interaction, and the combination of rotations/tilts of the BO6 and B0 O6 octahedra and A-site cation layering ordering facilitate ferroelectric order. We emphasize that this mechanism discussed here is general to a wide range of materials and different realizations of HIF. In HIF, the large electrical polarization P, which is quite different from the classical ferroelectric materials (always driven by gamma point instability) [8,13], has been identified by specific zone-boundary octahedral tilts in an AA0 BB0 O6 double perovskite block. These tilts are coupled to translational symmetry breaking in layered perovskites [14] and can generate HIF without requiring classical
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zone-center displacements. Here, the spontaneous electric polarization results as noncancellation of the antiferrodistortive displacements associated with the tilt at the interfaces between structural blocks. Because this mechanism relies on a ‘geometric’ effect (e.g. displacements of ions due to bond-coordination preferences and packing), in contrast to antagonistic chemical requirements there are many more potential routes for purposefully inducing and enhancing ferroelectricity by judicious selection of cation species [14,15]. In addition, HIF is no longer just theoretical ideas. For instance, in an exciting development, Oh and co-workers have authenticated polarization switching in Ca3Ti2O7 [11,16], one of the first predicted hybrid improper ferroelectrics. Weak ferromagnet Ca3Mn2O7 that has a similar structure with Ca3Ti2O7, was also predicted to be hybrid improper ferroelectrics [9,17]. Moreover, in this compound, the magnetization was predicted to be coupled with electric polarization when switching the direction of the polarization also results in a 180 deterministic switching of the magnetization. Very recently, Pitcher et al. have shown that the polar double perovskite (CaySr1y)1.15Tb1$85Fe2O7 is endowed with the polarization and magnetization at room temperature and that the polarization is induced by a hybrid improper mechanism [18]. The objective of this study is to looking for multiferroic materials combining both polarization and magnetization at room temperature. Polar P21 double perovskites, such as NaLaFeWO6 [19] and NaLaMnWO6 [20,21], in which the Na and La cation are layering ordering along the crystallographic c axis, while the Fe (Mn) and W cation are rock salt pattern, have been successfully synthesized under high temperature. These double perovskite compounds display the multiferroic behavior with a high ferroelectric transition temperature but a low antiferromagnetic transition temperature. It is suggest that one can enhanced the magnetic interaction in these polar compounds to achieve room temperature multiferroic materials [22]. Based on first-principles calculations, we predicted that polar P21 double perovskites NaLaFeMO6 (M ¼ Ru, Re, Os) are room temperature multiferroic materials. We showed that ferroelectric polarization was up to several mC/cm2 and the net magnetic moments are 3, 2, and 3 mB for NaLaFeRuO6, NaLaFeReO6, and NaLaFeOsO6, respectively. Moreover, there is a low-energy ferroelectric switching path, along which the magnetization is also likely reversed, evidencing the strong magnetoelectric coupling existing in this system. The critical temperature of the polarization and magnetization were both well above room temperature. Our results provide a new way to find strong magneto-electric multiferroic materials with large magnetization and electric polarization above room temperature. 2. Computational methods First-principles calculations were carried out using density functional theory [23] with projector augmented wave (PAW) potentials [24] as implemented in the Vienna ab initio simulation package (VASP) [25]. The PAW potentials explicitly include one valence electron for Na (3s1), 11 for La (4s24p64d15s2), for 14 for Fe (3p63d64s2), 8 for Ru (4d75s1), 13 for Re (5p65d56s2), 8 for Os (5d66s2) and six for O (2s22p4) atoms. The exchange-correlation part is approximated by the PBEsol functional [26], which improves the structural descriptions over standard LDA or GGA [27]. For transition-metal ions, we have included the on-site DMSO-d6 Coulomb interaction parameter U ¼ 5.0, 3.0, 3.0 and 2.5 eV for Fe3þ, Ru5þ, Re5þ, and Os5þ, respectively, and exchange interaction parameter J is fixed at 1.0 eV. To validate the parameter U in our approach, we first investigated the properties of G-type AFM bulk Ca2FeReO6 and Ca2FeOsO6. We correctly reproduced the lattice, electronic, and magnetic properties of ground-state structures of Ca2FeReO6 and Ca2FeOsO6, respectively (see Supplementary
