Polar Magnets in Double Corundum Oxides - Chemistry of Materials

Review pubs.acs.org/cm

Polar Magnets in Double Corundum Oxides Guo-Hong Cai,† Martha Greenblatt,*,‡ and Man-Rong Li*,† †

Key Laboratory of Bioinorganic and Synthetic Chemistry of Ministry of Education, School of Chemistry, Sun Yat-Sen University, Guangzhou 510275, P. R. China ‡ Department of Chemistry and Chemical Biology, Rutgers, The State University of New Jersey, 610 Taylor Road, Piscataway, New Jersey 08854, United States ABSTRACT: Polar magnets are promising materials for multiferroic and magnetoelectric applications in spintronic devices, owing to the coexistence of electrical polarization and magnetization and hence magnetoelectric effect. However, the design and preparation of polar magnets is a challenge due to the incompatible requirements for ferroelectricity and ferromagnetism on chemical bonding and electronic configurations. Corundum derivatives can incorporate magnetic ions into all the octahedral metal sites to enhance magnetic interactions accompanied by large spontaneous polarization if polar polymorph structures are adopted, providing an ideal platform for polar-magnet design. Considering the variable cationic combinations in A2BB′O6-type double corundum derivatives, a large number of new polar magnets are anticipated. However, so far only 14 compounds in this family have been reported, including 11 experimentally prepared and 3 theoretically predicted. The crystal structure types and physical properties of these compounds are found to largely depend on the synthesis conditions, chemical−geometrical factors, electronic configurations of cations, and spin structures, or a combination of any of the above. Therefore, it is essential to review the crystallization and transforming rules of known polar magnets and guide further exploration of new multifunctional materials in double corundum derivatives.

1. INTRODUCTION Polar magnets have been the focus of multiferroic materials for technological applications in spintronic devices.1−11 One significant strategy to achieve single-phase polar magnets is to incorporate magnetic transition-metal ions into electrical polar structure. However, the electrical polarization and magnetism are chemically contradicted, since the conventional offcentering polarization is related to d0 cations to enable the energy-lowering covalent bond formation, while the magnetic ordering requires the presence of unpaired dn cations to induce energy-raising electronic Coulomb repulsion.12,13 This intrinsic contradiction makes polar magnets rare and difficult to synthesize. Polarity also can be driven in the magnetically active BO3 network using a stereochemically active A-cation in perovskite-based compounds, such as Bi3+ and Pb2+ in BiFeO3,14 Bi2Mn4/3Ni2/3O6,15 and PbVO3.16−18 So far, only a very limited number of polar magnets have been reported, and the most intensively studied materials are perovskite-related ABO3 and A2BB′O6 oxides. To the best of our knowledge, BiFeO3,14 BiCoO3,19,20 ScFeO3,21,22 GaFeO3,23−30 InFeO3,31 hLuFeO3,32 and Mn2FeMoO633 are the only polar magnets with magnetic ordering above room temperature (RT); nevertheless, all of them have drawbacks such as weak magnetoelectric coupling or small spontaneous polarization (PS). Therefore, it is essential to explore new practical materials such as the emerging corundum derivatives. © 2017 American Chemical Society

Despite the similar formula and BO6/B′O6 sublattice connections with perovskite,34 the corundum derivatives ABO3 and A2BB′O6 uptake comparable sized A- and B/B′site cations and adopt highly distorted perovskite-related structures in rhombohedral symmetry.34 Mostly, these compounds can only be prepared at high pressure (HP), giving a small perovskite-related tolerance factor (t). The corundum derivatives can crystallize in the centrosymmetric corundum (space group R3̅c, like Al2O3), ilmenite (IL, R3̅, like natural FeTiO3), noncentrosymmetric polar LiNbO3 (LN, R3c), ordered ilmenite (OIL, R3, like Li2GeTeO6), or Ni3TeO6 (NTO, R3) type structure, depending on the cationic ordering patterns (Figure 1).35,36 These structural features (octahedral coordination at all cationic sites with large distortions) allow transition-metal occupation at both the A and B/B′-sites for enhanced magnetic interactions and also give large PS (usually above 50 μC/cm2) if polar structures are adopted.31 Compared with other polar magnets, the PS of ABO3/A2BB′O6 corundum derivatives is driven by ionic displacements triggered by Coulombic repulsion of face-sharing octahedral cations and is related to the ordering arrangement as shown in Figure 2;34,37,38 thus, the d0 configuration, or stereoactive lone-pair Received: April 16, 2017 Revised: June 6, 2017 Published: June 11, 2017 5447

