The rich physics of A-site-ordered quadruple perovskite manganites AMn₇O₁₂

Abstract

Perovskite-structure AMnO₃ manganites played an important role in the development of numerous physical concepts such as double exchange, small polarons, electron–phonon coupling, and Jahn–Teller effects, and they host a variety of important properties such as colossal magnetoresistance and spin-induced ferroelectric polarization (multiferroicity). A-site-ordered quadruple perovskite manganites AMn₇O₁₂ were discovered shortly after, but at that time their exploration was quite limited. Significant progress in their understanding has been reached in recent years after the wider use of high-pressure synthesis techniques needed to prepare such materials. Here we review this progress, and show that the AMn₇O₁₂ compounds host rich physics beyond the canonical AMnO₃ materials.

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Alexei A. Belik

Alexei A. Belik is a principal investigator at the National Institute for Materials Science (NIMS), Japan, which he jointed as a permanent member in 2006. He holds a PhD in Inorganic Chemistry from Moscow State University, Russia. He was a postdoctoral researcher at NIMS (2000–2002 and 2004–2006) and Kyoto University, Japan (2002–2004). His current interests are in high-pressure synthesis of new materials (mainly oxide perovskites) and their characterization.

Roger D. Johnson

Roger Johnson is a lecturer in condensed matter physics at University College London and a Royal Society University Research Fellow. He works in the area of quantum materials and physical crystallography. Crystal and magnetic structure solutions are obtained by multiple diffraction-based methods, and combined with symmetry analysis by group and representation theory, Roger determines structure–property relationships in inorganic oxides, halides, and hybrid organic–inorganic materials.

Dmitry D. Khalyavin

Dmitry D. Khalyavin is an instrument scientist at the ISIS Facility of the Rutherford Appleton Laboratory. He runs the high-resolution cold-neutron diffractometer WISH primarily designed for powder and single crystal diffraction in magnetic and large unit cell systems. The main Dmitry's expertise is magnetic crystallography, structural and magnetic phase transitions as well as diffraction methods in solid state physics.

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1. Introduction

Perovskite-structure manganites have experienced waves of intensive study,¹ starting in the late 1940s with the discovery of conductive and ferromagnetic (FM) properties and metal–insulator transitions in mixed-valence R_1−xA_xMnO₃ (R = trivalent cations and A = divalent cations). A theoretical understanding of these properties was quickly developed, including the theory of double exchange² and Goodenough's one-electron electronic structures.³ Then followed the discovery of colossal magnetoresistance (CMR),⁴ prompting intensive work on single crystals and thin films, and the proposal of magnetic and electronic phase separation scenarios.⁵ Perovskite manganites also played an important role in the revival of interest in multiferroic and magnetodielectric materials with RMnO₃ (R = Tb and Gd) hosting some of the largest values of spin-induced ferroelectric polarization.⁶ They were also intensively studied as catalysts,⁷ solid mixed-conductive electrolytes, electrode materials, thermoelectric ceramics and sensors. This remarkable diversity in physical properties is rooted in considerable structural and chemical flexibility. As such, the perovskite manganites have become canonical systems for the study of structure–property relationships in strongly correlated electron systems.

AMn₇O₁₂ manganites (with A = Na, divalent and trivalent cations) are a special subfamily of perovskite-type materials, namely the A-site-ordered quadruple perovskites⁸ with general chemical formula AA′₃B₄O₁₂. Three quarters of large A cations are replaced by small Mn³⁺ cations at the A′ sites with an effective square-planar coordination (Fig. 1). By heterovalent substitution of the A cations, which have a large 12-fold coordination (Fig. 1), one can obtain mixed-valence states of Mn at the B sites, i.e. Aⁿ⁺Mn³⁺₃(Mn³⁺_1+nMn⁴⁺_3−n)O₁₂, in close analogy to R_1−xA_xMnO₃. The AMn₇O₁₂ compounds are stabilized by very large tilts of the a⁺a⁺a⁺ type in Glazer's notation,⁹ requiring high-pressure high-temperature treatments for their preparation (except for CaMn₇O₁₂, which can be synthesised at ambient pressure). Such an ‘exotic’ synthesis procedure could be the main reason why they did not attract much attention immediately after their discovery despite great interest in the classical mixed-valence R_1−xA_xMnO₃ perovskites. Only with the widespread use of high-pressure facilities has research on AMn₇O₁₂ intensified, and significant progress in their understanding has been reached in recent years. In this work, we review the recent progress on AMn₇O₁₂ manganites.

Fig. 1 Crystal structure of the parent cubic modification of A-site-ordered quadruple perovskites AMn₇O₁₂ and AA′₃B₄O₁₂ in space group Im3̄ exemplified by the structure of NaMn₇O₁₂ at RT.¹² An Mn–O–Mn (B–O–B) angle is given. A-site polyhedra are shown on the left, and B-site octahedra – on the right.

Because of the space limitations we cannot cite all references, especially those devoted to CaMn₇O₁₂. Therefore, only foundational references are given that are widely cited in latter works.

2. NaMn₇O₁₂

NaMn₇O₁₂ was the first compound of the AMn₇O₁₂ series to be discovered (in 1973) and was found to crystallize in an Im3̄ cubic structure at room temperature (RT) (Fig. 1); now identified as the parent aristotype to all AMn₇O₁₂.¹⁰ A low-temperature (LT) structural phase transition near T_CO = 176–190 K (CO stands for charge order) was soon found (Fig. 2), below which a monoclinic I2/m crystal symmetry with 1Mn³⁺ : 1Mn⁴⁺ B site charge order was suggested (here, the pattern of charge ordering is analogous to the pattern of orbital ordering associated with the I2/m structure of LaMn₇O₁₂ (see part 4)).¹¹ Despite clear parallels with the widely studied half-doped R_0.5A_0.5MnO₃ perovskite manganites also containing a 1Mn³⁺ : 1Mn⁴⁺ mixture at the B sites, NaMn₇O₁₂ attracted little attention for nearly 30 years.

Fig. 2 A diagram of temperature-driven structural distortions in AMn₇O₁₂ manganites from the parent cubic structure. Transition temperatures are reported on the figure when available. All distortions keep the 2a_p × 2a_p × 2a_p cell (with α ≈ β ≈ γ ≈ 90°) except trigonal systems (with α = β = 90° and γ = 120°), C2/m (ref. 13 and 14; with α = γ = 90° and β ≈ 90°) and Ia (ref. 68; with α = γ = 90° and β ≈ 90°). Note that for the R3̄ distortion with 2√2a_p × 2√2a_p × √3a_p, the 2a_p × 2a_p × 2a_p cell (with α = β = γ ≈ 90°) can also be constructed (using rhombohedral axes and non-standard setting). For MnMn₇O₁₂, a 4a_p × 4a_p × 4a_p cell with F1̄ symmetry was also reported at RT.³⁷a_p ≈ 3.8 Å is a lattice parameter of the cubic ABO₃ perovskite (space group Pm3̄m). For underlined compositions there are no further structural transitions.