material Table S1 and Fig. S3). The wave function is expanded in a plane wave basis with an energy cutoff of 600 eV. A 6 6 4 Gcentered k-points sampling is used for reciprocal space integrations. We have carefully checked convergence with these settings by testing higher energy cutoffs and larger k meshes. Each self-consistent electronic calculation is converged to 106 eV and the tolerance force is set to 0.005 eV/Å for ionic relaxation. Noncollinear magnetization calculations were performed with L-S coupling, and the electric polarization was calculated using the Berry phase method as implemented in VASP [28]. To calculate the phonon dispersion of NaLaFeMO6, the structures are firstly atomically relaxed with a higher accuracy using the 6 6 4 G-centered k-points sampling and the tolerance force of 0.0001 eV/Å. The phonon dispersion is then calculated using the Phonopy code with a 2 2 2 supercell [29]. The force constants are calculated by VASP using a 3 3 2 G-centered k-points sampling for the supercell. 3. Results and discussions We have used first-principles total energy calculations to consider the complete various structures generating by different plausible combinations of different A-site configures (rock salt, columnar and layered ordering, see Supplementary Material Fig. S4) and BO6 or B0 O6 octahedral rotations for double perovskites NaLaFeMO6 (M ¼ Ru, Re, Os) [30,31]. The lowest energy structure we found has a polar P21 symmetry and it is illustrated in Fig. 1(d) (see Supplementary material Table S2). These materials in this structure displayed both ferroelectricity and ferrimagnetism. Spontaneous ferroelectric polarizations of the NaLaFeMO6 are calculated by Berry phase method, and the calculated results are listed in Table 1. In addition, the direction of polarization is pointing nearly along [010] direction, it should note that there is a small component along [001] direction is found in our calculations (about two orders of magnitude smaller than the [010] direction). At the magnetic level, our collinear spin calculations for NaLaFeMO6 exhibit a G-type ferrimagnetic arrangement with magnetic moment on Fe, Ru, Re, and Os, respectively (as summarize in Table 1). From these results we can concluded that the Fe ion takes the high-spin Fe3þ (d5) valence state. It is also clear that the Ru, Re and Os ions take the high-spin Ru5þ (d3), Re5þ (d2), and Os5þ (d3) valence state, respectively. Thus the net magnetic moments calculated by PBEsol þ U method are 3, 2, and 3 mB for NaLaFeRuO6, NaLaFeReO6, and NaLaFeOsO6, respectively. The symmetry of this P21 can be established by two symmetrylowering structural distortions of P4/nmm double perovskite structure (AA0 BB0 O6) which is the highest symmetry structure compatible with the mentioned order of the A and B sites: an inplane rotation of the BO6 octahedral about the cubic [001] axis and an out-of-phase tilt of the BO6 octahedral about the cubic [110] axis, as shown in Fig. 1(a), (b), respectively. These symmetrybreaking distortions can be distinguished with symmetries labeled as Gþ5 and G1 (see Fig. 1(a), (b)). The Gþ5 and G1 distortion modes can be seen to be essentially two tilting modes of the octahedron framework. Together these two distortions produce the Glazer rotation pattern aacþ [32]. When described with respect to a Pm-3m perovskite (ABO3), their usual labels are Rþ4 and Mþ3 and would give rise to a distorted non-polar structure of Pnma symmetry. Here, the structure of the modes are same, but the cation orderings suggest that the reference parent structure in AA0 BB0 O6 double perovskite structure has a smaller tetragonal symmetry with a larger unit cell, so that they correspond to G modes in this larger tetragonal supercell. It should note that none of these distortions modes give rise to a polar subgroup. Nonetheless, in AA0 BB0 O6 double perovskite these two modes are
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Fig. 1. The monocline NaLaFeMO6 double perovskite, space group P21. The structure, Glazer pattern a-a-cþ, is describe by three symmetrize basis modes of P4/nmm: (a) QRot, in-phase rotation of FeO6 and MO6 octahedra about [001] (G1); (b) QTilt, tilt of FeO6 and MO6 octahedra about [110] (Gþ5); (c) QAFE, antiferroelectric Na and La displacements (G5); (d) the relaxed crystal structure of NaLaFeMO6; (e) The group subgroup tree connecting the paraelectric P4/nmm phase to ferroelectric P21 phase. Yellow, green, gold, grey, and red spheres indicate Na, La, Fe, M, and O atoms, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Table 1 Theoretical optimized atomic lattice parameters of NaLaFeMO6 with a P21 (#4) crystal structures calculated by PBEsol þ U method. The DNa and DLa represent the displace in NaLaFeMO6 for Na and La, respectively. The DFe-O and DM-O represent the bond difference of Fe-O and M-O along the [010] direction, respectively. The P represents the spontaneous polarizations. mFe and mM is the magnetic moment on Fe and M, respectively.