DOI: 10.1021/acs.chemmater.7b01567 Chem. Mater. 2017, 29, 5447−5457

Review

Chemistry of Materials

the LN-type GaFeO3)26 to 0.83 Å (A = Mn2+, high spin (HS) in the NTO-type Mn2FeWO6)37 in known compounds.40 Thus, in principle, corundum phases can be formed when small ions (radii between 0.62 and 0.83 Å) are incorporated into the octahedral A-sites, including the followings by size: Ga3+ (0.62 Å) < Fe3+ (HS, 0.645 Å), Mn3+ (0.645 Å) < Ni2+ (0.69 Å) < Mg2+(0.72 Å) < Cu2+ (0.73 Å) < Zn2+ (0.74 Å) < Co2+ (HS, 0.745 Å) < Sc3+ (0.745 Å) < Li+ (0.76 Å) < Cu+ (0.77 Å) < Fe2+ (HS, 0.78 Å) < Cr2+ (HS, 0.80 Å), In3+ (0.8 Å) < Mn2+ (0.83 Å).40 For instance, in the double corundum A2BB′O6 family, the charge balance based combinations of A1+2B3+B′7+O6, A1+2B4+B′6+O6, A2+2B2+B′6+O6, A2+2B3+B′5+O6, and A3+2B2+B′4+O6 are all possible candidates with the small Asite cations given above. Moreover, in the OIL and NTO structures (Figure 1c,d), there are two crystallographically independent A-sites, denoted as A and A′ in AA′BB′O6, where the A, A′, and B sites can be all the same element, any two of them the same, or all different. Thus, a huge number of polar magnets are anticipated in corundum derivatives by considering the periodic table of elements. However, so far only around 30 polar oxides have been reported in corundum derivatives, including 17 in double A2BB′O6, namely, the nonmagnetic NTO-type Li2ZrTeO6,41,42 Li2HfTeO6,41 OIL-type Li2GeTeO6, and 14 polar magnets listed in Table 1. Therefore, it is essential to review the crystallization and transforming rules of known compounds, especially polar magnets in the double corundum family, to guide further exploration of new practical multiferroic/ magnetoelectric materials. The crystal structure types and physical properties of double corundum polar magnets are found to largely depend on (1) chemical and geometrical factors, (2) electron configurations, (3) spin structures, (4) synthesis conditions, or a combination of any of the above. The aim of this paper is to present the current status of polar and magnetic A2BB′O6 double corundum compounds in Table 1 and to reveal the rules to design optimal new polar magnets. The opportunities and challenges in possible future work are also discussed.

Figure 1. Crystal structure of A2BB′O6 double corundum viewed along the [110] direction.36 (a) IL-type structure with disordered B/B′ and alternative AO6 and (B/B′)O6 layers in the ab-plane; (b) LN-type structure with disordered B/B′ and mixed AO6-(B/B′)O6 in the abplane; (c) OIL-type structure derived from (a), giving ordered B and B′, distinct A and A′, and -A-B′-□-B-A′- chains of face-sharing octahedra along the c-axis; (d) NTO-type structure derived form (b), giving ordered B and B′, distinct A and A′, and -A′-B-□-A-B′- chains of face-sharing octahedra along the c-axis. □ is for the octahedral vacancy.

2. STRUCTURE RULES Theoretical calculations were carried out to understand the relation between electron states and crystal structures in our work. The first-principles spin-polarized calculations were performed in the context of density-functional theory (DFT) with the Vienna Ab-initio Simulation Package (VASP)43 using the generalized-gradient approximation parametrized by the Perdew−Burke−Ernzerhof (PBE) functional.44 The wave functions were expanded in a plane-wave basis for the projector-augmented-wave (PAW) valence electrons.45 For the localized d orbital transition metals, proper Hubbard U value was applied with the Dudarev DFT+U approach.46 A 4 × 4 × 4 or 5 × 5 × 5 Monkhorst−Pack k-point mesh was generated to sample the Brillouin zone.47 The PS was calculated with the Berry-phase formalism.48 2.1. Chemical and Geometrical Factors. As shown in Figure 1, the crystal structure of double corundum A2BB′O6 depends on the ordering degree of higher valent B and B′-sites given certain A-site cations. Ordered arrangements of the B and B′ sites initiate different atomic displacements of their facesharing counterparts and thus two crystallographically independent A-sites denoted as A and A′ in OIL (Figure 1c) or NTO (Figure 1d). When the B and B′ sites are disordered, the IL structure can be formed (Figure 1a). Similar with double

Figure 2. Face-sharing octahedral pairs along the c-axis in A2BB′O6 double corundum to show the structural distortion and PS originated from the ordering arrangement of B and B′ cations. dM (M = A1, A2, B, B′) indicates the atomic displacement from halfway between the caxis oxygen planes marked by dashed lines. Disordered arrangement of B and B′ (dB = dB′ = dB/B′) leads to identical atomic displacements of their counterpart A-site cations (dA1 = dA2), and thus the contribution from displacing up (+) and down (−) cancel each other, giving no effective macroscopic net polarization in centrosymmetric structure. Ordering B and B′ gives rise to inequivalent dM of each cation and hence net macroscopic PS.

electron cation, is not required, affording high freedom for materials design, especially in the double corundum A2BB′O6 system with a wide range of combinations of A, B, and B′, as in the double perovskites.39 The six-coordinated ionic radius of the A-site cation in the corundum phase varies from 0.62 Å (for example, A = Ga3+ in 5448


Review


Table 1. Comparison of the Cell Unit Parameters, CD and SD between B and B′ Cations, Synthesis Conditions (T and P), Structure Type, Magnetic Ordering Temperature (TC/TN), and PS of the Known Polar Magnets in Double Corundum A2BB′O6 Oxides

a

compound

a, Å

c, Å

V, Å3

CD

SD, Å

Ni2NiTeO6 Ni2ScSbO6 Ni2InSbO6 Mn2ScSbO6 Mn2MnWO6 Mn2FeWO6 Mn2FeNbO6 Mn2FeTaO6 Zn2FeTaO6 Mn2FeMoO6 Mn2FeMoO6c Zn2FeOsO6 Sc2FeMoO6 Lu2FeMoO6