Magnetic studies were performed in 2004, which showed two magnetic transitions at T_N1 = 125 K and T_N2 = 92 K.¹² It was suggested that Mn magnetic moments at the B sites order first at 125 K with an AFM-CE-type structure (AFM stands for antiferromagnetic), which can be described by two propagation vectors; k = (1/2, 0, −1/2) and k = (0, 0, 0). Mn moments at the A′ sites were reported to order at 92 K with an anti-body-centered arrangements of spins with propagation vector k = (0, 1, 0).¹² In this study the symmetry of the LT phase was taken to be I2/m (see above) with compressed Jahn–Teller (JT) distortions of the Mn³⁺ B sites. However, a theoretical study in 2014 pointed out inconsistencies between the reported experimental crystal and magnetic structures.¹³ The theoretical work¹³ proposed an alternative LT crystal structure, which was soon confirmed experimentally.¹⁴ This correct LT structure has C2/m symmetry, a 2√2a_p × 2a_p × 2√2a_p superstructure with α = γ = 90° and β ≈ 90° (where a_p is a lattice parameter of an ideal cubic ABO₃ perovskite), full static Mn³⁺/Mn⁴⁺ charge ordering, and elongated JT distortions of the Mn³⁺ B sites. This LT crystal structure can be described in terms of a commensurate modulation of the parent cubic structure with propagation vector k = (1/2, 0, −1/2). Importantly, this structural modulation is consistent with the magnetic propagation vectors observed below 125 K.

We believe that the magnetic structures of NaMn₇O₁₂ need re-investigation considering recent results on the magnetic structures of all other AMn₇O₁₂ and RMn₇O₁₂ manganites (see parts 3 and 4), where simultaneous ordering of Mn at the B and A′ sites was observed. An additional magnetic anomaly near 34 K was recently reported in NaMn₇O₁₂,¹⁵ which, in our opinion likely originates in an impurity: MnCO₃ has a magnetic transition with weak FM-like properties at this temperature, and an X-ray diffraction pattern reported in (ref. 16) gave evidence for the presence of an MnCO₃ impurity (a 100% peak of MnCO₃ near 31.5° was observed; note that (ref. 16) incorrectly assigned impurity peaks).

NaMn₇O₁₂ is a weak insulator with thermally activated charge transport, and resistivity increases by about one order of magnitude below T_CO.¹² NaMn₇O₁₂ ceramics also showed dielectric anomalies at T_CO and additional relatively sharp step-like frequency-dependent dielectric anomalies from 50 K (at f = 1 kHz) to 80 K (at f = 1 MHz).^15,17 These steps were originally left without explanation.¹⁷ Similar step-like dielectric behavior was observed in RMn₇O₁₂ (R = La, Ce, Sm, Eu and Gd) between 17 and 35 K, which was assigned to extrinsic effects (see part 4). No apparent dielectric anomalies were detected in NaMn₇O₁₂ at T_N1 and T_N2.¹⁷ Broad and symmetrical pyroelectric current anomalies were observed in NaMn₇O₁₂ from 20 K to 40 K, which were assigned to a (spin-induced) ferroelectric transition associated with the 34 K magnetic anomaly.¹⁵ Following the results of more recent detailed studies of other AMn₇O₁₂ compounds (see part 4), we expect that the dielectric and pyroelectric current anomalies in NaMn₇O₁₂ are most probably caused by extrinsic effects.

A number of works were devoted to the single-crystal growth of NaMn₇O₁₂.^16,18 It was found that small amounts of water and Na excess facilitate the crystal growth. The formation of good samples was observed in the pressure range of 2–6 GPa and temperature range of 670–1120 K with the best conditions at 6 GPa and 1100 K. Single-crystal X-ray diffraction studies gave the real chemical composition of the studied crystal as (Na_0.95Mn_0.05)Mn₇O₁₂.¹⁶ No structural phase transitions were found up to 40 GPa (at RT), but some anomalies in resistivity near 18 GPa gave evidence for charge transfer from the B site to the A′ site.¹⁹

3. AMn₇O₁₂ (A = Mn, Cd, Ca, Sr, Hg and Pb)

Perovskites with A = Ca, Cd and Sr were first reported by Bochu et al.²⁰ and synthesized under high-pressure and high-temperature (HT) conditions. Later, Horowitz and Longo²¹ prepared powder samples of CaMn₇O₁₂ at ambient pressure and so far this is the only member whose synthesis does not require extreme conditions. The authors also pointed out the mixed-valence character of this oxide. The charge degree of freedom has been found to be mainly localized on the B-site Mn ions, resulting in 3 : 1 charge order between Mn³⁺ and Mn⁴⁺ in the RT trigonal structure with R3̄ symmetry and apically compressed Mn³⁺O₆ octahedra.²² The latter implies that, unlike the vast majority of known JT systems with two longer and four shorter Mn–O distances (JT elongation), the Mn³⁺O₆ octahedra in CaMn₇O₁₂ are characterized by four longer and two shorter Mn–O distances (JT contraction, Fig. 3a). Hence, it was suggested that this perovskite represented a new type of JT distortion of Mn³⁺ cations in oxides, with x²–y²-type orbital ordering.²² This is a very unusual situation because the occupation of x²–y² orbitals of Mn³⁺ with locally compressed octahedra has been shown by Khomskii and van den Brink to be unstable due to anharmonic effects which always stabilize elongated octahedra.²³ The transition to the trigonal charge-ordered phase takes place well above RT and is associated with phase coexistence in the temperature range of 409–448 K where the LT trigonal phase coexists with the HT cubic one.²⁴ The LT structural studies^25–28 revealed another transition at T_OO = 260 K (OO stands for orbital order), where the crystal structure of CaMn₇O₁₂ develops an incommensurate structural modulation with propagation vector k_S = (0, 0, γ) (γ = 0.9215 at T = 113 K,²⁹ in the following discussion we will use the equivalent propagation vector (0, 0, 3) − k_S = (0, 0, 2.0785) to emphasize its relation with the modulation of the magnetic order). Initially, the modulation was assigned to charge ordering,²⁵ however, subsequent quantitative structure refinement of synchrotron X-ray and neutron powder diffraction data in the R3̄(0,0,γ)0 superspace group²⁷ did not support this interpretation and instead revealed a complex modulation of Mn–O bond distances. The model was confirmed by Perks et al.³⁰ using X-ray single-crystal data, and the modulation was interpreted as an incommensurate orbital ordering (orbital density wave) localised on the B-site Mn³⁺ cations. The density wave implies a periodic change of the 3x²–r² and 3y²–r² orbital occupancies passing through the x²–y² state only at the nodal points (Fig. 3b). In other words, in the modulated structure most of the octahedra are locally elongated along one of two axes that alternate periodically within the crystal, giving rise to the apical compression of octahedra on average.

