Transition-metal (TM) oxides with ABO₃ perovskite and/or perovskite-like structures have received much attention due to their varied crystal structures and their physical properties such as ferroelectricity, piezoelectricity, multiferroicity, superconductivity, colossal magnetoresistance, and catalysis.^[1–12] As shown in Fig. 1(a), the B site in an ABO₃ perovskite oxide is usually occupied by a TM ion with BO₆ octahedral coordination, which dominates the electronic properties, while the A site often accommodates a relatively large cation such as an alkaline metal, alkaline-earth metal or rare earth element, located in the octahedral voids to sustain the structural framework. Since the crystal structure of perovskite is very flexible, one may prepare various structurally ordered perovskite oxides by appropriate chemical substitution. For instance, when a TM ion resides in the B site, a B-site ordered double perovskite A₂BB′O₆ can be formed (see Fig. 1(b)). One well-known example is the half-metallic ferrimagnetic compound Sr₂FeMoO₆ with a high Curie temperature (T_C) of about 420 K.^[13] This relatively high T_C has stimulated considerable research on the family of 3d–4d and 3d–5d hybrid magnetic materials with high spin ordering temperatures. In particular, in the series of Cr-based double perovskites Sr₂CrB′O₆, the T_C increases from 458 K for B′ = W to 635 K for B′ = Re and further to 725 K for B′ = Os.^[13–19] This trend in increasing T_C has been interpreted as a strong super-exchange interaction between fully occupied up-spin Cr-t_2g and Os-t_2g electrons.^[16]

Fig. 1.

Figure Option ViewDownloadNew Window

Fig. 1. (a) Crystal structure of simple perovskite ABO3 with a Pm-3m space group. Atomic sites: A 1a (0, 0, 0), B 1b (0.5, 0.5, 0.5), O 3c (0, 0.5, 0.5); (b) crystal structure of B-site ordered double perovskite A2BB′O6 with an Fm-3m space group. Atomic sites: A 8c (0.25, 0.25, 0.25), B 4a (0, 0, 0), B′ 4b (0.5, 0.5, 0.5), O 24e (x, 0, 0); (c) crystal structure of A-site ordered quadruple perovskite with an Im-3 space group. Atomic sites: A 2a (0, 0, 0), A′ 6b (0, 0.5, 0.5), B 8c (0.25, 0.25, 0.25), O 24g (x, y, 0).

In addition to the B-site ordered double perovskites, so-called A-site ordered quadruple perovskites with chemical formula of also exist and can be obtained when three fourths of the A sites in a simple ABO₃ perovskite are occupied by TM ions A′.^[20] This specially ordered perovskite usually crystallizes to a cubic lattice with space group Im-3 as shown in Fig. 1(c). Owing to the introduction of TM ions, which have smaller ionic radii, at the initially 12-fold-coordinated A site, the BO₆ octahedra are highly tilted in this ordered structure (A typical B–O–B bond angle is about 140°). As a result, high pressure is often necessary to prepare A-site ordered perovskites. Unlike BO₆ octahedral coordination, a transition metal at the A′ site forms a square-planar-coordinated A′O₄ unit. As a result, some Jahn–Teller active ions like Cu^{2 +} and Mn^{3 +} can often occupy this site. Since both A′ and B sites accommodate transition metals in A-site ordered quadruple perovskites, multiple magnetic and electrical interactions can take place through A′–A′, B–B, and/or A′–B interaction pathways, giving rise to many interesting physical properties and potential applications. For example, ferromagnetism caused by the A′-site Cu^{2 +} was found in the B-site nonmagnetic CaCu₃B₄O₁₂ (B = Ge, Sn).^[21] Colossal and temperature-independent dielectric constants (≈ 10⁵) were observed in CaCu₃Ti₄O₁₂.^[22,23] Large low-field magnetoresistance effects were shown in Ca/La/BiCu₃Mn₄O₁₂.^[24–26] Magnetic and dielectric coupling occur in BiMn₃Mn₄O₁₂.^[27] A recent study of LaMn₃Ti₄O₁₂ revealed that the A site can be occupied by Mn with an unusual low valence state rather than Jahn–Teller Mn^{3 +}.^[28] Some of these intriguing physical properties have already been reviewed in a few articles.^[20,29]

In the present invited review, we focus on the recent progress in A-site ordered quadruple perovskite oxides, including the intermetallic charge transfer between the A-site Cu and the B-site Fe in ACu₃Fe₄O₁₂ (A = La–Tb, and Bi), and magnetoelectric multiferroicity in the cubic perovskite-structure LaMn₃Cr₄O₁₂.^[30–36]

Charge transfer occurring between two different transition metals can simultaneously change the valence states and electronic configurations of these two TM ions. It may lead to a series of related phase transitions in lattice, spin, charge and orbital degrees of freedom. Although intermetallic charge transfer is often observed in organic–inorganic hybridized systems,^[37–40] only a few inorganic solid-state oxides show this phenomenon. Several A-site ordered perovskites ACu₃Fe₄O₁₂ (A = La–Tb, and Bi) were found to display intermetallic charge transfer between the A′-site Cu and the B-site Fe ions.^[31–35]

The ACu₃Fe₄O₁₂ can be synthesized at 8–15 GPa and 1200–1500 K. For instance, figure 2(a) shows the synchrotron x-ray diffraction (SXRD) pattern of LaCu₃Fe₄O₁₂ (LCFO) measured at 300 K. It can be well fitted based on an A-site ordered double perovskite structure model with a cubic Im-3 space group. In the structure, A-site La and A′ -site Cu are 1:3 ordered at special sites 2a (0, 0, 0) and 6b (0, 0.5, 0.5), respectively. B-site Fe occupies special site 8c (0.25, 0.25, 0.25) and O occupies site 24g (x, y, 0). The refinement for occupation factors of atoms is near unity, indicating good chemical stoichiometry.