NaLaFeRuO6 NaLaFeReO6 NaLaFeOsO6
DNa (Å)
DLa (Å)
DFe-O (Å)
DM-O (Å)
P (mC cm2)
mFe (mB)
mM (mB)
0.117 0.105 0.115
0.171 0.172 0.175
0.080 0.085 0.085
0.023 0.050 0.025
11.79 2.40 10.99
4.13 4.08 4.12
1.83 1.33 1.95
sufficient to reduce the symmetry (P4/nmm) to P21 phase, which allows the presence of a secondary induced polar distortion. It can be seen that the intersection of the two mentioned isotropy subgroups is the observed P21 group, as it is their largest common subgroup. This means that the combination of these two tilting modes is able to induce a polar phase (although they do not produce a polarization by themselves). It must be stressed that the original Rþ4 and Mþ3 unstable modes in pure Pm-3m perovskites preserve in all cases a non-polar Pnma symmetry. It is only the fact that the cation ordering reduces the parent high symmetry (Pm3m) to P4/nmm, which permits, in the family of these compound, that two typical unstable non-polar perovskite tilting modes produce a polar structure, and, as a consequence, an improper ferroelectric. Let us move our focus another distortion mode in polar P21 phase labeled G5 (Xþ5 in Pm-3m perovskite). As shown in Fig. 1(c) it is a polar mode frozen, which is responsible for spontaneous ferroelectric polarization present in the family of these compounds [12,21,33,34]. The atomic displacements for this mode are mostly along the crystallographic [110] direction (polar axis). Na and La atoms displace in opposite directions (antipolar displacements)
and the calculated results of the displacements are listed in Table 1. It can be elucidated that the two rotation distortions QRot (Gþ5) and QTilt (G1) are break inversion symmetry at the A and A0 -site of the P4/nmm structure, whereas the A/A' cation layering ordering breaks B and B0 -site inversion symmetry. As a result, the A cation displacements are no longer equal in magnitude thus cause a macroscopic polarization (see Table 1). More interesting, these antipolar displacements are trilinearly coupled to the two rotation distortions in the free energy of the P4/nmm structure, F ¼ QAFEQRotQTilt, where QAFE (G5), QRot, and QTilt are the amplitudes of the antipolar distortions, rotation, and tilt, respectively. It indicates that reversing the sense of either rotation or tilt will affect the antipolar displacements QAFE. Another fact is that the magnetic properties are coupled with the QRot distortion in P21 double perovskites, and hence the sense of this particular rotation and the magnetism are naturally coupled in nontrivial way. If one of the rotations/tilts can be switched by the macroscopic polarization, then the magnetism can be tuned by the external electric-field. Thus it is expected that the polar P21 double perovskites AA0 BB0 O6 are the systems in which the magnetism and ferroelectricity can be naturally coupled by though tuning octahedral tilts.