5.1087(8) 5.1678(3) 5.2168(3) 5.3419(5) 8.8931(18) 5.2966 5.2740(1) 5.2721(1) 5.1709(2) 5.2505(1) 5.2053(1) 5.204 5.053 5.391

13.767(1) 14.0117(5) 14.0166(4) 14.0603(2) 10.4782(19) 13.9392 13.9338(2) 13.8892(3) 13.9353(4) 13.8355(1) 14.2424(1) 13.785 13.511 14.330

311.17 324.06 330.24 347.47 717.67 338.65 335.65(1) 334.33(1) 322.68(3) 330.3(1) 334.2(1) 323.30 298.75 360.66

4 2 2 2 4 4 2 2 2 2 2 2 0 0

0.13 0.145 0.2 0.145 0.23 0.18 0.005 0.005 0.005 0.035 0.035 0.07 0.13 0.13

conditions 1073 K, 1073 K, 1073 K, 1523 K, 1673 K, 1673 K, 1573 K, 1573 K, 1623 K, 1623 K, 1623 K, theory theory theory

AP AP AP 5.5 GPa 8 GPa 8 GPa 7 GPa 7 GPa 9 GPa 8 GPa 8 GPa

type

TC/TN

PS, μC/cm2

ref

NTO NTO NTO NTO NTO NTO LN LN LN NTO OIL NTO NTO NTO

TN = 52 K TN = 60 K TN = 76 K TC = 42 K TN = 58 K TN = 75 K TN = 90 K TN = 80 K TN = 22 K TC = 337 K TC = 229 K TC = 394 K TC = 923 K TC = 895 K

0.33a 7 7 28.3 62.9/69b 59.5/67.8b 32 23 50 68 55 54.7 7.1 8.7

41 59 59 60 45 37 36 36 34 33 74 72 73 73

Experimentally observed. bCalculated from point-charge model/first-principles calculations. cThe OIL polymorph.

Table 2. Radii and d-Orbital Electron Configurations (elec. config.) of Selected Ions in Octahedral Coordination cation 3+

radius, Å elec. config.

2+

3+

Cr

Fe

Fe

0.615 3d3

0.78 3d6

0.645 3d5

Mn2+

Mo3+

Mo5+

Mo6+

0.83 3d5

0.65 4d3

0.61 4d1

0.59 4d0

Sb

Sc3+

Ta5+

Te6+

W6+

0.6 4d10

0.745 3d0

0.64 5d0

0.56 4d10

0.6 5d0

In

3+

0.8 4d10 cation

5+

radius, Å elec. config.

2+

5+

Nb

Ni

Os

0.64 4d0

0.69 3d8

0.575 5d3

5+

1573 K. The large SD (0.145/0.2 Å) between Sc3+/In3+ and Sb5+ is responsible for the B/B′-site ordering. Their polar NTO-type structures were established by powder X-ray and neutron diffractions (PXD and PND). Second harmonic generation (SHG) and dielectric measurements suggest ferroelectric response in both compounds above 1000 K with estimated PS of ∼7(2) μC/cm2. Long-range AFM order is observed at low temperature, TN = 60 and 76 K, respectively, for Ni2ScSbO6 and Ni2InSbO6. Unlike the collinear AFM structure in Ni2NiTeO6,58 the incommensurate helical magnetic structures and higher TN in Ni2ScSbO6 and Ni2InSbO6 are probably connected to a doping induced (enhanced) AFM interaction and an accompanying spin frustration.59 SHG signals indicate that the ferroelectric/paraelectric transition temperatures of Ni2ScSbO6 and Ni2InSbO6 are around 1100 and 1030 K, respectively. 2.1.2. Mn2BB′O6 (B = Sc, B′ = Sb; B = Mn, Fe, B′ = W). Mn2ScSbO6. The NTO-type polymorph was prepared at 5.5 GPa and 1523 K.60 As discussed above in Ni2ScSbO6,59 although the CD is small, the SD between Sc3+/Sb5+ can order the B/B′-sites as corroborated by PXD, PND, and electron diffractions. About 12.3% site-selective Mn/Sc antisite disordering is observed, which weakens the structural distortion and gives a PS of 28.3 μC/cm2 as calculated from point charge model.61 This NTO-Mn2ScSbO6 exhibits FM order below 42 K with the spins lying in the ab plane. An FM component of 0.6 μB has been determined to arise from unusual site-selective Mn/Sc disorder. Thus, Mn2ScSbO6 is a potential multiferroic material. Mn2BWO6 (B = Mn, Fe). Mn2MnWO6 and Mn2FeWO6 synthesized at 1673 K under 8 GPa crystallize in NTO-type