Fig. 2.

	Figure Option ViewDownloadNew Window
	Fig. 2. SXRD patterns and the Rietveld refinement profiles of LaCu3Fe4O12 at (a) 300 K and (b) 425 K. The observed (circles), calculated (red line), and difference (blue line) patterns are shown. Ticks show the positions of the Bragg reflections.[31]

The oxygen content can be further determined by thermogravimetric (TG) measurement as shown in Fig. 3. The compound starts to decompose at a temperature around 820 K, losing 3.25% of its mass. According to the decomposition reaction (LaCu₃Fe₄O₁₂ → LaFeO₃ + 3/2CuFe₂O₄ + 3/2CuO + 3/4O₂), the expected TG loss is about 3.22%, which is very close to the observed one. Therefore, oxygen content in LCFO is almost stoichiometric. Figure 3 also shows a differential thermal analysis (DTA) of LCFO. Obviously, when the temperature increases to a critical temperature (T_C) 393 K, a sharp endothermic peak is observed in the DTA curve. However, there is no change in the TG curve near T_C. These observations thus strongly suggest an intrinsic phase transition occurring at around 393 K.

Fig. 3.

	Figure Option ViewDownloadNew Window
	Fig. 3. Thermogravimetry and differential thermal analysis of LaCu3Fe4O12.[31]

To understand the origin of the phase transition at T_C, high-temperature SXRD was performed. Figure 2(b) shows the SXRD pattern of LCFO measured at 450 K (> T_C). Structural analysis demonstrates that the crystal symmetry above T_C is completely identical with that of the phase below T_C, suggesting that the phase transition occurring at 393 K is an isostructural one. Moreover, when the unit cell volume as a function of temperature is examined (see Fig. 4), one can find a sharp volume variation of about 1.2%, revealing the first-order nature of this isostructural phase transition. Note that the volume change of LCFO around T_C differs from the usual thermal expansion, exhibiting anomalous shrinkage during the phase transition.

Fig. 4.

	Figure Option ViewDownloadNew Window
	Fig. 4. Temperature dependence of the unit cell volume of LaCu3Fe4O12. The data were obtained from conventional XRD , SXRD , and NPD .[31]

The cell volume in the A-site ordered perovskite is closely related to the B–O bond length. According to structure refinement results (Table 1), the temperature dependence of Fe–O and Cu–O distances is obtained as shown in Fig. 5(a). Clearly, the Fe–O bond length sharply decreases around T_C, giving rise to the drastic volume contraction. In contrast, the Cu–O distance increases remarkably near the critical temperature. The band valence sums were calculated based on the Fe–O and Cu–O bond lengths (see Fig. 5(b)). The valence states of Fe and Cu below T_C are both close to +3, forming a charge combination with the very rare Cu³⁺ residing at the square-planar A′-site. Above T_C, however, the unusually high Cu^{3 +} is reduced to a Cu^{2 +}, whereas the valence state of Fe becomes much higher than + 3. On account of the stoichiometric composition of LaCu₃Fe₄O₁₂, the high-temperature charge combination should change to , which is the same as that of other A-site ordered perovskites such as and .^[25,26]

Table 1.

Table 1.

Table 1. Crystal structure parameters of LaCu3Fe4O12, determined by Rietveld refinements of SXRD and NPD data. . LaCu3Fe4O12 SXRD SXRD NPD NPD T/K 300 450 300 425 space group Im-3 Im-3 Im-3 Im-3 Z 2 2 2 2 a/Å 7.43283(4) 7.41420(6) 7.4351(1) 7.4345(8) V/Å3 410.641(7) 407.561(9) 411.02(2) 410.9(1) Ox 0.3111(3) 0.3070(4) 0.3110(2) 0.302(3) Oy 0.1711(4) 0.1764(4) 0.1690(3) 0.174(3) Uiso(La/Bi)/102 Å2 0.26(2) 0.42(2) 0.5(1) 3(1) Uiso(Cu)/102 Å2 1.09(2) 1.48(3) 1.19(6) 2.9(5) Uiso(Fe)/102 Å2 0.14(2) 0.22(2) 0.79(3) 6.7(6) Uiso(O)/102 Å2 0.36(7) 0.67(8) 0.80 (3) 4.9(4) Cu–O/4 Å 1.895(2) 1.939(3) 1.885(2) 1.96(2) 2.819(3) 2.794(4) 2.834(2) 2.84(6) 3.364(6) 3.307(7) 3.377(2) 3.30(4) Fe–O/6 Å 2.0007(9) 1.978(1) 2.0059(7) 1.981 (5) Fe–O–Fe/(°) 136.5(1) 139.2(2) 135.8(1) 139.5(8) Rwp/% 6.70 7.71 5.09 4.54 Rp/% 4.70 5.42 4.31 3.96

Table 1. Crystal structure parameters of LaCu3Fe4O12, determined by Rietveld refinements of SXRD and NPD data. .