Fig. 3 (a) Compression of Mn³⁺O₆ octahedra in CaMn₇O₁₂ at the phase transition from the disordered cubic Im3̄ to the charge-ordered trigonal structure (Mn–O bond distances are taken from ref. 24 and 22 for the cubic and trigonal structures, respectively). Orbital density wave in CaMn₇O₁₂ (b), ξ-Mn₂O₃ (c) and CdMn₇O₁₂ (d), illustrating the change of orbital state of Mn³⁺ upon propagation along the trigonal axis. In the latter case, the commensurate orbital density wave splits the Mn position into two sites with fully and partially polarised states.

The systematic structural study by Belik et al.²⁹ revealed a similar modulation in other members of the family with A = Sr, Cd and Pb, taking place at T_OO = 265 K, 254 K and 294 K, respectively (Fig. 2). The propagation vector for the Sr-perovskite is also incommensurate with the magnitude very close to the Ca-counterpart; k_S = (0, 0, 2.0765) at T = 113 K. The modulation was found to be commensurate, k_S = (0, 0, 2), in the case of CdMn₇O₁₂, giving rise to the primitive unit cell with P3̄ symmetry. The commensurate nature of the orbital density wave was interpreted as an activation of a third-power lock-in term allowed in the Landau free-energy decomposition when the γ-component of the propagation vector takes the commensurate value.³¹ The centrosymmetric space group fixes the global phase of the commensurate orbital density wave and imposes a stacking of fully and partially polarized orbital states (Fig. 3d).

Note that some samples of CdMn₇O₁₂ showed phase separation below about 60 K,^31,32 characterised by a mixture of P3̄ and I2/m phases and large hysteresis in properties.³³ This coexistence likely reflects small variations in the real chemical compositions of such samples, and the appearance of the I2/m phase needs detailed investigations as it usually appears in R³⁺Mn₇O₁₂ (Fig. 2).

The situation with PbMn₇O₁₂ has been found to be more complicated.³⁴ Just below the transition at T_OO = 294 K the modulation is incommensurate with γ ∼2.08. At T_OO2 = 110 K another structural transition takes place where the propagation vector suddenly drops down to a quasicommensurate value k_S = (0, 0, 2.0060(6)). The quasicommensurate phase is stable in the temperature range of 40–110 K, and below T_OO3 = 40 K the propagation vector jumps back to the incommensurate value k_S = (0, 0, 2.060(6)). Both the LT structural transitions are strongly first order with large thermal hysteresis. The orbital density wave in the quasicommensurate phase has been found to be substantially suppressed in comparison with the incommensurate phases, and this behaviour was attributed to a competition between the Pb²⁺ lone electron pair and Mn³⁺ JT instabilities. This makes this perovskite particularly attractive as a new playground for various charge doping strategies by analogy with the BiMn₇O₁₂ system (see section 5, below), where a light hole doping has been shown to stabilize exotic electric dipole and orbital textures due to a fine tuning of the relative strength of these two electronic instabilities.³⁵ Similar to CaMn₇O₁₂, the perovskites with A = Sr, Cd and Pb exhibit a HT transition to the cubic Im3̄ structure at T_CO = 404 K, 493 K and 397 K, respectively, as determined by differential scanning calorimetry.³³ We note that in other studies, T_CO for PbMn₇O₁₂ was reported to be 380 K,³⁶ and for CaMn₇O₁₂ prepared at high pressure – to be 462 K,³³ suggesting that T_CO, and also T_OO, are sensitive to the sample quality.

Another member of the A²⁺Mn₇O₁₂ family is the ξ-polymorph of Mn₂O₃. As has been shown by Ovsyannikov et al.,³⁷ at high temperature (above 1000 K) and at high-pressure (above 18 GPa), Mn₂O₃ transforms to a perovskite modification which can be quenched into a metastable phase at ambient conditions. This metastable phase exhibits a unique charge disproportionation phenomenon stabilizing the quadruple perovskite structure Mn²⁺Mn³⁺₃Mn^3.25+₄O₁₂ with an additional 3Mn³⁺ : 1Mn⁴⁺ charge ordering and commensurate orbital density wave with k_S = (0, 0, 9/4), localized in the B-site perovskite position. The charge ordered modulated structure possesses R3̄ symmetry with a 2√2a_p × 2√2a_p × 4√3a_p supercell defined with respect to the pseudocubic simple perovskite structure which is prototype for all families of perovskite materials. Here, the orbital density wave represents a sequence of 3x²–r² and 3y²–r² orbital states ordered in a ++−− fashion (where + and − indicate distinct states) upon propagation along the trigonal axis (Fig. 3c). The commensurate nature of the orbital density wave and the associated structural modulation has been explained by a coupling of the orbital ordering to an independent structural distortion, which improves the poor bonding conditions of Mn²⁺ in the A-site perovskite position.³⁸ The trigonal structure has been reported to be stable at RT,³⁷ but the temperatures at which the B-site charge and orbital ordering onset are yet to be determined.

One more perovskite with a divalent A-site cation, HgMn₇O₁₂, has been recently reported by Chen et al.³⁹ Similar to other members of the family, it exhibits a cubic to trigonal structural transition due to the 3Mn³⁺ : 1Mn⁴⁺ charge ordering in the B-site manganese position. The transition is first order and takes place via phase coexistence in the temperature range of 470–490 K. However, instead of the modulated trigonal ground state, the LT structure of HgMn₇O₁₂ to a good approximation is commensurate orthorhombic with the polar Pnn2 symmetry. The transition to the orthorhombic phase takes place at 240–260 K and is associated with a further charge disproportionation where 1/3 of Mn³⁺ in the A′ position become Mn²⁺, giving rise to 1Mn²⁺ : 2Mn³⁺ charge ordering in the A′ square planar position as well as 1Mn³⁺ : 1Mn⁴⁺ charge and orbital ordering in the B-site position (Fig. 4). The polar symmetry is a result of the common action of two irreducible order parameters. One of them is the charge/orbital order and another serves to improve the coordination environment of the A′-site Mn²⁺ cations by making the environment more regular through shortening the second-nearest-neighbour distances. The charge transfer between the A′ and B sites has been suggested as an alternative mechanism to the orbital density wave formation to release the instability associated with the compressed octahedra in the 3 : 1 charge ordered trigonal phase. The B-site Mn³⁺ in this phase was assumed to exhibit orbital disorder between the 3x²–r²/3y²–r² states. Whether this is the case, or the x²–y² orbital state is imposed by the bilinear coupling to the atomic displacement mode accompanying the 3 : 1 charge order⁴⁰ is an interesting open question.

