Rise of A-site columnar-ordered A2A′A′′B4O12 quadruple perovskites with intrinsic triple order

A-site-ordered AA'3B4O12 quadruple perovskites (with twelve-fold coordinated A and square-planar coordinated A' sites) were discovered in 1967. Since then, there have been considerable research efforts to synthesize and characterize new members of such perovskites. These efforts have led to the discoveries of many interesting physical and chemical properties, such as inter-site charge transfer and disproportionation, giant dielectric constant, multiferroic properties, reentrant structural transitions and high catalytic activity. The first member of A-site columnar-ordered A2A'A''B4O12 quadruple perovskites (with ten-fold coordinated A, square-planar coordinated A' and tetrahedrally coordinated A'' sites), CaFeTi2O6, was discovered in 1995, and for 19 years it was the only representative of this family. In the last few years, A2A'A''B4O12 perovskites have experienced rapid growth. Herein, we present a brief overview of the recent developments in this field and highlight an under-investigated status and great potential of A2A'A''B4O12, which can be prepared mainly at high pressure and high temperature. The presence of the A'' site gives an additional degree of freedom in designing such perovskites. The A2A'A''B4O12 perovskites are discussed in comparison with well-known AA'3B4O12 perovskites.

Introduction ABO 3 compounds crystallize in a number of structure types [e.g., perovskites, LiNbO 3 , corundum, ilmenite, hexagonal BaMnO 3 -type structures (2H, 4H, 6H, 15R and so on), hexagonal LuMnO 3 -type, pyroxenes, rare earth sesquioxide structures (A, B and C (bixbyite)), AlFeO 3 , KSbO 3 , PbReO 3 , CaIrO 3 and others] depending on the relative size of the A and B cations and on the nature of cations. 1 The perovskite-type structure is one of the most important and adaptive structures in inorganic chemistry, and it has the largest number of representatives. [2][3][4] It is built from a framework of cornershared BO 6 octahedra that form cavities, which are filled with A cations. The ideal perovskite structure is cubic (space group Pm3m) with a p ≈ 3.8 Å. However, the cubic structure is rarely realized at room temperature because of the mismatch among the sizes of A, B and O. The mismatch, which is usually described by the Goldschmidt tolerance factor, 5 leads to different distortions. Distortions can be considered as tilts of rigid BO 6 octahedra in a first approximation. And tilts, in turn, are described by using the Glazer tilt system and B-O-B bond angles. 6 There are basically 15 tilt systems in ABO 3 perovskites. 4 In simple ABO 3 perovskites, the B-O-B tilt angles are within the range of 140-180°.
A special class of the perovskite family is formed for the a + a + a + tilt system with very large B-O-B tilt angles of about 140-145°(space group of the parent structure is Im3). 7,8 It is which have a twelve-fold coordinated A site and a squareplanar coordinated A′ site. The A′ site is typically occupied by Jahn-Teller cations [such as, Cu 2+ and Mn 3+ ] or other cations which allow a square-planar coordination: Cu 3+ , 8 Fe 2+ , 9,10 Co 2+ , 11 Pd 2+ , 12 Pb 4+ (ref. 13) and Mn 2+ (ref. 14), and most of the AA′ 3 B 4 O 12 compounds need high pressure (HP) and high temperature (HT) for their preparation. The AA′ 3 B 4 O 12 quadruple perovskite subfamily of the perovskite family has also numerous representatives with A = Na + , Mn 2+ , Cd 2+ , Ca 2+ , Sr 2+ , Pb 2+ , R 3+ (R = rare earths), Ce 4+ , Bi 3+ and Th 4+ , and B = Mn 3+ , Mn 4+ , Fe 3+ , Cr 3+ , Al 3+ , Ti 4+ , V 4+ , Ge 4+ , Sn 4+ , Ru 4+ , Ir 4+ , Ta 5+ , Nb 5+ , Sb 5+ and others. 7 This subfamily was discovered in 1967 in CaCu 3 Ti 4 O 12 during Cu 2+ doping of CaTiO 3 . 