Fig. 5.

	Figure Option ViewDownloadNew Window
	Fig. 5. Temperature dependence (a) lengths of Cu–O and Fe–O bonds and (b) calculated BVS values for Cu and Fe ions in LaCu3Fe4O12.[30]

The valence state change of Fe can be confirmed further by Mössbauer spectrum (MS) measurements. Figure 6 shows the MS results of LCFO collected at different temperatures. Below T_C (e.g., at 4.2 K and 298 K), the MS very consistently shows one spectral feature, a single magnetic sextuplet. The isomer shift (IS) values obtained at 4.2 K and 298 K are respectively 0.47 and 0.34 mm/s, typical values for Fe^{3 +} with a high-spin configuration,^[41,42] further confirming the charge combination of below the transition temperature. In contrast, the MS measured above T_C displays an essentially different feature, which consists of a paramagnetic singlet, as shown in Fig. 6(c). The related IS value is fitted to be 0.17 mm/s, which is an intermediate value between ∼ 0.07 mm/s for an Fe⁴⁺ state and ∼0.35 mm/s for an Fe³⁺ state,^[43,44] in accordance with the high-temperature charge combination. The changes in the valence state strongly indicate the occurrence of intermetallic charge transfer between the A′ -site Cu and the B-site Fe ions (3Cu³⁺+ 3e→3Cu²⁺; 4Fe³⁺ − 3e→4Fe^3.75+).

Fig. 6.

	Figure Option ViewDownloadNew Window
	Fig. 6. Mössbauer spectra of LaCu3Fe4O12 at (a) 4.2 K, (b) 298 K, and (c) 423 K. Arrows in panel (c) show spectral features due to a small amount of α-Fe2O3 impurity.[31]

The first-order charge-transfer transition changes the electronic configurations of Cu and Fe ions simultaneously, so in addition to the sharp variation in unit cell configuration, the magnetism and electrical transport properties are also expected to change significantly. Figure 7(a) shows the temperature dependence of magnetic susceptibility. A dramatic anomaly is obvious where temperature passes T_C, suggesting the presence of a magnetic phase transition accompanying the charge transfer. Actually, the observed magnetic sextuplet in the MS below T_C indicates long-range spin ordering of Fe³⁺ ions, while the singlet above T_C demonstrates the nonmagnetic nature. Furthermore, the temperature dependent hyperfine field (HF) obtained based on the MS measurements also agrees with the spin order-to-disorder transition (Fig. 7(b)). The exact zero HF value above T_C confirms the paramagnetic state. However, the HF increases sharply when the charge combination changes from the high-temperature to the low-temperature , reflecting the development of long-range spin ordering below T_C. Taking into account the linear magnetization behavior in the spin ordered phase, shown in the inset in Fig. 7(a), long-range antiferromagnetic (AFM) ordering is expected.

Fig. 7.

	Figure Option ViewDownloadNew Window
	Fig. 7. Temperature dependence of (a) magnetic susceptibility χ measured at an applied field of 0.1 T, (b) hyperfine field HF and isomer shift IS , and (c) magnetic moment of Fe obtained form NPD analysis of LaCu3Fe4O12. The inset in panel (a) shows the linear magnetization behavior at 300 K and 200 K .[30]

To further confirm the charge-transfer-induced spin order transition, neutron powder diffraction (NPD) was performed at different temperatures (see Fig. 8). The NPD pattern measured at 425 K (Fig. 8(b)) can be fitted well based on the cubic Im-3 crystal structure model as mentioned before, and no magnetic diffraction peak is visible above T_C. Below the critical temperature, however, strong magnetic contributions are observed, as clearly seen by the 111 and 113 magnetic Bragg reflections (Fig. 8(a)). The refinement reveals a magnetic superstructure with a (1/2 1/2 1/2) propagation vector of the cubic cell, producing a G-type AFM structure, where each Fe³⁺ spin aligns antiparallel to the six nearest neighbors, as shown in Fig. 9. This AFM ordering is also consistent with the linear magnetization behavior (inset in Fig. 7(a)). The refined magnetic moments of the B-site Fe are 4.03(2)μ_B and 3.28(3)μ_B at 50 K and 375 K, respectively (Fig. 7(c)). Both of them are reduced from the ideal value of 5.0μ_B for a high-spin Fe³⁺ (S = 5/2), probably implying some Fe–O covalency effects. No magnetic contribution from the square-planar-coordinated 6c site is found. Because the square-planar-coordinated Cu results in considerable energy splitting between the d_x²−y² and d_3z²−r² orbitals, the 3d electrons in Cu³⁺ (3d⁸) ions fully occupy the d_xz, d_yz, d_xy, and d_3z²−r² orbitals, making the d_x²−y² orbital empty with a total spin S = 0. The AFM ordering thus originates from the B-site Fe³⁺ only.

Fig. 8.