perovskites, the B and B′ site arrangement in double corundum are strongly correlated to the charge and size difference (CD and SD) between the B and B′ cations. Small CD and SD favors disordering B and B′ as observed in the IL-type Mn2+2Fe3+Sb5+O6, where the CD and SD are 2 and 0.045 Å, respectively (Table 2).40,49−53 The large CD and/or SD are expected to order the B and B′ as in Ni2NiTeO6, Ni2ScSbO6, Ni2InSbO6, Mn2ScSbO6, Mn2MnWO6, and Mn2FeWO6 in Table 1. 2.1.1. Ni2BB′O6 (B = Ni, B′ = Te; B = Sc, In, B′ = Sb). The Ni2BB′O6 series in Table 1 are the only three double corundum polar magnets that have been synthesized at ambient pressure (AP). In these compounds, their polar structures are stemming from large SD and/or CD between the B and the B′ cations as discussed below. Ni2NiTeO6. This compound can be easily prepared at AP between 973 and 1123 K. The crystal structure was originally determined to be R3 in 1967 and then was revisited in 2006.54,55 The moderate SD (0.13 Å) and large CD (4) between Ni2+ and Te6+ well explain the B/B′ ordering in Ni2+2Ni2+Te6+O6. Ni2NiTeO6 is a collinear antiferromagnet with ferromagnetic (FM) honeycomb planes,56 where the three d8-configuration Ni2+ ions contribute to an antiferromagnetic (AFM) ordering (Néel temperature TN) up to 58 K.57 More recently, nonhysteretic colossal magnetoelectricity was discovered in single crystal samples of Ni2NiTeO6, which resembles the large piezoelectric effect at the morphotropic phase boundary in ferroelectrics.58 Ni2NiTeO6 was reported to be ferroelectric below 1000 K.59 Ni2BSbO6 (B = Sc, In). The polycrystalline Ni2ScSbO6 and Ni2InSbO6 were synthesized via solid state reaction at AP and 5449


Review


Figure 3. (a) Positive portion of magnetization loops between 2 and 400 K for Mn2FeWO6; the labels 1, 2, and 3 correspond to the first- and second-order magnetic transitions, respectively. Features 1 and 2 denote to a two-step process of the first-order AFM transition suppressed upon increasing field, while the decreasing field second-order continuous transition is marked as feature 3 in the figure.28 (b) Wavelength-dependent SHG response evidenced the polar nature of Mn2FeWO6 at RT. (c) The ground FiM udu state of single-cell Mn2FeWO6 slab structure with Mn2 moments antiparallel to both Mn1 and Fe moments. (d) Plot of the density of states in the udu magnetic structure of Mn2FeWO6.37 This figure is reused with permission from ref 37. Copyright 2015 Wiley Publishing Group.

structure.37,62−64 X-ray absorption near edge spectroscopy (XANES) clearly indicates the formal oxidation states of Mn2+2Mn2+W6+O6 and Mn2+2Fe2+W6+O6. Here the absence of mixed valence ((Mn,Fe)2+/3+/W6+/5+) over the B/B′-sites is due to the high stability of B′−W6+ in the octahedral environment,65 which drives the B-site Mn and Fe to be divalent. In addition, the face-sharing octahedral-pair connection does not favor any Jahn−Teller distortion of octahedral HS-Mn3+; hence, Mn2+ in Mn2MnWO6. Accordingly, the large CD (4) and SD (0.23 and 0.18 Å for Mn2+/W6+ and Fe2+/W6+, respectively) account well for the cationic ordering and R3 structure here. Mn2FeWO6 shows complex AFM order below 75 K and field-induced first-order transition to a ferrimagnetic (FiM) phase below ∼30 K (Figure 3a). First-principles calculations predict a FiM (spin up−down−up (udu) for Mn1−Mn2−Fe, Figure 3b) ground state in Mn2FeWO6, which has not been experimentally determined as of yet. 37 Mn2MnWO6 displays a sharp AFM transition at ∼58 K and a small FM component or canted spins state below 20 K that suggest some frustration and competition between different magnetic interactions, or domain effects. The magnetic structure of Mn2MnWO6 has been determined by PND and can be described as a superposition of commensurate AFM ordering along the c-axis and a helical component in the ab

plane, which gives rise to the conical-AFM spin structure propagating along [001]. The polar features of Mn2MnWO6 and Mn2FeWO6 have been confirmed by SHG measurements (Figure 3c), and the estimated PS values of 63.3 and 67.8 μC/cm2, respectively, were obtained by the point charge method. The polarization of Mn2FeWO6 is not switchable, due to a metallic intermediate state of the d-orbitals of Fe from first-principles calculations (Figure 3d); this prediction has not been experimentally confirmed yet. The polarization switching in Mn2MnWO6 was first predicted by first-principles calculations and then confirmed by piezo-response force microscopy (PFM) measurements.62,64,66 Magnetostriction-polarization coupling around the magnetic transition ordering temperature in Mn2MnWO6 is evidenced by temperature-dependent PND analysis, SHG effect, and magnetic-field-dependent pyroresponse behavior, which together with the magnetic-fielddependent polarization measurements qualitatively indicate magnetoelectric coupling. Thus, the multiferroic properties of Mn2FeWO6 need further experimental validation, while Mn2MnWO6 appears to be magnetoelectric. 2.2. Electron Configurations. The A2BB′O6 double corundum is expected to crystallize in IL structure when SD and CD between the B and the B′ sites are small. A good example is Mn2Fe3+Sb5+O6, which is a near RT FM insulator 5450