15 Since then, there have been considerable research efforts to synthesize and characterize new members of such quadruple perovskites. These efforts have led to the discoveries of many interesting physical and chemical properties, for example, giant dielectric constant, 7 inter-site charge transfer and disproportionation, 8 multiferroic properties, reentrant structural transitions, 16 and high catalytic activity. 17 Another special class of the perovskite family can be formed with the a + a + c − tilt system and with very large B-O-B tilt angles of about 140-150°(space group of the parent structure is P4 2 /nmc). 3,4 In such a case, compounds with the A 2 A′A″ B 4 O 12 stoichiometry are formed. Therefore, they can also be called A-site-ordered quadruple perovskites, where A′ is the site with a square-planar coordination and A″ is the site with a tetrahedral coordination. To distinguish them from AA′ 3 B 4 O 12 , we suggest calling them A-site columnar-ordered 18 quadruple perovskites. The first representative of this subfamily, CaFeTi 2 O 6 , was discovered just in 1995. 9,19,20 CaFeTi 2 O 6 was the only representative of such quadruple perovskites for 19 years, and this distortion of perovskites was considered to be highly exotic and rare. 3,4 Only in 2014 was another representative reported, CaMnTi 2 O 6 . 21 In the last few years, A 2 A′A″B 4 O 12 quadruple perovskites have experienced rapid growth. 18,[22][23][24] The purpose of this frontier article is to highlight their underinvestigated status and great potential and to attract attention of the perovskite and high-pressure communities.  25,26 The ABO 3 perovskites with such strong tilts usually have GdFeO 3 -related distortions 26 with the (ideal) space group Pnma (√2a p × 2a p × √2a p ) and the tilt system of a − b + a − , which means that BO 6 octahedra are rotated in one direction (in-phase) along the b axis and in opposite directions (out-of-phase) along the a and c axes (in cubic axes of the orig-inal Pm3m cell) (Fig. 1a). The AA′ 3 B 4 O 12 quadruple perovskites have a 2a p × 2a p × 2a p cell and the a + a + a + tilt system, which means that BO 6 octahedra are rotated in one direction along all three crystallographic directions (Fig. 1b). The A 2 A′A″B 4 O 12 quadruple perovskites have a 2a p × 2a p × 2a p cell and the a + a + c − tilt system, which means that BO 6 octahedra are rotated in one direction along the a and b axes and in opposite directions along the c axis (Fig. 1c). Therefore, on considering the B sublattice, all three perovskites are very similar to each other and differ from each other by a number of the in-phase (very strong) tilts of the BO 6 octahedra.
The different numbers of the in-phase BO 6 tilts (determined, of course, primarily by the stoichiometry) create different numbers and types of cavities for A cations (Fig. 2). There is one type of cavity in the case of ABO 3 , and the coordination number is reduced from twelve (in the ideal cubic ABO 3 ) to eight. The AO 8 polyhedra are connected by edges to form a three-dimensional (3D) network (Fig. 2a).
There are two types of cavities in the case of AA′ 3 B 4 O 12 with a ratio of 1 : 3. The A site keeps a twelve-fold coordination as in the ideal cubic ABO 3 , and the A′ site has four very short A′-O bond lengths, four much longer A′-O bond lengths, and four very long A′-O bond lengths (in total, still twelve). The four very short A′-O bond lengths form a square-planar coordination. The AO 12 polyhedra are isolated from each other. The A′O 4 squares are also isolated from each other (Fig. 2b), and they are oriented in such a way that they are orthogonal to each other, but they are 3D-connected through the longer A′-O bond lengths. The AO 12 and A′O 4 polyhedra are 3D-connected through edges.