	Figure Option ViewDownloadNew Window
	Fig. 8. The NPD patterns and Rietveld refinement profiles of LaCu3Fe4O12 at (a) 300 K and (b) 425 K. The observed (circles), calculated (red line), and difference (blue line) patterns are shown. Green ticks show the positions of the Bragg reflections, and pink ticks in panel (a) show the positions of magnetic reflections from the G-type antiferromagnetic ordering of the B-site spins.[31]

In the A-site ordered perovskites, the A′O₄ units are spatially isolated from each other, so the electrical conductivity must be dominated by the corner-sharing BO₆ octahedra (see Fig. 1(c)). As shown in Fig. 10, the low-temperature AFM phase with Fe³⁺ displays insulating behavior. The temperature dependence of resistivity between 100 K and 300 K can be fitted well based on a Mott 3D variable-range hopping (VRH) model: R(T) = R₀exp(T₀/T)^1/4 (inset of Fig. 10). However, when the B-site Fe³⁺ is changed to a mixed Fe^3.75+, an insulator-to-metal transition is observed at T_C. The observed thermal hysteresis in resistance is also consistent with the first-order nature of the intermetallic charge transfer transition.

Fig. 9.

	Figure Option ViewDownloadNew Window
	Fig. 9. The G-type antiferromagnetic structure of B-site Fe3+ spins in LaCu3Fe4O12. Only magnetically ordered Fe3+ ions are shown. Spins are drawn along the [001] direction because the exact orientation of the magnetic moments cannot be determined by NPD.[32]

Fig. 10.

	Figure Option ViewDownloadNew Window
	Fig. 10. Temperature dependence of normalized resistivity of LaCu3Fe4O12. Inset shows the result obtained by fitting data in the temperature range between 100 K and 300 K to a 3D VRH model.[31]

In addition to LCFO, the Cu–Fe intermetallic charge transfer is observed in other ACu₃Fe₄O₁₂ systems, systems with A = Pr, Nd, Sm, Eu, Gd, Tb, or Bi, giving rise to similar interrelated changes in unit cell, magnetism and electrical conductivity.^[31,34,35] Moreover, with decreasing size of the ion at the A-site, the charge-transfer critical temperature gradually decreases. When high pressure is applied to tune the unit cell volume, a pressure-induced charge transfer is found to occur in LCFO at room temperature.^[33] Note that if another rare earth ion with smaller ionic radius, such as Dy, Ho, Er, Tm, Yb, Lu or Y, is substituted at the A-site, charge disproportion of iron ions (8Fe^3.75+ → 3Fe⁵⁺+ 5Fe³⁺) takes place instead of Cu–Fe intermetallic charge transfer (3Cu³⁺+ 4Fe³⁺ → 3Cu²⁺+ 4Fe^3.75+).^[35,45] It has been reported that the strength of the crystal-field splitting and the relative energy ordering between Cu 3d_xy and Fe 3d states are the key parameters determining the intermetallic charge transfer (charge disproportionation) in ACu₃Fe₄O₁₂ compounds with light (heavy) rare earth metals.^[46]

Magnetoelectric (ME) multiferroicity with coupled ferroelectric and magnetic orders has received much attention due to its great potential for numerous applications.^[47–54] Perovskites are one of the most important material systems for multiferroic study. Since the discovery of multiferroic behavior in perovskites BiFeO₃ and TbMnO₃,^[48,49] a many multiferroic materials with different physical mechanisms have been found in the last decade.^[55–59] Among them, the spin-induced multiferroics have received the most attention because their ferroelectricity is induced by magnetic structures, leading scientists to expect a strong ME coupling.^[60–62] Several theories such as the spin-current model (or inverse Dzyaloshinskii–Moriya interaction), exchange striction mechanism and d–p hybridization mechanism have been proposed to account for the spin-induced ferroelectricity in ME multiferroics by special spin textures such as non-collinear spiral spin structures and collinear E-type AFM structure with zigzag spin chains.^[63–67] It is well known that a cubic perovskite lattice is unfavorable for ferroelectricity due to the existence of an inversion center. However, the total symmetry for an ME multiferroics reflects the crystal and magnetic symmetries together. Therefore, in principle, it is possible to find ME multiferroics in a cubic perovskite system if the system’s magnetic structure breaks the space inversion symmetry. Nevertheless, such an intriguing case was never found in previous studies. The -type A-site ordered perovskite provides an opportunity for researching ME multiferroics in a cubic lattice. Since both A′ and B sites accommodate magnetic transition-metal ions, multiple magnetic and electrical interactions may develop, while the crystal structure can be finely tuned by selecting appropriate A′ and B elements to maintain the cubic lattice.^{[24,30,68–70]}

In this section, a spin-driven multiferroic phase with strong ME coupling effects in the A-site ordered perovskite LaMn₃Cr₄O₁₂ (LMCO) with cubic symmetry will be described. The unique multiferroic behavior in this cubic perovskite originates from a nontrivial effect involving the interactions between two magnetic sublattices. The present study not only provides the first example of multiferroics in a cubic perovskite system but also presents new insights into the physical mechanisms of multiferroics.

LMCO can be prepared by using high pressure and high temperature conditions, as detailed in Ref. [28]. Temperature dependent XRD shows that this compound always possesses an A-site ordered perovskite structure with cubic space group Im-3 from 23 K to 293 K (Fig. 11). The stability of this long-range cubic crystal structure is also confirmed by low-temperature (10–300 K) Raman scattering as shown in Fig. 12(a).

Fig. 11.

	Figure Option ViewDownloadNew Window
	Fig. 11. (a) Temperature dependent x-ray diffraction of LaMn3Cr4O12. Diffraction peaks were indexed based on space group Im-3. Stars show the diffraction peaks originating from a small amount of Cr2O3 impurity. (b)–(e) The enlarged views for several representative diffraction peaks. No structural phase transition occurs as temperature decreases from 293 K to 23 K.