Review


Figure 4. (a) Selected-area (left column) and convergent-beam (right column) electron diffractions showing the polar nature of Mn2FeNbO6.36 (b) Total and Mn d, Mn1 d, Fe d, Nb/Ta d, and O p projected density of states for Mn2FeNbO6 ground state.36 Figures are reused with permission from ref 36. Copyright 2013 Wiley Publishing Group. (c) Temperature dependence of the susceptibility of Zn2FeTaO6 at 1000 Oe. Inset shows the crystal structure of the face-sharing ZnO6/(Fe/Ta)O6 octahedral pair. The atomic displacements (ds) away from the ZnO6 and (Fe/Ta)O6 octahedral site centroids (highlighted by dashed circles) are indicated as dZn (0.542(1) Å) and dFe/Ta (0.111(1) Å), respectively.34 (d) Electric-field-dependent polarization measurements of Zn2FeTaO6 at 10 K in zero magnetic field show a nearly flat “loop” and give only very small values for the switchable polarization as shown in the inset.34 Figures are reused with permission from ref 34. Copyright 2014 American Chemical Society.

(T C ∼ 270 K) and shows promising applications in spintronics.50,52,67 Therefore, more IL-type FM insulators are expected by elemental substitution in Mn2FeSbO6. An ideal strategy is to keep the strong magnetically active HS-d5 cations Mn2+ and Fe3+ at the A and B sites but replace the B′-site Sb5+ by other transition metal ions. HP-syntheses of Mn2FeNbO6 and Mn2FeTaO6 did yield corundum based phases but in polar LN-type structure, not the IL phase, i.e., Fe3+ and Nb5+/Ta5+ are disordered at the B and B′-sites, while the overall cationic arrangements follow the LN-type patterns. Apparently, the asymmetry of double corundum A2BB′O6 can also be effected by the electron configurations of B′-site cation. Presumably, A2BB′O6 prefers to crystallize in polar LN-type structure if the B′-site is occupied by a d0-cation despite the small SD and CD between B and B′. Theoretical calculations indicate that the second order Jahn−Teller (SOJT) distortion68 of the B′-site d0cation has significantly lower energy to stabilize the LN instead of the IL structure.69−71 This prediction has been further confirmed experimentally by the discovery of LN-type Zn2FeTaO6.34 Mn2FeB′O6 (B′ = Nb, Ta). Both compounds were prepared at 1573 K under 7 GPa.36 Electron diffraction clearly reveals the polar natures of both compounds (Figure 4a) and thus excludes the R3̅c space group and leaves the LN-type structure as the only possibility from synchrotron PXD analysis. XANES studies

imply Mn2+2Fe3+B′5+O6 with SD of 0.05 Å and CD of 2 between Fe3+ and B′5+, which are almost identical with those in Mn2FeSbO6. DFT calculations indicate that the finite polarizations of both compounds are due to the SOJT effect of d0 ions Nb5+ (4p65d0) and Ta5+ (5p66d0) (Figure 4b). The Mn2+− Fe3+ (HS d5) exchange interactions contribute to AFM states in Mn2FeNbO6 and Mn2FeTaO6 below 90 and 80 K, respectively, and short-range magnetic order up to 200 K. The magnetic nature of Mn2FeB′O6 is further confirmed by Mössbauer spectra. The PS values are calculated to be 32 and 23 μC/cm2 for B = Nb and Ta, respectively. Although there is no ferroelectric response/magnetoelectric coupling observed on the as-made polycrystalline samples, pyroelectricity was found at lower temperature, where the samples are less conductive.36 Zn2FeTaO6. The synthesis of this compound was motivated by the prediction indicated above, that the SOJT d0 Ta5+ would stabilize the polar LN-type structure. Moreover, the replacement of Mn2+ by nonmagnetic Zn2+ in Zn2FeTaO6 is expected to lead to a more insulating state than Mn2FeTaO6 and thus warrant ferroelectric behavior. The LN-type polycrystalline Zn2FeTaO6 was synthesized at 9 GPa and 1623 K,34 where higher pressure is required compared with the Mn-analogues since the smaller ionic radius of Zn2+ (0.74 Å) than Mn2+ (0.83 Å) gives a smaller t (Table 2).36 The magnetic measurements show an AFM transition at 22 K with a weaker magnetic 5451