Fig. 4 Charge (left) and orbital (right) ordering in the orthorhombic Pnn2 phase of HgMn₇O₁₂ perovskite.³⁹

The perovskites of the A²⁺Mn₇O₁₂ family attracted great attention after the discovery of prominent multiferroic properties in CaMn₇O₁₂.^41,42 Long-range magnetic ordering in this material takes place at T_N1 ∼90 K with the incommensurate propagation vector, k₀, locked to the structural modulation such that k₀ = k_S/2.^26–28 Below T_N2 ∼48 K, the magnetic subsystem delocks from the structural modulation giving rise to a complex multi-k magnetic ground state.⁴³ The initially reported giant spin-driven polarization was found to onset at T_N1. Later studies⁴⁴ confirmed the multiferroic properties of CaMn₇O₁₂ but the electrical polarization was found only below the second magnetic transition at T_N2 with substantially lower magnitude. The corresponding ground state magnetic structure was quantitatively determined using high-resolution neutron powder and single crystal diffraction data⁴³ and was found to represent an unprecedented example of helical order with modulated spin chirality (Fig. 5). Unlike usual helical structures with a constant magnetic phase between spins related by a lattice translation along the propagation vector, the magnetic phase of the spins in the ground state of CaMn₇O₁₂ is incommensurately modulated with the periodicity of the orbital density wave. The magnetic structure decomposes into a set of magnetic order parameters with distinct propagation vectors, k_n±, along the trigonal axis. A symmetry based phenomenological approach⁴³ revealed that this exotic ground state is a result of coupling between the primary magnetic order, stabilized by competing exchange interactions and referred to as the fundamental component k₀ = (0, 0, 1.12354(8)), and the orbital density wave k_S = (0, 0, 2.0775(1)) at T = 1.5 K (magneto-orbital coupling). By symmetry, the fundamental helical order alone cannot lock to the structural modulation, and hence the coupling introduces additional magnetic components with k_n± = k₀ ± nk_S propagation vectors. Experimentally, the components up to n = 2 have been confirmed.⁴³ Microscopically, the magneto-orbital coupling implies that the orbital density wave modulates the competing exchange interactions and local anisotropies resulting in faster and slower rotations of spins upon propagation along the trigonal axis.

Fig. 5 Schematic representation of the anharmonic spin density wave (SDW) and the phase modulated helix, corresponding to the high-temperature lock-in phase and the ground state of A²⁺Mn₇O₁₂ manganites.⁴³

The spin-driven electric polarization in CaMn₇O₁₂ has been explained by the ferroaxial mechanism⁴¹ first proposed to explain multiferroic properties of Cu₃Nb₂O₈.⁴⁵ The mechanism describes a bi-linear coupling between spin chirality and polarization in crystals with axial distortions, known as ferroaxiality. The latter is a ferroic property like ferroelectricity and ferromagnetism, characterized by the presence of a well-defined rotation between different elements of the crystal structure (octahedral tilting in the given case). The trigonal crystal structure of A²⁺Mn₇O₁₂ with point group 3̄ belongs to the ferroaxial class. The relevant microscopic interaction giving rise to the macroscopic polarization is antisymmetric Dzyaloshinskii–Moriya (DM) exchange. This exchange can gain energy by distorting the crystal structure and/or the electronic density in the presence of non collinear spins.⁴⁶ A discussion of the ferroaxiality and the polar distortions optimizing the antisymmetric exchange in CaMn₇O₁₂ can be found in the work by Perks et al.³⁰

Unlike the helical order, a spin density wave can be locked to the structural modulation associated with the orbital density wave.⁴³ This type of ordering therefore is the prime candidate for the magnetic structure of CaMn₇O₁₂ in the temperature range of T_N2 < T < T_N1, where the magnetic and structural modulations are commensurate with each other, holding the k₀ = k_S/2 ratio (Fig. 5). The magneto-orbital coupling is expected to yield additional magnetic components making the spin density wave anharmonic, which was confirmed experimentally through the observation of higher order satellites (in particular the 3k₀ propagation vector).^27,43 It has to be pointed out that experimentally it is challenging to distinguish the spin-density wave with the spins confined within the (ab)-plane of the trigonal structure and the helical order. However, the commensurate relation between the magnetic and structural modulations and the absence of electrical polarization in the lock-in phase⁴⁴ strongly support the existence of a spin density wave above T_N2. Another argument in favour of this scenario comes from the precise magnetic structure determination in the ξ-polymorph of Mn₂O₃.^38,47 Similar to CaMn₇O₁₂, this perovskite also exhibits two magnetic transitions at T_N1 = 100 K and T_N2 = 50 K, and mutiferroic properties below T_N2. The HT magnetic phase has been found to be commensurate and locked to the structural modulation. The spins in this phase are polarized along the c-axis forming an anharmonic longitudinal spin density wave. The magnetic structure is only partially ordered and contains 1/4 of the A-site Mn²⁺ cations with zero ordered moment. Below T_N2, the magnetic propagation vector becomes incommensurate (k₀ = (0, 0, 1.2439(3)) at T = 1.5 K) and the magnetic structure turns into a phase modulated constant moment cycloid with only a small admixture of a helical component. Thus, the magnetic behaviour of CaMn₇O₁₂ and ξ-Mn₂O₃ is very similar apart from the different magnetic anisotropy which is an easy-plane type in the former case and easy axis (along the trigonal axis) in the latter. The longitudinal spin density wave can be unambiguously distinguished from any other solution and therefore the sequence paramagnetic – spin density wave – constant moment magnetic structure with rotating spins is a well-established experimental observation for this perovskite.

Magnetic structures of the perovskites with A = Sr and Cd are very similar to the Ca-counterparts.³¹ For these materials T_N1 is at 87 K and 88 K, respectively and the LT T_N2 transition occurs at 63 K for A = Sr and 33 K for A = Cd. The magnetic propagation vector k₀ for the former is (0, 0, 1.15427(6)) and for the latter (0, 0, 1.0682(1)) at T = 1.5 K, indicating that the periodicity of the fundamental helical component depends on the radius of the A-site cation. The PbMn₇O₁₂ perovskite exhibits an additional intermediate magnetic phase^31,48 related to the fact that the magnetic ordering onsets within the quasicommensurate structural phase with a substantially suppressed orbital density wave. Like in other manganites of this series, the magnetic propagation vector of PbMn₇O₁₂ is locked to the structural modulation just below T_N1 = 83 K. The lock-in phase is stable only in a narrow temperature range and at T_N2 = 77 K the magnetic propagation vector delocks from the structural modulation giving rise to the incommensurate helical order with only weakly modulated spin chirality. In an early study,³¹ this weakly modulated intermediate magnetic phase was interpreted as an unmodulated single-k helix, where the magneto-orbital coupling is fully suppressed. However, the latest work³⁴ confirmed the presence of very weak magnetic components k_n± indicating a finite magneto-orbital coupling. At T_OO3 = 40 K, the re-entrant transition to the incommensurate structural phase takes place, re-establishing the orbital polarization which in turn triggers a strong magneto-orbital coupling in the ground state helical structure of PbMn₇O₁₂ with the periodicity of the fundamental magnetic component being k₀ = (0, 0, 1.18410(8)) at 1.5 K.