Fig. 12.

	Figure Option ViewDownloadNew Window
	Fig. 12. (a) Raman spectra measured at different temperatures for LaMn3Cr4O12. No long-range structural phase transition is observed between 300 K and 10 K. Temperature dependence of (b) Raman shift and (c) the full width at half maximum (FWHM) for the two strongest Raman modes Ag(2) and Eg(2). Anomalies around 180 K may indicate local structural changes, as described in text.

Magnetic susceptibility and specific heat measurements reveal two AFM transitions in LMCO, occurring at T_Mn ∼ 50 K and T_Cr ∼ 150 K, respectively (Fig. 13). To clarify the origin of these two AFM phase transitions, NPD was performed at different temperatures. The NPD data shown in Fig. 14 demonstrates that the cubic Im-3 crystal structure persists down to 2 K, in agreement with the low-temperature XRD and Raman results. Meanwhile, based on the temperature dependence of the magnetic peaks (111) and (100) (Figs. 15(a) and 15(b)), the NPD results confirm that the spin orderings of the Mn and Cr sublattices lead to the AFM transitions at T_Mn ∼ 50 K and T_Cr ∼ 150 K, respectively. Furthermore, the NPD refinements produce collinear G-type AFM spin structures for both the A′-site Mn-sublattice and the B-site Cr-sublattice, with the propagation vector of (111)/(100) for the Cr/Mn-sublattice and the spin orientations most probably along the equivalent [111] direction (Fig. 16). This collinear AFM spin configuration is consistent with the linear magnetization behaviors observed at different temperatures, shown in Fig. 13(a).

Fig. 13.

	Figure Option ViewDownloadNew Window
	Fig. 13. (a) Magnetic field dependence of magnetization measured at different temperatures. The linear magnetization behaviors are consistent with the collinear G-type antiferromagnetic structure of LaMn3Cr4O12 as revealed by neutron powder diffraction. (b) Temperature dependence of susceptibility χ of LMCO. (c) Temperature dependence of specific heat CP of LMCO.

Figure 17(a) shows the temperature dependence of the dielectric constant (ε). Corresponding to the AFM phase transition occurring at T_Mn, ε also displays a sharp anomaly. Moreover, this dielectric variation is independent of frequency, implying the possibility of a ferroelectric phase transition coupled with AFM ordering of the Mn spins. Thus, the ME coupling may occur at the onset of T_Mn in the cubic perovskite LMCO. Looking further, we see another broadening and frequency-dependent dielectric anomaly at about 110 K for 10 kHz and 155 K for 1 MHz. This relaxation behavior is reminiscent of a ferroelectric transition, probably originating from local structure inhomogeneity and/or some extrinsic effects, as will be discussed later.^[73]

Fig. 14.

	Figure Option ViewDownloadNew Window
	Fig. 14. Rietveld refinements for neutron powder diffraction data of LaMn3Cr4O12 collected at (a) 170 K, (b) 80 K, (c) 35 K, and (d) 2 K. Small amounts of Cr2O3 and MnCr2O4 impurity phases (< 5 wt%) were observed.

Fig. 15.

	Figure Option ViewDownloadNew Window
	Fig. 15. Temperature dependence of integrated NPD intensities of (111) (a) and (100) (b) peaks, respectively.

Fig. 16.

	Figure Option ViewDownloadNew Window
	Fig. 16. G-type AFM structures of the B-site Cr-sublattice (a) and the A′-site Mn-sublattice (b), both with spin orientation along the [111] direction. (c) A complete set of spin alignment composed of Cr and Mn spins below TMn. For clarity, La and O atoms are omitted in the structures. Blue ball: Cr atom; red ball: Mn atom.

These two ferroelectric phase transitions were further studied by measuring pyroelectric current (I_p) to derive the ferroelectric polarization (P) with both positive and negative electric (E) poling procedures from 200 K down to 5 K, as shown in Figs. 17(b) and 17(c). Obviously, the I_p and P are completely switchable by the poling E reversal. The most striking finding is that the Mn spin ordering transition is coupled with a sharp change in both I_p and P at T_Mn (Figs. 17(b) and 17(c) and the insets), strongly indicating that the presence of this low-temperature ferroelectric phase transition (FE1) is closely related to the magnetic ordering of the Mn sublattice, in agreement with the dielectric constant measurements. In addition, in the high temperature region, I_p and P were found to emerge gradually below about 180 K, and then a broad peak in I_p appears near 125 K (Fig. 17(b)). Since these two characteristic temperatures (180 K and 125 K) differ from the value of T_Cr (150 K), the associated ferroelectric phase (FE2) seems to be of non-magnetic origin.