Review

Chemistry of Materials interaction for the diamagnetic Zn2+ (Figure 4c).72 A small switchable component (∼0.15 μC/cm2) was detected at low temperature (10 K), which is much smaller than the calculated PS of 50 μC/cm2 (Figure 4d), and can be understood as experimental resolution of a lower boundary for a possible switchable component in the multidomain polycrystalline sample. 2.3. Spin Structure. The energy effect of SOJT d0-ions at the B′ site well explains the structural difference between polarLN type Mn2FeB′O6 (B′ = Nb, Ta) and IL-type Mn2FeSbO6. For dn (0 < n ≤ 10) ions at the B′ site and small SD and same CD between B- and B′-site cations, IL phases with stronger magnetic interactions may be anticipated. For instance, substitution of the d10 ion Sb5+ by d1-Mo5+ may induce above RT magnetic ordering in IL-Mn2+2Fe3+Mo5+O6. Although corundum-based Mn2FeMoO6 does appear from HP synthesis, it adopts the polar NTO structure instead of the IL polymorph, which is totally unexpected considering the SD (0.035 Å) and CD (2) between Fe3+ and Mo5+ and the absence of B′-site d0 ions. It seems that the structure type of the A2BB′O6 double corundum is not only affected by the conditions of synthesis, chemical composition, and SOJT effect of B′-site d0 cations but also affected by the magnetic interactions given small CD and SD between B/B′ cations. Theoretical calculations reveal that the lowest-energy ground state is achieved in the NTO-type B/ B′-site ordering with a specific spin structure; namely, the structural polarization of double corundum magnets is stabilized by spin structure as discussed below in the NTOtype Mn2FeMoO6 and theoretically predicted Sc2FeMoO6, Lu2FeMoO6, and Zn2FeOsO6.33,64,72,73 Mn2FeMoO6. The NTO-type Mn2FeMoO6 was obtained in attempts to make an above-room-temperature IL-type FM insulator at 1623 K under 8 GPa.33 Unlike Mn2+2Fe2+W6+O6, XANES indicated the formal oxidation state of cations of Mn2+, Fe3+, and Mo5+; hence, it was originally refined as IL structure (R3̅) from synchrotron PXD analysis. Subsequent SHG and PND studies unambiguously evidenced a polar NTO structure with almost fully ordered Fe3+/Mo5+, which is unexpected, considering the small SD (0.035 Å) and CD (2) of Fe3+/Mo5+. The answer to the paradox is in the spin structure (Figure 5a, Mn1 and Fe up, Mn2 and Mo down), as determined from PND data, which lowers the ground state energy (Figure 5b) compared to other possible configurations by 80 (Mn1−Fe− Mo up, Mn2 down) to 300 meV (Mn, Fe, Mo all aligned parallel). The strong magnetic interactions and highly polarized spin structure represent an above RT ferrimagnetic (Curie temperature TC of 337 K) semiconducting state. The PS of Mn2FeMoO6 is around 68 μC/cm2, making it a promising multiferroic material for practical applications. An unusually low-temperature cationic rearrangement (Fe and Mn in the face-shared pairs switch positions) occurs in Mn2FeMoO6 upon heating between 423 and 573 K, which cause an NTO-to-OIL type phase transition around 483 K.74 This polymorph of Mn2FeMoO6 is the second known OIL phase, isostructural with Li2GeTeO6.35 Compared with the NTO-Mn2FeMoO6, the OIL analogue displays about 120 K lower TC (229 K), and it is about three thousand times more insulating. Zn2FeOsO6. Zn2FeOsO6 is described as an LN-type structure (R3c), but in fact the calculations were carried out on an NTOtype phase (R3).72 Theoretical calculations show that the R3 structure has lower energy over other possible structures in P21/n, R3̅, or C2 symmetry. The density of states plot suggests HS Fe3+ (d5), almost fully occupied majority and empty

Figure 5. (a) Magnetic structure of Mn2FeMoO6 at 10 K demonstrating the spin polarization, the net magnetic moment M = m(Mn1) + m(Fe) − m(Mn2) − m(Mo). (b) DFT calculations of density of states in the ground-state (up−up−down−down) magnetic configuration projected to Mn1, Mn2, Fe, Mo, and O sites of Mn2FeMoO6. This magnetic configuration is found to be energetically favorable over the FiM (up−up−down−up) and ferromagnetic configurations.33 This figure is reused with permission from ref 33. Copyright 2014 Wiley Publishing Group.

minority Fe 3d states, which suggests ordered Fe3+/Os5+. Magnetic interactions between Fe3+(3d5)−Os5+(5d3) are believed to originate FiM ordering above RT (TC = 394 K) and insulating behavior. The spin structure likewise realizes a switchable polarization along with strong magnetoelectric coupling. The PS is evaluated to be 54.7 μC/cm2. Thus, Zn2FeOsO6 is a promising above RT magnetoelectric material. Given the small SD (0.07 Å) and CD (2) between Fe3+ and Os5+, their ordering in NTO-type structure was calculated to originate from the FiM state with the Fe and Os moments aligned antiparallel in the ab plane; this spin structure is lower in energy by 0.55 meV/f.u. than the FiM state with the Fe and Os moments aligned antiparallel along the c-axis and including spin−orbit coupling in the DFT calculations.33 A2FeMoO6 (A= Sc, Lu). First-principle calculations suggest that A2FeMoO6 (A = Sc, Lu) form in the NTO-structure (R3) with computed PS above 7 μC/cm2 (7.1 μC/cm2 for A = Sc and 8.7 μC/cm2 for A = Lu).64 The d5/d3 magnetic superexchange coupling in Fe3+−Mo3+ causes FiM ordering up to 923 and 895 K for A = Sc and Lu, respectively. The paraelectric-ferrielectric transition temperatures are also above RT: T > 410/550 K for Sc2FeMoO6/Lu2FeMoO6. Strong intrinsic magnetoelectric coupling is also ensured, because the magnetic ions are involved in both the magnetic moment formation and the polarization. Although the NTO-type Sc2FeMoO 6 and Lu2FeMoO6 structures are predicted to be stable, chemically the small SD (0.045 Å) and CD (0) between Fe3+ and Mo3+ are unlikely to order them at the B and B′ sites, unless the spin structure can induce significant energy lowering, as observed in Mn2FeMoO6. The paraelectric to ferrielectric transition temperatures of Sc2FeMoO6 and Lu2FeMoO6 were estimated to be above 410 and 550 K, respectively. 2.4. Synthesis Conditions. The synthesis conditions, especially the pressure, play an important role in forming corundum phases. Isomeric corundum compounds can be prepared under different pressures. In the simple ABO3 family, the AP or lower-pressure made IL phase can transform into LN-type structure under higher pressure, such as the IL/LNtype MnTiO3 (B = Ti, Sn) at AP/7 GPa,75 FeTiO3 at AP/18 5452