There are three types of cavities in the case of A 2 A′A″B 4 O 12 with a ratio of 2 : 1 : 1. Therefore, such perovskites have intrinsic triple A-site ordering. The A site has a ten-fold coordination ( plus two very long bond lengths), and both A′ and A″ sites have four very short A′-O and A″-O bond lengths with similar values of 1.9-2.1 Å, four much longer bond lengths, and four very long bond lengths (in total, still twelve). The four very short A′-O bond lengths form a square-planar coordination. However, the four very short A″-O bond lengths form a tetrahedral coordination (Fig. 2c). Therefore, the A′ and A″ sites have fundamentally different coordination environments, and they should be distinguished even though they have similar bond lengths. The AO 10 polyhedra are connected through edges and form chains (columns) along the c axis. The A′O 4 squares and A″O 4 tetrahedra are separated from each other, but they are connected through the longer A′-O bonds to form chains (columns) along the c axis. Because of the existence of the -AO 10 -AO 10columns and the -A′O 4+4 -A″O 4columns (or columns consisting of isolated A′O 4 and A″O 4 units), A 2 A′A″ B 4 O 12 perovskites can be called A-site columnar-ordered perovskites. Connections of the AO 10 and A′O 4 polyhedra through edges, the AO 10 and A″O 4 polyhedra through corners and the -AO 10 -AO 10columns through corners create a 3D network. Tetrahedral coordination is usually not realized in oxygen-stoichiometric ABO 3 perovskites; only the removal of oxygen in ordered manners creates tetrahedral sites. 4 The A 2 A′A″B 4 O 12 perovskites are oxygen-stoichiometric perovskites with tetrahedral sites.
Because of the similarities in the B sublattice ( Fig. 1), it is expected that the B site of A 2 A′A″B 4 O 12 can be occupied by most of the B-type cations for perovskites and their different combinations (a list of examples is given in the second paragraph of Introduction).
The A sites in all three families retain large environments with some variations in the coordination numbers. Therefore, it is expected that the A site of A 2 A′A″B 4 O 12 can be occupied by many typical A cations for perovskites (a list of examples is This fact can put additional limits on the size of A-type cations that can be forced into the A site. All rare-earth elements (except Ce and Pm) and Ca 2+ were found so far at the A site of A 2 A′A″B 4 O 12 .
The size of Na + is close to those of Ca 2+ and La 3+ ; 34 therefore, we can also expect such compounds with A = Na + . We also emphasize that depending on compositions at the A′, A″ and B sites, ranges of stability of A 2 A′A″B 4 O 12 (A = R = rare-earths) vary from R = La-Sm 22 for RMnMnSbO 6 to R = Gd-Tm and Y 23 for RMnMn 2 O 6 (in all cases, we always mean the synthesis conditions used; stability ranges can change if the synthesis pressure is increased or other conditions are altered). It means that a number of different rare-earth elements should always be checked when preparing such compounds with different B-site contents. A similar tendency was also observed in AA′ 3 B 4 O 12 : for example, RMn 3 (AlTi 3 )O 12 is formed for R = La-Sm, but not for R = Gd-Lu; 14 RMn 7 O 12 is formed for R = La-Er and Y, but not for R = Tm-Lu. 23 On the other hand, RCu 3 Mn 4 O 12 can be prepared for all R at a relatively low pressure of 2 GPa. 35 The A′O 4 sites of AA′ 3 B 4 O 12 and A 2 A′A″B 4 O 12 are identical. Therefore, it is expected that they can be occupied by the same cations. They are listed and highlighted by bold letters in Table 1, which also gives some other cations with a possible square-planar coordination. We note that there are reports about the presence of Li + (e.g., in (Li 1 Table 2 gives a list of some cations that can have a tetrahedral coordination environment and their ionic radii. 34 Cu 2+ , Fe 2+ and Mn 2+ were found so far in the A″ site of A 2 A′A″B 4 O 12 and they probably accidentally overlap with cations found at the A′ site (Fig. 3). The charge and size of Co 2+ , Mg 2+ and Zn 2+ , for example, are close to those of Cu 2+ , Fe 2+ and Mn 2+ , but they  should preferably occupy the tetrahedral A″ site instead of the square-planar A′ site. 39 On the other hand, however, all cations shown in Table 2 can have an octahedral coordination, and some of them (e.g., Ni 2+ , Sn 4+ and Ti 4+ ) show a very strong preference for such an environment. 39  An attempt to prove the above concept (about the location of different elements at the A′ and A″ sites) was made as shown in ref. 24  The presence of the A″ site gives an additional degree of freedom in A 2 A′A″B 4 O 12 , and the number of elements that can have a tetrahedral environment is larger than that with a square-planar environment (Fig. 3). Therefore, it is expected that A 2 A′A″B 4 O 12 perovskites should be numerous and versatile.