Note that the drastic changes of I_p at T_Mn are not a single peak or dip but unusual dip-peak features and vice versa for the +poled and −poled curves, respectively (inset of Fig. 17(b)). Accordingly, the obtained P(T) curves slightly decreases and then increases or vice versa for +poled or −poled on cooling around T_Mn (inset of Fig. 17(c)). This implies that two independent polarizations are superposed below T_Mn. To prove this point, two different poling E schemes were performed, passing either 180 K or T_Mn (= 50 K) only. In sharp contrast to the dip-peak features in I_p when poling E across both T_Mn and 180 K, only a single dip (200−75 K, +poled) or peak (75–30 K,+ poled) in I_p was observed in each poling scheme, respectively, as shown in Figs. 18(a) and 18(b). Correspondingly, the obtained net polarization changes (ΔP = P(T) − P (50 K)), which represent the influence of Mn ordering upon the P values, show negative values when E is applied only across 180 K, whereas positive ΔP values are obtained with E applied only across T_Mn, as shown in Fig. 18(c). The single dip in I_p (200–75 K,+ poled) means that, although the FE2 phase sets in at a temperature much higher than T_Mn, the spin ordering of Mn ions still causes a decrease of in the magnitude of P in this phase. More interestingly, the peak in I_p (75–30 K and +poled) reveals that the FE1 phase, which develops at T_Mn, is a ferroelectric phase that is independent of the FE2 phase. Since the FE1 phase strongly couples with the AFM ordering of the Mn-sublattice, the present cubic perovskite LMCO can be regarded as a new case of spin-driven multiferroics below T_Mn.

Fig. 17.

	Figure Option ViewDownloadNew Window
	Fig. 17. Temperature dependence of (a) dielectric constant ε and magnetic susceptibility χ, (b) pyroelectric current Ip and (c) ferroelectric polarization P in both+ poled and –poled conditions. The ε and Ip were measured without magnetic field. Insets of panels (b) and (c) show enlarged views near 50 K.[36]

To further confirm that the observed pyroelectric signals come from intrinsic ferroelectricity instead of a plausible space charge effect, different external magnetic fields are applied to measure the pyroelectric and dielectric properties. Considerable anisotropic ME and magnetodielectric effects are found in these two FE phases at and below T_Mn. As shown in Fig. 19(a), when an external magnetic field H||E is applied up to 12 T in the poling and measuring processes, the absolute values of I_p near T_Mn are enhanced by about one order of magnitude for both phases. The calculated ∣ΔP∣ values in both FE phases also increase from ∼ 15 μC/m² to ∼ 68 μC/m² at 30 K (Fig. 19(b)). In the H⊥E configuration, however, the I_p near T_Mn is found to be completely suppressed above 7 T field (not shown here).

Fig. 18.

Figure Option ViewDownloadNew Window

Fig. 18. Poling procedure dependence of electric behaviors below TMn. (a) Temperature dependence of pyroelectric current Ip by+ poled and –poled under 200–75 K and 75–30 K poling conditions. Temperature dependence of (b) Ip and (c) the difference of polarization δP (= P(T)-P(50 K)) after being+ poled from 200 K down to the selected temperatures. The δP is obtained by integration of Ip in panel (b) as a function of time. As shown in panel (b), a dip-peak feature is observed when E passes through both 180 K and TMn, whereas only a single dip is observed when E is turned off at temperatures higher than TMn. Therefore, the dip in Ip at TMn must be contributed by the FE2 phase, and the peak in Ip at TMn originates from the FE1 phase. The corresponding negative δ P indicates that electric polarization of the FE2 phase decreases in magnitude below TMn.

Similarly, the dielectric constant ε also shows significant changes under magnetic field at and below T_Mn. For the H||E configuration, the sudden jump in ε around T_Mn for μ₀H = 0 changes into a sharp peak for μ₀H ≥ 3 T (Fig. 20(a)). By comparison, the H⊥E configuration shows a remarkably smaller dielectric jump at T_Mn, so much so that almost no dielectric anomaly is observed with field above 7 T (Fig. 20(b)), consistent with the complete suppression of electric polarization at this H and E configuration under high field mentioned above. On the other hand, however, with increasing magnetic field, there is no remarkable change in ε above T_Mn in either the H||E or the H⊥E configuration, revealing that the FE1 and FE2 phases have different origins. Anyway, our magnetic-field dependent measurements show that the FE1 phase has strong anisotropic H dependent behavior, excluding any extrinsic origin of the space charge for this multiferroic phase.

Fig. 19.

	Figure Option ViewDownloadNew Window
	Fig. 19. (a) Temperature dependence of Ip and (b) difference of polarization δP under different poling conditions and different magnetic fields below 50 K.[36]

Fig. 20.

	Figure Option ViewDownloadNew Window
	Fig. 20. Temperature dependence of ε measured at 1 MHz and different magnetic fields with H||E and H⊥E configurations, respectively. Data have been shifted for clarity.[36]