Thus, the magnetic properties of the divalent A-site quadruple perovskites reveal a universal interplay between magnetic and orbital degrees of freedom, leading to the concept of magneto-orbital coupling. In the HT ordered state the periodicities of the magnetic and orbital subsystems lock together via commensurate magneto-orbital coupling. On cooling, these periodicities delock, allowing the system to evolve towards a multi-k magnetic ground state in which incommensurate magneto-orbital coupling gives rise to a modulation of the spin helicity. The stability of the locked and delocked magnetic phases is controlled by the balance between the entropy term (promoting a partially ordered state at higher temperatures), lock-in term, and magnetic exchange interaction requiring a propagation vector different from the orbital modulation.^31,43 While T_N1 remains approximately constant across the series (apart from ξ-Mn₂O₃ which has the additional A-site magnetic sublattice and therefore a noticeably higher T_N1), the periodicity of the ground state magnetic structure and the LT transition T_N2 both monotonically increase with increasing A²⁺ ionic radius. The only member of the family whose magnetic properties might differ significantly from that described above is HgMn₇O₁₂. Although, the magnetic structure is yet to be reported for this perovskite, there is no reason to believe that it should obey the common scenario where the lock-in phase is followed by the delocked phase-modulated ground state, imposed by the magneto-orbital coupling. Its crystal structure does not support the orbital density wave, adopting instead the alternative mechanism associated with the inter-site charge transfer that results in distinct charge and orbital patterns. Interplay between these electronic degrees of freedom with magnetism is therefore a very exciting topic for future studies.

Finally, let us mention the very recent X-ray resonant elastic scattering study of CaMn₇O₁₂,⁴⁹ where using polarization analysis it was found that the satellites with k₀ propagation vector are not purely magnetic. The authors conclude that there is one more phase transition around 30 K, where the periodicity of the magnetic ground state locks to the second harmonic of the orbital modulation (a second lock-in phase). It is quite hard to understand this conclusion based on symmetry grounds because this would require a free-energy term linear in the magnetic order parameter components and quadratic in the orbital density wave which is forbidden by time reversal symmetry. As discussed above, the ground state of CaMn₇O₁₂ is the multi-k modulated helix which consists of a set of magnetic order parameters creating additional structural modulations through magneto-elastic coupling. The periodicities of these structural modulations are twice bigger than the periodicities of the corresponding magnetic components and they have distinct symmetries from the orbital density wave. For instance, if one takes the second harmonic of the k₁₊ = k₀ + k_S (k₀ and k_S are found to be (0, 0, 1.12) and (0, 0, 0.94), respectively for the studied crystal), it coincides with k₀ and can be the origin of the observed charge-like contribution to the corresponding satellites. Since k₁₊ is not an independent order parameter, its second harmonic can also be expressed through a higher order coupling term using the k₀ and k_S order parameters. In particular, the relevant term will be linear in respect of the magneto-elastic structural modulation and quadratic in respect of both k₀ and k_S, whose explicit form can be worked out using the information provided in (ref. 43). The presence of this structural modulation is a natural consequence of the magneto-elastic coupling and does not require a phase transition. Thus, the interesting results reported by Gautam et al.⁴⁹ need a further detailed study, with a particular attention to the observed splitting of the orbital modulation below T_N2.

As CaMn₇O₁₂ is often prepared at ambient pressure in air it may contain different impurities. Magnetic anomalies from impurities are sometimes erroneously attributed to additional magnetic transitions of the main CaMn₇O₁₂ phase, for example, a FM-like anomaly near 43 K from an Mn₃O₄ impurity.

4. RMn₇O₁₂ (R = Y, La, Ce, Pr, Nd and Sm–Er)

Quadruple perovskite manganites with trivalent rare earth cations at the A site (R³⁺Mn₇O₁₂) with R³⁺ = La,^7,20,50–61 Ce,^59,62 Pr,⁶³ Nd,^20,59 Sm,^59,64 Eu,^59,64 Gd,⁶⁴ Tb,⁶⁴ Dy,⁶⁵ and Y^66–68 (in order of decreasing ionic radii) have been reported in the literature. The authors have also synthesised compounds with R³⁺ = Ho and Er, but the results are yet to be published. Compounds with R³⁺ = Tm–Lu appear to lie beyond the stability range of the AMn₇O₁₂ structural framework (when prepared at 6–8 GPa) owing to their small ionic radii. Indeed, emergent dipolar-glass-like states have been observed in DyMn₇O₁₂ and YMn₇O₁₂,^65,67 understood to arise from the underbonding of R³⁺ cations as the boundary of structural stability is approached (discussed in detail below).

Given the trivalency of the rare-earth cations, all manganese ions adopt a formal 3+ oxidation state in the stoichiometric charge balanced system. RMn₇O₁₂ can be prepared in the stoichiometric composition for R³⁺ = La–Gd. However, they take (R_1−xMn_x)Mn₇O₁₂ compositions for R³⁺ = Tb–Er, determined through (1) the synthesis of single-phase samples of corresponding compositions, (2) the neutron powder diffraction structural analysis of (Dy_0.91Mn_0.09)Mn₇O₁₂ (ref. 65) and (3) the single-crystal X-ray diffraction structural analysis of (Y_1−xMn_x)Mn₇O₁₂ (N.B. in this case, the structural analysis cannot distinguish between the Y_1−yMn₇O₁₂ and (Y_1−xMn_x)Mn₇O₁₂ models).⁶⁸ Therefore, manganese at the A sites could then take the 2+ oxidation state in (R_1−xMn_x)Mn₇O₁₂. For simplicity, we will often use the RMn₇O₁₂ chemical formula.