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Now let us clarify how the magnetic properties will be switched by an external electric-field in this system. We expect to determine the switching path. Unfortunately, finding the precise switching path is still a challenging problem, because it is a complex dynamic, also strongly influenced by defects, and certainly beyond the scope of density functional theory at 0 K. Nevertheless, Zanolli et al. have demonstrated that the switching path does depend on the energy barriers DEi ¼ Ei EP21 between the ground state and the intermediate state such as the P21/m, P4/n, and P4/nmm phases [34]. The energy barriers can be estimated from the full relaxation of the intermediate phases which are DEP4/nmm, DEP4/n, and DEP21/m. The calculated results are summarized in Fig. 2. We found that the DEP21/m was the smallest barrier among the calculated results. From these results we can conclude that it is more likely that the QRot would be switched when the polarization switches in all these compounds. Since the QRot switching will switch the magnetic properties (see Table 2), thus the NaLaFeMO6 systems do appear to be likely candidates to pursue the external electric-field control the magnetization [33,34]. Previous theoretical researches have shown that in Pmc21 or Pnma phase, the spins are nevertheless not forced be symmetry to stay exactly antiparallel but can rotate to give rise to a weak magnetic moment [34]. The octahedral rotations/tilts in P21 phase are same with the Pmc21 or Pnma phase as describe above (in Glazer natation: aacþ). Thus it is expect that similar switching properties will take place in the P21 phase. To quantify this effect in NaLaFeMO6 double perovskite compounds, we included spinorbital interaction and performed noncollinear spin calculations. The calculated results listed in Fig. 3(a), (b) revealed that the easy axis for the spins are along the [010] and [001] direction for the P21 and P21/m phase, respectively. It should note that in the P21 the easy axis is in-plane and parallel to the polarization direction. Moreover, letting the spin relax produces a net spin-canted moment and the magnitude of the components of the magnetization resulting from a spin canting are summarized in Table 2. From the knowledge of the magnetic space group, group theory analysis shows that the QTilt/QRot will control the sign of the magnetization. Previous studies have shown that switching Pxy together with QTilt switches the direction of the weak magnetization from [001] to [001] [34], and switching Pxy together with QRot leaves the net magnetic moment unchanged, instead. From Table 2, we can see that the magnitude and direction of magnetization will be switched by the switching of QRot. It is indicate that electric switching of the magnetization is a priori achievable in P21 AA0 BB0 O6 double perovskite system, as long as the switching of the polarization is accompanied by the switching of QRot. Now let us discuss the electric structure of NaLaFeMO6. As shown in Fig. 4, we report the density of states (DOS) on the d levels of Fe and M sites. For these three compounds, we can clearly see that the spin-up Fe-3d states are fully occupied while the spindown states are nearly empty. It should note that there are spin down states for Fe3þ (d5), it mainly because the spin down states of Fe3þ (d5) will hybridize with the O2 (p6) ions around it (see Supplementary Material Fig. S7). Therefore, the electronic configure of Fe-3d state is t32ge2g . For the NaLaFeRuO6 and NaLaFeOsO6 (see Fig. 4(a), (c)), the valence band is formed by the spin-down Ru-4dt2g and Os-5d-t2g states, while the spin up Ru-4d-t2g and Os-5d-t2g states are completely empty and form the conduction band. The band gaps are 0.85 and 0.77 eV for the NaLaFeRuO6 and NaLaFeOsO6, respectively. For the NaLaFeReO6, however the electric structure is quite different from NaLaFeRuO6 and NaLaFeOsO6, the valence band is formed by the spin-down Re-5d-t2g states, while the conduction band is also formed by the spin-down Re-5d-t2g states. The band gap is 0.14 eV for NaLaFeReO6. As shown in Fig. 4(b), we can see that the band of NaLaFeReO6 originate from the
Fig. 2. Intrinsic energy barriers (meV/f.u.) associated with various ferroelectric switching paths in the P21 phase of NaLaFeMO6.