Note that, as can be seen from the XRD and NPD patterns (Figs. 11 and 14), small amounts of Cr₂O₃ and MnCr₂O₄ impurity phases (< 5 wt%) were found in our high-pressure product. Although these two phases exhibit multiferroic behaviors, they do not affect the intrinsic physical properties of LMCO. Specifically, Cr₂O₃ displays an ME effect below 307 K,^[67] but this phase transition temperature is much different from both the T_Mn (= 50 K) and the T_Cr (= 150 K) observed in our LMCO (Fig. 13). Moreover, there is no visible polarization above 180 K (Figs. 17(b) and 17(c)), indicating that the magnetic and electric transitions, as well as the ME coupling, of LMCO are not related to the Cr₂O₃ impurity. In addition, MnCr₂O₄ shows a sharp ferrimagnetic transition at 43 K and exhibits significant spontaneous magnetization with a saturated moment of about 1.0μ_B f.u.⁻¹ at 5 K.^[72] In the present LMCO, however, there is no magnetic anomaly around 43 K (Fig. 13(a)), and the magnetic field dependence of magnetization shows a completely linear relationship at 5 K (Fig. 13(b)). Therefore, any effect of MnCr₂O₄ on the intrinsic physical properties of LMCO can also be safely ruled out. Recently, a centrosymmetric perovskite, SmFeO₃ has been reported to have multiferroicity that is induced by noncollinear G-type AFM order.^[74] Unfortunately, however, this reported ferroelectricity was later disproven by theoretical work^[75] and other experiments.^[76] In particular, Kuo et al.^[76] suggested that magnetoelastic coupling can give rise to artificial pyroelectric current, as has been observed in SmFeO₃. However, this is not the case for the LMCO sample. Magnetoelastic-coupling induced pyroelectric current usually is not switchable by poling electric field, as pointed out by Johnson et al. for the case of CaBaCo₄O₇.^[77] Nevertheless, the pyroelectric current of LMCO can be reversed by poling electric field. Moreover, the sign of the magnetoelectric coefficient (dP/dH) can also be reversed by changing the direction of the poling electric field. These two facts completely rule out the magnetoelastic-coupling mechanism in LMCO. Therefore, the ferroelectricity observed in LMCO below T_Mn = 50 K must be intrinsic in origin.

Next we discuss some possible mechanisms responsible for the low-temperature Mn spin ordering induced ferroelectricity in the cubic perovskite LMCO. First, both the inverse Dzyaloshinskii–Moriya interaction and the spin-current model, both of which are related to the cross products of spins, are excluded due to the collinear spin configuration of LMCO (Figs. 16(a)–16(c)). The exchange striction mechanism-induced electric polarization is related to the dot product of a pair of spins, which is independent of the spin orientations if the two spins are always parallel or antiparallel with each other. In contrast, based on the magnetic point group analysis and theoretical calculations to be shown later, the polarization direction of FE1 phase is always simultaneously changed with the spin orientations (in one of the equivalent [111] directions). This means that the exchange striction mechanism does not contribute to the polarization in FE1 phase if there is any. As a consequence, these conventional ME mechanisms simply cannot explain the present ferroelectric behaviors.

In the temperature region of T_Mn < T < T_Cr, the Cr sublattice is ordered in a G-type AFM manner with spin orientation along the [111] direction (Fig. 16(a)). Since the crystal space group is Im-3, the magnetic point group must be a non-polar −3′ group with a space inversion center. At T < T_Mn, the Mn sublattice is also ordered in a G-type AFM structure with non-polar −3 group as its own magnetic point group (Fig. 16(b)). Therefore, no polarization can be induced by either Cr or Mn spin ordering alone. However, when the Mn and Cr sublattices are considered together below T_Mn, the system magnetic point group is polar group 3 (Fig. 16(c)), which allows polarity along the spin direction. This suggests that the ferroelectric polarization of the FE1 phase most probably arises from the Mn and Cr spin configurations together, ruling out any possibility of a single spin mechanism, e.g., the d–p hybrid model.^[66]

Density functional theory calculations have been performed to better understand the spin-driven ferroelectricity of the FE1 phase. The calculated density of states with a band gap at about 1.75 eV reveals the insulating nature of LMCO (see Fig. 21). The calculated local moments for the Mn (3.907μ_B) and Cr (2.799μ_B) ions also agree with the NPD refinement results (Table 2). The ferroelectric polarization was calculated using the Berry phase method.^[78] The experimental magnetic orders were adopted and the structure was relaxed starting from the experimental one. The results show: 1) Without considering the spin–orbit coupling (SOC) of the magnetic ions, the calculated ferroelectric polarization for the experimental magnetic ground state is exactly zero in the FE1 phase; 2) If the SOC is considered, with all spins pointing parallel or antiparallel to the [111] axis, as the NPD study suggested, even the exact high-symmetric structure can induce a small but nonzero ferroelectric polarization ∼ 3.4 C/m² along the [111] direction. This result, without any contribution from ionic displacement, is the pure electronic polarization; 3) The direction of pure electronic polarization can be switched by rotating the magnetic axis. These results support excluding any possible contribution from inaccuracy of the ionic relaxation calculation, and support the proposal that the intrinsic ferroelectricity is caused by the spin ordering; 4) When the ionic positions are further relaxed with SOC considered, the model gives a total polarization up to ∼ 7.5 μC/m², still along the [111] axis. Although this small value may be not very precise due to the inaccuracy of ionic displacements, the value is comparable in order of magnitude with experimental observations at zero field (∼ 15 μC/m², see Fig. 18(c)), and also consistent with magnetic symmetry analysis, in that the ground state magnetic structure is polarized. Note that since the three conventional mechanisms for spin-driven ferroelectricity have been shown not to be applicable in the present cubic perovskite system, other, more exotic mechanisms involving the relativistic exchange interactions are plausible, and they generate only a moderate polarization.

Fig. 21.

	Figure Option ViewDownloadNew Window
	Fig. 21. DFT results with dual G-type antiferromagnetism (without SOC). Projected density of states (PDOS) for each atom species is shown. The calculated band gap (∼ 1.75 eV) reveals the insulating nature of LaMn3Cr4O12.

Table 2.

Table 2.