B site ions are predominantly Mn³⁺ and hence JT active. LaMnO₃-type⁶⁹ B site orbital order has been observed at RT in all RMn₇O₁₂ compounds, which imposes I2/m space group symmetry (N.B. PrMn₇O₁₂ was found to adopt both I2/m (two variations with different degrees of monoclinic distortions) and R3̄ structures at RT, with the phase fractions controllable by synthesis conditions).⁶³ The I2/m orbital order can be understood in terms of a long-range checkerboard alternation of JT axes in the monoclinic ac plane, which are coaligned on stacking along the b axis (Fig. 6). Melting of the orbital order has been reported for all RMn₇O₁₂ except R = Pr, Nd, and Dy, as evidenced by a first order phase transition to the Im3̄ aristotype occurring in the range 630–665 K at ambient pressure,^51,62,64,67 and under hydrostatic pressures greater than 34 GPa at RT (in LaMn₇O₁₂).⁶¹ This Im3̄ phase appears to be ubiquitous to the AMn₇O₁₂ materials (Fig. 2), and we anticipate its discovery in the R = Pr, Nd, and Dy compounds should HT diffraction measurements be made. The orbitally ordered I2/m crystal structure has been found to persist down to the lowest measured temperatures with the exception of YMn₇O₁₂, in which a P2₁/n ground state was found to accompany the disordered yttrium dipolar glass.⁶⁷ Ferroelectric ground states have recently been proposed for compounds with R = La and Y, which would imply non-centrosymmetric structures at LT.^60,68

Fig. 6 LaMnO₃-type orbital order spanning the B site Mn³⁺ ions in any given ac-plane in monoclinic R³⁺Mn₇O₁₂. The orbital order is co-aligned on moving along b (perpendicular to this figure) from one layer to the next.

The RMn₇O₁₂ family of quadruple perovskite manganites have been considered in the context of functional material properties such as catalysis,^7,56,57 however most studies have focused on the microscopic cross-coupling of dipolar, orbital and magnetic degrees of freedom. Hence, it is this latter topic that we will focus on in the remainder of this section.

CeMn₇O₁₂, SmMn₇O₁₂ and EuMn₇O₁₂ undergo a single magnetic phase transition at T_N1 = 80, 87 and 87 K, respectively.^59,62,64 Both A′ and B site Mn³⁺ magnetic moments adopt long range order below T_N1 with propagation vector k = (0, 0, 0). The A′-sites form a collinear ferrimagnetic structure, with magnetic moments lying in the ac plane and rotated away from the c-axis towards −a by 38.7(3)°, 34.7(4)°, and 32.1(5)° for R = Ce, Sm and Eu, respectively.⁵⁹ One in every three A′ site moments is uncompensated, giving a net ferrimagnetic moment as observed in magnetometry measurements. The B site Mn³⁺ magnetic moments form a C-type AFM structure (following the notation of Bertaut),⁷⁰ in which nearest neighbour moments are antiferromagnetically aligned in the ac plane, and coupled ferromagnetically along the b axis. B site spin canting is allowed by symmetry but could not be detected in neutron powder diffraction experiments. Hence, a minimal model with B site moments collinear with the A′ site moments was proposed (Fig. 7).⁵⁹ Importantly, the magnetic structures on both sublattices transform by the same irreducible representation (Γ₂⁺, defined w.r.t. the I2/m paramagnetic parent), hence the two are directly coupled and can develop together below a single phase transition. Based upon the Goodenough–Kanamori–Anderson rules³ taken in the limit of 180° Mn–O–Mn bonds, the LaMnO₃ type orbital order should stabilise an A-type magnetic structure on the B sites (FM layers stacked AFM). This magnetic structure was indeed observed in LaMnO₃,⁷¹ but it is the exact opposite of what is found in the above RMn₇O₁₂ compounds. The octahedral tilting in RMn₇O₁₂ is large compared to that of the RMnO₃ perovskites, leading to a more significant departure from 180° Mn–O–Mn bonds that may weaken or even change the sign of the superexchange interaction. In addition, the RMn₇O₁₂ compounds host strong d–d superexchange between A′ and B sublattices. Such A′–B exchange may compete with B–B exchange and play a key role in stabilising the C-type structure. We note that a B site A-type structure transforms by a different k = (0, 1, 0) irreducible representation to the observed k = (0, 0, 0) C-type structure, hence the energy gain through A′–B interactions would average to zero in this case.

Fig. 7 The A′ site ferrimagnetic structure (red, left) and B site C-type antiferromagnetic structure (green, right) observed for R = La, Ce, Nd, Sm, Eu, Dy and Y, and likely common to all R³⁺Mn₇O₁₂ compounds below T_N1.^59,65,67 The cubes represent the unit cell. The monoclinic b-axis points up the page, and the c-axis to the right.

Magnetic susceptibility and heat capacity measurements of GdMn₇O₁₂ and TbMn₇O₁₂ show anomalous behaviour at T_N1 = 86 and 82 K, respectively, qualitatively similar to the behaviour of the R = Ce, Sm and Eu samples; hence consistent with a phase transition to the same ferrimagnetic ground state.⁶⁴ However, the microscopic nature of the long range magnetic order is yet to be confirmed, for example, by neutron powder diffraction experiments. Measurements of the isothermal magnetisation at 5 K indicate a sizeable uncompensated ferrimagnetic moment in both GdMn₇O₁₂ and TbMn₇O₁₂, which is enhanced compared to the R = Ce, Sm and Eu compounds likely due to the large moments carried by Gd and Tb. For all five samples discussed above, no direct evidence has been provided for long-range magnetic order of the rare-earth ions. However, a Schottky-like anomaly was observed in the specific heat of GdMn₇O₁₂ below ∼10 K that was largely suppressed by a 9 T magnetic field.⁶⁴ This result may point towards Gd ions playing a significant role in the ground state. In addition, magnetic and specific heat measurements gave evidence that a second LT magnetic transition could emerge under magnetic fields in R = Sm and Eu.⁶⁴

The dielectric constant of the R = Ce, Sm, Eu, Gd and Tb compounds has been reported,^62,64 measured as a function of both temperature and excitation frequency. In all cases a small kink-like anomaly was observed at T_N1, with the LT behaviour (frequency-dependent sharp steps between 18 and 35 K) otherwise dominated by extrinsic relaxation processes typical of these and related material systems. As such, there exists no evidence for dipolar or ferroelectric properties in these five compounds. N.B. Sharp steps in dielectric constant near 30 K were also reported in LaMn₇O₁₂, discussed below.⁶⁰

PrMn₇O₁₂ is the only member of the RMn₇O₁₂ family that has two polymorphs at RT.⁶³ The I2/m phase supports the same orbital order and ferrimagnetic magnetization below a single phase transition (T_N1 = 70 K) as is characteristic of the compounds with R = Ce, Sm, Eu, Gd and Tb. Again, one might therefore speculate that the I2/m polymorph of PrMn₇O₁₂ adopts the same ferrimagnetic structure below T_N1, but this is yet to be confirmed. The R3̄ polymorph was reported to have the same crystal structure as CaMn₇O₁₂, implying a 3 : 1 splitting of B sites. In CaMn₇O₁₂ this splitting can be understood in terms of a 3 : 1 charge ordering of Mn³⁺ and Mn⁴⁺ ions from an average valence of Mn^3.25+ imposed by the divalent Ca cation. It is therefore somewhat surprising to find this polymorph in the RMn₇O₁₂ family (Fig. 2). Nonetheless, this R3̄ phase displays altogether different magnetic behaviour with T_N1 = 44 K,⁶³ and it has been proposed that in the R3̄ symmetry the B-site Mn³⁺ ions split into three high spin and one low spin per formula unit, with the low spin ion at the undistorted octahedral site occupied by Mn⁴⁺ in CaMn₇O₁₂.