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Chemistry of Materials GPa,76 and ZnBO3 (B = Ti at AP/16 GPa and B = Sn) at AP/7 GPa.77−80 In some cases, the bixbyite phase can also convert into corundum at HP. For example, the AP-prepared bixbyite structure ScFeO3 (cubic, Ia3̅, specified as ScFeO3-I), transforms into LN structure (∼8% Sc3+/Fe3+ ordering, denoted as ScFeO3-II) at 6 GPa. ScFeO3-II demonstrates above RT weak FM (TC ∼ 356 K) response.21 At 15 GPa, ScFeO3-II changed into an orthorhombic perovskite phase (ScFeO3-III, Pnma or Pn21a),22 which is unstable and transforms to LN-type ScFeO3-II upon decompression, giving fully ordered Sc3+/Fe3+ (denoted as decompressed phase) other than the only 8% Sc3+/ Fe3+ ordered phase directly prepared at 6 GPa. The higher ordering degree of Sc3+/Fe3+ in the decompressed LN phase leads to much larger PS (100 μC/cm2) and higher TC (545 K) in comparison with those (3.3 μC/cm2 and 356 K) for the ∼8% Sc3+/Fe3+ ordered sample.22 Similar isomeric IL-to-NTO-to-perovskite transitions upon pressing have also been reported in the double corundum family. The IL-Mn2ScSbO6 prepared at AP can switch to NTOtype structure at 5.5 GPa and further to a perovskite structure (P21/n) at 12 GPa (Figure 6),49,60 accompanied by dramatic

3. OPPORTUNITY AND CHALLENGE The rarity of the above RT multiferroic materials has evoked substantial theoretical and experimental work to reveal design rules other than incorporation of d0 or lone-pair electron (6s2) ions,9 including spin spirals,87,88 charge ordering,89,90 and geometric improper and hybrid improper ferroelectricity.91,92 The perovskite-related polar corundum derivatives possess robust PS (typically above 50 μC/cm2) and allow incorporation of magnetic transition-metal ions in both the A- and B/B′-sites, providing an attractive approach for polar and magnetic multiferroics. To the best of our knowledge, most of the known above RT multiferroic materials crystallize in corundum-based structure, including the LN-type BiFeO3 (TN = 643 K),14 ScFeO3 (TC = 545 K in the phase decompressed from higher pressure perovskite polymorph),21,22 GaFeO3 (TC = 408 K),26 InFeO3 (TN = 545 K),31 and NTO-type Mn2FeMoO6 (TC = 337 K).33 The two exceptions are hexagonal LuFeO3 (P63cm, TN = 440 K)32 and Z-type Sr3Co2Fe24O41 ferrites (P63/mmc, TC = 670 K).93 Therefore, many more practical multiferroics are expected in polar corundum derivatives, especially in the more flexible A2BB′O6 double corundum system. Preferably, materials-genome-initiative calculations over the periodic table of elements are strongly desired to guide targeted exploration in the future. In addition to the discoveries of new practical multiferroic materials, efforts are also focused on the applications of known compounds. Unfortunately, most of these polar magnets are prepared from HP syntheses in multidomain polycrystalline forms, which make the ferroelectric properties measurements difficult with most remaining unclear. For example, in doublecorundum polar magnets, ferroelectricity is only qualitatively observed in Zn2FeTaO6 and Mn2MnWO6: the former one shows a small switchable component at low temperature,34 and the latter exhibits weak ferroelectric and magnetoelectric responses at RT.62 Thus, the growth of single crystal samples is essential, but a challenge: first, the HP synthesis operation is complicated and hard to scale up, and second, it is a big project to search for proper salt-flux, because the melting point of a flux usually increases steeply under pressure (for example, KCl can be easily melted below 1273 K at AP but remains solid at 1773 K under 5 GPa). Thus, eventually crystal growth methods at AP should be developed. One possible way is to grow single crystals using the hydrothermal method as for the multiferroic YMnO3 perovskite HP-phase.94 The other practical solution could be heterostructural thin film growth of HP-made phases at AP. Thin-film deposition enables metastable materials to be tailored and stabilized via atomic-scale interface induction.95,96 This technology has been successfully applied for the thin-film growth of HP-made polar corundum phases at AP, and good examples are the depositions of LN-type ScFeO3 and ZnSnO3 films (Figure 7),21,79,97 which could shed light on the thin-film growth of HP-made A2BB′O6 compounds by manipulating the B/B′-site ordering degree.