Table 2 The components of the magnetization for the P21/m and P21 phase NaLaFeMO6 calculated by PBEsol þ U þ SOC method. The Mx, My, and Mz represent the x, y, and z components, respectively. The units are all in mB.
NaLaFeRuO6 NaLaFeReO6 NaLaFeOsO6
P21/m P21 P21/m P21 P21/m P21
Mx
My
Mz
0.179 0.011 0.059 0.011 0.401 0.018
0.004 4.014 0.004 6.158 0.007 4.324
4.031 0.374 6.183 0.596 4.372 0.406
splitting of the spin-down Re-5d-t2g. It should be noted that only when we adopt a large value Ueff of 3.0 eV both Fe and Re does a finite energy gap appear which is consistent with previous LSDA þ U study [35]. In addition, we can conclude that the electronic configures of Ru-4d, Re-5d and Os-5d states are t32ge0g , t22ge0g , and t32ge0g , respectively. According the electronic configure we can conclude that only antiferromagnetic super-exchange interactions between Fe3þ and M5þ via single O-2p orbitals are allowed. From previous work, the robustness and universality of the electric control the magnetic properties are clear. However, we must address the issue whether the spontaneous polarizations and magnetic ordering can be persisted above room temperature. To study the critical temperature (Tc) of the polar distortions in NaLaFeMO6, we can calculate the energy difference between the para-electric phase (P21/m) and ferroelectric phase (P21), and then compare it with the NaLaFeWO6 that has been synthesized experimentally, and may exhibit a polar P21 ground state at room temperature. The energy differences are 202, 126, and 130 meV for NaLaFeRuO6, NaLaFeReO6, and NaLaFeOsO6, respectively, while in NaLaFeWO6, the energy difference is 112 meV. Therefore, it is implied that the Tc will be well above room temperature in NaLaFeMO6. Next let us discuss the Curie temperature (Tcr) for the ferrimagnetic orderings in NaLaFeMO6. A relatively straightforward mean field approach to calculate the Tcr involves mapping total energy calculations onto a Heisenberg model, from which the magnetic exchange interaction could be extracted. However, it is well known that the results gained through this approach depend sensitively on the particular value of Hubbard Ueff. Here, we can also take the advantage of the fact that the experimental values of Tcr are known for the double perovskite
G. Song et al. / Journal of Alloys and Compounds 690 (2017) 923e929
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Fig. 3. The magnetocrystalline anisotropy energy of P21 and P21/m phase of NaLaFeMO6. We take the energy of [010] and [001] as the reference for the P21 and P21/m, respectively. The black, red, and blue columns indicate the magnetocrystalline anisotropy energy for NaLaFeRuO6, NaLaFeReO6, and NaLaFeOsO6, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
Fig. 4. Calculated density of states for (a) NaLaFeRuO6, (b) NaLaFeReO6, and (c) NaLaFeOsO6 in P21 symmetry with PBEsol þ U method. The Fermi level is located at 0 eV.
that have same magnetic ions such as Ca2FeReO6 (540 K) and Ca2FeOsO6 (320 K) [35e37]. Table 3 shows the calculated values of Tcr for NaLaFeMO6 at a fixed value Ueff, considering up to the second nearest neighbors exchange interactions, and we found that the dominant interaction is only between nearest neighbors (NNs) spins and the calculated average NNs exchange interaction (Jnn avg) of the NaLaFeReO6 and NaLaFeOsO6 is almost equal in value to that of Ca2FeReO6 and Ca2FeOsO6 (see Table 3) [35e37]. In addition, when compared with the experimental values, our results generally overestimated Tcr. To obtain authentic values for the NaLaFeMO6, we rescale the calculate values with the measured values. Given in this, the Tcr is expected to be 317, 397, and 464 K for NaLaFeRuO6, NaLaFeReO6, and NaLaFeOsO6. This leads us to propose that these compounds are expected to order magnetically above room temperature. The high magnetic transition temperature is driven by the strong superexchange between Fe3þ and M5þ, as we discuss above. It remains to be verified that the structure of ferroelectric and ferrimagnetic NaLaFeMO6 insulators are robust structures and can be prepared by the usual laboratory method. Therefore, the phonon dispersion spectra are calculated using the frozen-phonon method. The calculated phonon dispersions are plotted in Fig. 5 for the compounds NaLaFeMO6. It is clear that the soft-phonon modes are absent in the entire Brillouin Zone which indicate that the P21 NaLaFeMO6 structure do correspond to stable structures.