LaMn₇O₁₂ is arguably the most studied of all RMn₇O₁₂ compounds. Unlike the above, LaMn₇O₁₂ displays two magnetic phase transitions at T_N1 = 79.5 and T_N2 = 22.5 K.⁵² The HT transition was first assigned to the onset of the same B site C-type AFM structure described above, but independent of A′ site Mn order which was instead assigned to the LT transition – an observation akin to the behaviour of NaMn₇O₁₂.¹² The proposed LT A′ site order had propagation vector k = (0, 1, 0), with FM layers in the ac plane, stacked AFM along b. Owing to the different symmetries, the A′ sites could naturally order independently of the B sites. Both A′ and B sublattice magnetic structures refined against neutron powder diffraction experiments⁵² did not have a net ferrimagnetic moment – a result inconsistent with magnetometry measurements showing a net magnetisation similar to that measured for R = Ce, Pr, Sm, Eu, Gd and Tb. It was therefore proposed that the net moment in LaMn₇O₁₂ arose through an exceptionally large canting of the B site magnetic structure induced by the Dzyaloshinskii–Moriya interaction.⁵² The application of the same model to YMn₇O₁₂ led to the suggestion that the A′ Mn sublattice remains disordered as only one magnetic transition was found.⁶⁶ More recently, analysis of high resolution neutron powder diffraction data has shown that both A′ and B Mn moments order together at the HT transition with the same magnetic structure found for R = Ce, Sm and Eu, hence providing a more natural explanation for the sizeable ferrimagnetic moment.⁵⁹ We note that these two different scenarios manifest in remarkably subtle changes in the neutron powder diffraction pattern.⁵⁹ The latter scenario requires a more complex explanation for the LT transition, and it was proposed that LaMn₇O₁₂ enters into a ground state in which B site moments adopt a canted magnetic structure characterised by an admixture of commensurate C-type and A-type modes.⁵⁹ Intriguingly, such a ground state points towards an underlying instability towards the A-type structure expected in the presence of LaMnO₃-type orbital order – perhaps acting in competition A′–B superexchange.

NdMn₇O₁₂ was found to undergo three magnetic phase transitions, one at T_N1 = 85 K, and a further two at low temperature (T_N2 = 12 and T_N3 = 8.5 K). Both A′ and B sublattices were found to order below T_N1 with ferrimagnetic and C-type magnetic structures, respectively – in common with all of the above RMn₇O₁₂ compounds.⁵⁹ It was reported that below the second transition there developed an incommensurate modulation of the B-site magnetic structure with k = (0.248(2), 1, 0.064(3)), which corresponds to an admixture of commensurate C-type and incommensurate A-type modes. In comparison with LaMn₇O₁₂, the incommensurate modulation of NdMn₇O₁₂ can be thought of as a spatially varying unidirectional canting (addition of an orthogonal spin density wave) or as a conical rotation of moments (addition of an orthogonal cycloid). These two scenarios could not be differentiated by neutron powder diffraction, but both support the argument for competing magnetic instabilities in both R = La and Nd compounds (it is well established that incommensurate structures can be stabilised by competing interactions). Below the third transition the incommensurate propagation vector was found to jump to k = (0.3231(7), 1, 0.0069(7)), accompanied by a finite ordered moment appearing on the Nd ions.

It is apparent that the additional LT magnetic transitions occur for compounds with rare earth ions of largest ionic radii, with the exceptions of CeMn₇O₁₂ and PrMn₇O₁₂. It was suggested that this discrepancy may arise due to Ce_1−xMn_7+xO₁₂ or PrMn₇O_12+d off-stoichiometry of the measured samples. Indeed, the second transition was found to be suppressed in non-stoichiometric La_0.9Mn_7.1O₁₂.^59,62 The experimental results published to date indicate complex behaviour at low temperatures, and we suggest future studies, both experimental and theoretical, are required to establish the full microscopic details of the ground state magnetic structures of LaMn₇O₁₂ and NdMn₇O₁₂, and the underlying competing interactions in the RMn₇O₁₂ family.

Unpublished dielectric measurements of LaMn₇O₁₂ and NdMn₇O₁₂ indicate qualitatively similar behaviour to the non-polar compounds with R = Ce, Sm, Eu, Gd and Tb. Recently, however, a large electric polarisation of up to 0.56 μC cm⁻² has been suggested for LaMn₇O₁₂ developing below T_N1,⁶⁰ based on the observation of very strong, broad and symmetrical pyroelectric-current peaks. Following the reported giant ferroelectric polarisation in CaMn₇O₁₂ (ref. 41) some debate ensued regarding the intrinsic nature of the polarisation in these systems. Indeed, other works have assigned such pyroelectric-current peaks to extrinsic effects.^44,48,62,64 In light of this, we suggest that it is important for extrinsic effects, for example those due to thermally stimulated currents, to be ruled out in the case of LaMn₇O₁₂.

Specific heat and magnetometry measurements showed that YMn₇O₁₂ supports a single ferrimagnetic phase transition at T_N1 = 108 K;⁶⁶ approximately 20–30 K higher than the RMn₇O₁₂ compounds discussed above. Unlike the other RMn₇O₁₂ compounds, YMn₇O₁₂ was found to undergo a structural phase transition at T_s = 200 K that was clearly marked by anomalous behaviour in the temperature dependence of the specific heat and spontaneous negative thermal expansion of the lattice.⁶⁶ The microscopic details of both phase transitions were established in a later publication, in which the same ferrimagnetic structure discussed above was reported to occur below T_N1, apparently independent of the structural transition at T_s.⁶⁷ The ground state crystal structure was characterised by an ordered pattern of atomic displacements that lowered the crystal symmetry to P2₁/n, accompanied by disordered displacements of yttrium ions forming a so-called dipolar glass that naturally explained the observed negative thermal expansion.⁶⁷ A recent publication based on single crystal diffraction measurements showed that the yttrium ions can form partial antiferroelectric order out of the dipolar glass state,⁶⁸ the extent of which is likely sample dependent. The structural modifications below T_s could in principle occur independent of one another, but they all improve the bonding conditions of the yttrium ions that were shown to be somewhat underbonded above T_s.⁶⁷ Hence, YMn₇O₁₂ has a pseudo-JT instability associated with A site cations – phenomena usually associated with B site cations in perovskite-derived materials – that can drive unusual LT structural phase transitions. We note that, compared to the RMnO₃ systems, the quadruple perovskites may be prone to underbonding of R cations as the octahedral tilts primarily generate square planar coordinations for the majority A′ site Mn³⁺ ions, perhaps at the expense of the minority A site R ions. Pyroelectric current measurements similar to those reported for LaMn₇O₁₂ have also led to the suggestion of a large ferroelectric polarisation developing in YMn₇O₁₂ at low temperature.⁶⁸ As before, we stress a similar level of caution when interpreting the results of these measurements.