Figure 6. Crystal structure of Mn2ScSbO6 in (a) IL-structure prepared at AP, (b) NTO-structure prepared at 5.5 GPa, and (c) perovskite structure prepared at 12 GPa.60 The Mn−O polyhedra were omitted for clarity and comparison.

physical properties modificationspolar ferrimagnet (PS ∼ 28.3 μC/cm2, TC = 42 K) in NTO and centrosymmetric AFM ordering in perovskite (TN = 22 K). In contrast, the FM ILMn2FeSbO6 (TC = 270 K) directly transforms into AFM perovskite structure (P21/n, TN = 22 K) above 5 GPa without any intermediate NTO state,50,52,81 mainly because of the small SD and CD between Fe3+/Sb5+ as discussed in Section 2.1. Generally, the IL phase can convert to polar LN/NTO and further to perovskite structures under increasing pressure in ABO3/A2BB′O6 corundum derivatives. Besides the impact from chemical and geometrical factors (SD and CD), electron configurations, and spin structures, the unit cell volume tends to be minimized under higher pressure.74 For example, the unit cell volumes of known IL-ABO3 are about 1.5% smaller than their LN-type analogues prepared at higher pressures.75−80,82 In double corundum, the conditions gets more complicated, since the B/B’-site combination and ordering status involve more variables. Sometimes, the competing phases are obtained, such as in Mn2BReO6 (B = Mn, Fe), where only double perovskite phases have been reported between 5 and 11 GPa to date.83−86 Whatever the case, the polar and magnetic corundum derivatives (if they exist) should be prepared under appropriate pressure to avoid the IL/perovskite phases under lower/higher pressure.

4. GENERAL DISCUSSION AND CONCLUSION In summary, we have comprehensively classified the structural design and synthesis rules of known polar and magnetic A2BB′O6 double corundum derivatives. The crystalline polymorphs depend not only on the geometrical and chemical factors (size and charge difference between cations), electron configurations (second-order Jahn−Teller effect of the B′-site d0 cations), and spin structures but also synthesis conditions or 5453


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will stimulate further interest in double corundum polar magnets from both experimental and theoretical communities.

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AUTHOR INFORMATION

Corresponding Authors

*(M.-R.L.) E-mail: [email protected]. *(M.G.) E-mail: [email protected]. ORCID

Man-Rong Li: 0000-0001-8424-9134 Author Contributions

The manuscript was written through contributions of all authors. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the “One Thousand Youth Talents” Program of China. M.G. thanks the NSF-DMR1507252 grant of the United States. The authors would like to thank Prof. David Walker at LDEO at Columbia University for helping with the high pressure syntheses.

Figure 7. Measurements on the thin films of the HP prepared LN-type ScFeO3 and ZnSnO3 grown on SrTiO3/SrRuO3 (STO/SRO) substrates at AP.21,79 (a) High resolution high angle annular dark field scanning transmission electron microscopy image of the ScFeO3 substrate film interface; the white arrow indicates a boundary between two twin domains. This twinning is due to the rhombohedral distortion having four possible orientations when growing on the cubic STO surface. (b) The vertical PFM amplitude of ScFeO3.21 (c) Electric field dependent polarization hysteresis loops of the epitaxial (111) ZnSnO3 thin film,79 showing PS ∼ 47 μC/cm2. (d) Atomic force microscopy image of the epitaxial (111) ZnSnO3 thin film, indicating a layer-by-layer growth mode. These figures are reused with permission from refs 21 and 79. Copyright 2012 and 2009 American Chemical Society.

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a combination of any of the above. Presumably, doublecorundum polar magnets can be prepared if the A2BB′O6 corundum meets any of the following conditions: (1) The B′-site d0 ion favors polar LiNbO3-type structure with small size and charge difference between B and B′ Mn2FeNbO6, Mn2FeTaO6, and Zn2FeTaO6. (2) Large size and/or charge difference between B and B′ prefers to order B and B′ in Ni3TeO6-type structure Ni 2 NiTeO 6 , Ni 2 ScSbO 6 , Ni 2 InSbO 6 , Mn 2 FeWO 6 , Mn2MnWO6, and Mn2ScSbO6. (3) The structural polarization can be stabilized by spin structure given the small size and charge difference between B and B′Mn2FeMoO6 (Ni3TeO6-type), Mn2FeMoO6 (ordered ilmenite type), Zn2FeOsO6, Sc2FeMoO6, and Lu2FeMoO6. (4) Proper pressure should be applied to avoid the formation of competing centrosymmetric phases such as ilmenite or perovskiteMn2ScSbO6. Even so, there are only 11 compounds experimentally prepared so far; the above rules are far from optimal and may be improved with new discoveries. Some new rules may also be refined in the future. At the same time, theoretical prediction will be a significant plus to predict and guide the experimental work considering the huge number of possible candidates. Single crystal or thin film sample growth at ambient pressure is another important aspect to study and optimize the physical properties, especially the ferroelectric and/or magnetoelectric response for spintronic applications. We hope that our work

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ABBREVIATIONS RT = room temperature HP = high pressure AP = ambient pressure t = perovskite-related tolerance factor IL = ilmenite LN = LiNbO3 OIL = ordered ilmenite NTO = Ni3TeO6 HS = high spin SD = size difference CD = charge difference SOJT = second order Jahn−Teller PXD = powder X-ray diffraction PND = powder neutron diffraction XANES = X-ray absorption near edge spectroscopy FM = ferromagnetic AFM = antiferromagnetic FiM = ferrimagnetic TN = antiferromagnetic Néel temperature TC = ferromagnetic/ferrimagnetic Curie temperature PS = spontaneous polarization SHG = second harmonic generation PFM = piezo-response force microscopy DFT = density functional theory fu = formula unit REFERENCES

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