Table 3 Computed super-exchange constants (Jij) and magnetic transition temperatures nn calculated by mean field approach. Jnn p and Jap represent nearest neighbor Fe-M interaction mediated via planner and apical oxygen, respectively. The average nn nn interaction is calculated by Jnn avg ¼ (4 Jp þ 2 Jap )/6. System
Jnn p
Jnn ap
Jnn avg
Tcr Computed
Experiment
Ca2FeReO6 Ca2FeOsO6 NaLaFeRuO6 NaLaFeReO6 NaLaFeOsO6
15.1 8.0 6.9 10.2 10.1
15.3 7.7 9.5 13.1 14.0
15.2 7.8 7.8 11.2 11.4
704 547 541 517 793
540 [35] 320 [37]
The reason why we practically proposed NaLaFeMO6 as a possible multiferroic is threefold. First, in NaLaFeMO6, the Na and La cations are ordered in layers along the crystallographic c axis. Combining with the common aacþ octahedral rotations pattern, this structure is capable of lifting inversion symmetry through a hybrid improper mechanism. Second, it was experimentally showed that Ca2FeReO6 and Ca2FeOsO6 crystallize into a rock salt ordered double-perovskite structure with a space group of P21/c under high pressure and high temperature, and Ca2FeReO6 and Ca2FeOsO6 presents a long-range ferrimagnetic transition above room temperature [35,37]. Third, a number of A-site layer and Bsite rock salt ordered members of this family, such as NaLaFeWO6
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Fig. 5. Phonon dispersion of P21 NaLaFeMO6 calculated by PBEsol þ U method. (a) NaLaFeRuO6. (b) NaLaFeReO6. (c) NaLaFeOsO6. The wave vector takes a path along the high symmetrical points of the Brillouin Zone: G (0, 0, 0) / X (1/2, 0, 0) / M (1/2, 1/2, 0) / R (1/2, 1/2, 1/2) / G (1/2, 1/2, 0).
and NaLaMnWO6 [19e21], and so on, have been synthesized experimentally, and many exhibit a polar P21 ground state at room temperature. 4. Conclusion In conclusion, based on first-principles calculations we have shown that the NaLaFeMO6 (M ¼ Ru, Re, and Os) exhibits a multiferroic P21 ground state combing ferroelectricity and ferrimagnetism. The calculated ferroelectric polarization is up to several mC/ cm2 in these proposed materials and the net magnetic moments are 3, 2, and 3 mB for NaLaFeRuO6, NaLaFeReO6, and NaLaFeOsO6, respectively. More importantly, we found a low-energy ferroelectric switching path, along which the magnetization is also likely switched, evidencing the strong magnetoelectric coupling existing in this system. By mean field approach and compared with the experimental values, we have proved that the critical temperatures for both electric polarization and magnetization are well above room temperature. The presented results imply that such system is a promising candidate to achieve electric controlling of the magnetization at room temperature. Acknowledgements We are grateful to the High Performance Computing Center (HPCC) of Nanjing University for doing the numerical calculations in this paper on its IBM Blade cluster system. Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.jallcom.2016.08.209. References [1] S.-W. Cheong, M. Mostovoy, Multiferroics: a magnetic twist for ferroelectricity, Nat. Mater. 6 (2007) 13e20. [2] W. Eerenstein, N.D. Mathur, J.F. Scott, Multiferroic and magnetoelectric materials, Nature 442 (2006) 759e765. [3] R. Ramesh, N.A. Spaldin, Multiferroics: progress and prospects in thin films, Nat. Mater. 6 (2007) 21e29.
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