Finally, the reported phenomenology of DyMn₇O₁₂ is similar to that of YMn₇O₁₂ but with one key difference; the structural and magnetic transitions come together (T_N1 and T_s are merged) to create a single, first order magneto-structural phase transition at T_N1 ∼95 K.⁶⁵ Below T_N1 the Dy dipolar glass and ferrimagnetic order parameters were found to be cross-coupled (note that in DyMn₇O₁₂ ordered atomic displacements were not observed below T_N1),⁶⁵ as demonstrated by temperature and field dependent dielectric constant measurements (Fig. 8) (N.B. when T_N1 and T_s are separated as in YMn₇O₁₂ no dielectric anomalies were found at the both temperatures).⁶⁵ In addition, long-range FM ordering of Dy magnetic moments was found below 5.5 K.⁶⁵

Fig. 8 The magnetostructural dipolar glass found in (Dy_0.91Mn_0.09)Mn₇O₁₂: (a) The temperature dependence of the disordered Dy atomic displacement amplitudes established through structural refinements against neutron powder diffraction data,⁶⁵ and (b) the temperature dependence of the real dielectric constant measured in 0 T (black) and 9 T (red) applied magnetic fields.⁶⁵ The inset illustrates the disordered Dy dipolar glass (circles are ideal positions of Dy atoms at the (0,0,0) site; arrows show displacements).

In summary, all RMn₇O₁₂ compounds host a common magnetic structure composed of a ferrimagnetic A′ site Mn³⁺ sublattice with one uncompensated Mn³⁺ moment per unit cell, and a C-type AFM B site sublattice (Fig. 7). In addition, LaMn₇O₁₂ and NdMn₇O₁₂ show LT magnetic phase transitions likely associated with the competition between A′–B and B–B exchange. For compounds with small R ionic radius (R = Dy and Y), the R cations adopt a pseudo-JT instability that leads to exotic LT phases characterised by cross-coupled magnetic and electric degrees of freedom.

5. BiMn₇O₁₂

Compared with RMn₇O₁₂, BiMn₇O₁₂ has an electronic instability originating from the presence of the lone-electron pair of Bi³⁺ cations. As a result, it exhibits distinct structural, magnetic and dielectric properties. BiMn₇O₁₂ was first reported in 2008,⁷² and its RT crystal structure was often described using a centrosymmetric I2/m model derived from powder diffraction experiments.^53,58,73,74 On the other hand, more sensitive single-crystal structural investigations gave evidence for polar Im symmetry at RT.^58,75 A number of additional structural phase transitions were later found,^58,76 and the sequence of phase transitions is now well established (on cooling) as Im3̄ ⇒ I2/m ⇒ [R1̄(αβγ)0] ⇒ Im ⇒ I1 with transitions at about 608 K, 460 K, and 295 K, respectively, where [R1̄(αβγ)0] denotes an incipient phase, which appears only as diffuse scattering in undoped BiMn₇O₁₂ between the I2/m and Im phases.⁵⁸ The proper stabilisation of the R1̄(αβγ)0 phase can be triggered by small Cu²⁺ or Fe³⁺ doping.³⁵ The Im3̄ ⇒ I2/m transition is related to orbital ordering of Mn³⁺ similar to RMn₇O₁₂, and the I2/m ⇒ Im transition – to the development of a ferroelectric polarization associated with the Bi³⁺ lone pair electrons. However, no direct confirmation of ferroelectricity (such as P–E loops) has been obtained to date.

Two magnetic transitions were widely reported in BiMn₇O₁₂ at about T_N1 = 59 K and T_N2 = 21 K in analogy with LaMn₇O₁₂,^72,74,75,77 despite the first paper (ref. 72) reporting evidence for three magnetic transitions from specific heat measurements. In comparison with RMn₇O₁₂, frequency-independent peaks in the dielectric constant of BiMn₇O₁₂ were observed at all (three) magnetic transition temperatures without any extrinsic steps,^72,75,78 but no pyroelectric current anomalies have been detected. Therefore, the origin of dielectric peaks remains unclear and needs further investigation.

The only neutron diffraction study of the magnetic structures assumed that Mn at the B sites are ordered at T_N1, and Mn at the A′ sites are ordered at T_N2, in analogy with LaMn₇O₁₂.⁷⁴ In addition, the total zero moment was assumed for both A′ and B sites despite the observation of large uncompensated moments on M versus H curves (e.g., about 1μ_B at 2 K and 0.8μ_B at 40 K).^72,77 Furthermore, in the analysis of the magnetic structures the (crystal) symmetry was considered to be Im,⁷⁴ while the real ground-state symmetry is I1. Hence, we suggest that the magnetic structures of BiMn₇O₁₂ need careful re-investigation.

Similar to PrMn₇O₁₂, several modifications of BiMn₇O₁₂ were reported at RT (monoclinic, rhombohedral and cubic).^73,77–79 However, in this case, the polymorphism was assigned to cation non-stoichiometry (Bi_1−x/3(Mn³⁺₃)(Mn³⁺_4−xMn⁴⁺_x)O₁₂ and Bi_0.94Mn_6.91O₁₂) and the appearance of Mn⁴⁺ at the B sites. We believe the same should be true for PrMn₇O₁₂. Magnetic properties of non-stoichiometric BiMn₇O₁₂ were noticeably different from stoichiometric BiMn₇O₁₂.

6. Conclusions

We have reviewed the current state of research on AMn₇O₁₂ quadruple perovskite manganites and identified some future directions, such as the re-investigation of magnetic structures of NaMn₇O₁₂ and BiMn₇O₁₂ and understanding dielectric behavior of all members, in particular, BiMn₇O₁₂. Investigations of different solid solutions^35,80–82 may also yield fascinating results, as it allows continuous variations of Mn oxidation states at the B sites, while keeping nearly the same B-site Mn–O–Mn bond angles,⁸² as was extensively studied in the mixed-valence R_1−xA_xMnO₃ perovskites.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was partly supported by JSPS KAKENHI Grant Number JP20H05276 and Innovative Science and Technology Initiative for Security from Acquisition, Technology, and Logistics Agency (ATLA), Japan. R. D. J. acknowledges support from a Royal Society University Research Fellowship.

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