Table 2. Refined structural parameters from the NPD data of LaMn3Cr4O12 at different temperatures. Space group: Im-3 (No. 204); atomic positions: La 2a (0, 0, 0), Mn 6b (0, 0.5, 0.5), Cr 8c (0.25, 0.25, 0.25), O 24g (0, y, z). . LaMn3Cr4O12 2 K 35 K 80 K 170 K a/Å 7.39805(9) 7.3988(1) 7.3996 (1) 7.4028(1) y(O) 0.3104(4) 0.3096(4) 0.3099(4) 0.3102(3) z(O) 0.1771(4) 0.1765(5) 0.1767 (4) 0.1757(4) Uiso(O) 0.004(2) 0.004(2) 0.004(2) 0.004(2) Uiso(La) 0.009(3) 0.005(3) 0.008(3) 0.009(3) Uiso(Mn) 0.040(3) 0.036(3) 0.037(3) 0.032(3) Uiso/(Cr) 0.054(3) 0.055(3) 0.048(3) 0.048(3) dMn-O/4 Å 1.919(3) 1.921(3) 1.921(3) 1.915(2) dCr-O/6 Å 1.978(3) 1.978(4) 1.978(3) 1.981(5) dLa-O/12 Å 2.644(3) 2.637(3) 2.639(3) 2.639(1) ∠Cr-O-Cr/(°) 138.52(4) 138.54(5) 138.55(4) 138.14(4) MMn/μB 3.40(8) 2.66(9) 0 0 MCr/μB 2.89(6) 2.81(6) 2.50(3) 0 RBragg/% 1.60 3.70 2.79 2.88 χ2 1.81 1.77 1.73 1.68

Table 2. Refined structural parameters from the NPD data of LaMn3Cr4O12 at different temperatures. Space group: Im-3 (No. 204); atomic positions: La 2a (0, 0, 0), Mn 6b (0, 0.5, 0.5), Cr 8c (0.25, 0.25, 0.25), O 24g (0, y, z). .

As for the FE2 phase, since the pyroelectric current emerges above T_Cr and exhibits a broad peak at about 125 K, its origin is clearly not related to any spin ordering. Such a feature, on one hand, may be ascribed to an extrinsic effect such as space charges trapped at the grain boundaries or possible defects, as reported elsewhere.^[79,80] On the other hand, some ABO₃ perovskites like YCrO₃ and SmCrO₃ with Cr³⁺ ions at the B site reportedly display similar electric polarizations above their AFM temperatures.^[81,82] Neutron pair distribution function (PDF) was used to illustrate that this type of polarization originates from a “local non-centrosymmetric effect” caused by local displacement of the second-order Jahn–Teller Cr³⁺ cations, whereas the macroscopic crystal structure was unchanged, remaining centrosymmetric. In the present LMCO, although the long-range crystal structure is stable down to 2 K, similar local displacements of Cr³⁺ cations are possible, as implied by the relaxation behavior of the dielectric constant in the high-temperature region (Fig. 17(a)). To further explore the possible local displacements of Cr cations in the present LMCO, low-temperature Raman scattering was performed, as presented in Fig. 12. In agreement with NPD and XRD data, the Raman spectra show no long-range crystal structure phase transition at temperatures down to 10 K. However, some Raman peaks that reflect the vibrations of CrO₆ octahedra somewhat change vibration frequency as well as full width at half maximum at around 180 K,^[83] perhaps implying a local-structure origin for the FE2 phase. However, more experimental methods, such as high-resolution neutron pair distribution function, are needed to clarify the exact origin of the FE2 phase.

Anyway, it should be emphasized that the ME multiferroicity found in the present LMCO with onset at about 50 K is quite unique among all the known multiferroic systems in that it occurs in a true cubic perovskite system with simple and collinear spin alignments. Due to the highly symmetric lattice and spin structures, the three major mechanisms that induce ferroelectric polarization by magnetic ordering cannot play roles. Since pure electronic polarization shows up in the FE1 phase, the cubic LMCO may become a prototype for future studies of electronic mechanisms of ferroelectricity. The present work therefore not only provides the first example of cubic perovskite multiferroics but also opens up a new arena for study of the unexpected ME coupling mechanisms.

In this review paper, the Cu–Fe intermetallic charge transfer in LaCu₃Fe₄O₁₂ and the magnetoelectric multiferroicity in LaMn₃Cr₄O₁₂ are described. Both compounds are prepared under high pressure and temperature, and they crystallize to A-site ordered perovskite structures. Due to the simultaneous changes of Cu and Fe electronic configurations, the charge transfer in LCFO gives rise to a series of interrelated phase transitions in lattice, spin, charge and orbital degrees of freedom. Although a cubic perovskite lattice is unfavorable for ferroelectricity due to the existence of an inversion center in its structure, the spin–orbit coupling effect of Cr and Mn ions plays an important role in the electric polarization of LMCO. These interesting findings are closely related to the peculiar crystal structure of A-site ordered perovskites, wherein both A′ and B sites accommodate TM ions, providing multiple magnetic and electrical interactions via A′–A′, A′ –B, and/or B–B pathways. One can thus design special functional compounds by selecting appropriate transition metals at different atomic positions to modify the magnetic and transport properties. Furthermore, if a third transition metal is partially substituted in the B site, both A-site and B-site ordered perovskites with specific functional properties can be formed. Therefore, the present A-site ordered perovskites pave the way to design new functional materials and find new physics and functionalities.