Known distortions
The parent structure of AA′ 3 B 4 O 12 has the space group Im3 (no. 204). All distortions from the direct group-subgroup relations are experimentally realized (except for the same Im3 symmetry with 6a p × 6a p × 6a p ) (Fig. 4). These distortions are exemplified in CaCu 3 Ti 4 O 12 (the parent structure), 15 16 Most of these distortions are temperature-driven, that is, they are observed on cooling for a particular composition, and there exists a high-temperature parent modification. However, there are a few composition-driven distortions, that is, they are determined by a particular composition and take place during the synthesis. 41,42 The I23 distortion in (Li 1.333 Cu 1.333 )Nb 4 O 12 could be temperature-driven (caused by Nb displacements), but no evidence (no phase transitions to the parent structure) was reported; 36 this is why we call it composition-driven. There are a number of temperature-driven distortions that cannot be described by the direct group-subgroup paths, for example, in   to the effects of the lone electron pair of Bi 3+ . 46 But the ferroelectricity of BiMn 7 O 12 has not been demonstrated yet. The parent structure of A 2 A′A″B 4 O 12 has the space group P4 2 /nmc (no. 137). There are seven distortions from the direct group-subgroup relations (except for the same P4 2 /nmc symmetry with 2a p × 2a p × 6a p and 6a p × 6a p × 2a p ) (Fig. 5). Three of them have already been found experimentally. Surprisingly, a temperature-driven proper polar distortion takes place in CaMnTi 2 O 6 without any effects of lone electron pairs. 21 This is a quite promising fact in comparison with the AA′ 3 B 4 O 12 family. Rock-salt B-site (space group P4 2 /n) 22,24 and layered B-site (space group Pmmn) 23 orders have already been realized in A 2 A′A″B 4 O 12 . The reported P4 2 /n distortion is compositiondriven. The Pmmn distortion in RMnMn 2 O 6 could be temperature-driven, but no evidence (no phase transitions to the parent structure) was found so far; this is why we call it composition-driven. It is interesting that the Pmmn model has potential for an additional 1 : 1 rock-salt A-site order (that is, it has two independent A sites: A1 and A2), which might be realized, for example, in a hypothetical compound [

Physical and chemical properties of A 2 A'A''B 4 O 12
As already mentioned, CaMnTi 2 O 6 crystallizes in a polar space group. This compound shows a structural phase transition from P4 2 mc to the parent P4 2 /nmc structure at 630 K. The phase transition is accompanied by sharp dielectric constant anomalies and the loss of second-harmonic generation signals. Moreover, a room-temperature ferroelectric P-E hysteresis loop was demonstrated. 21 These results proved that CaMnTi 2 O 6 is ferroelectric at a ferroelectric Curie temperature of 630 K. The shifts of Mn 2+ cations at the A′ site from the square-planar plane and Ti 4+ cations from the center of the TiO 6 octahedra are responsible for the polar distortion. 21,29 Polarization was calculated to be about 0.3 C m −2 , and a highly tunable semiconducting energy band gap was predicted in CaMnTi 2 O 6 . 29 The P4 2 mc-to-P4 2 /nmc ferroelectric transition was also found at room temperature at about 7 GPa. 28 Without the assistance from the B sublattice, the interaction among magnetic cations at the A′ and A″ sites is usually very weak (at least, among Mn 2+ ): CaMnTi 2 O 6 has the Néel  temperature (T A,N ) of about 10 K, 21 while SmMnGaTiO 6 was reported to order at T A,N = 3 K, and no ordering was found in GdMnGaTiO 6 . 18 In the case of SmMnGaTiO 6 and GdMnGaTiO 6 , even small disordering of Ga 3+ and Mn 2+ between the A″ and B sites could suppress a long-range magnetic ordering. On the other hand, magnetic interactions through Ti 4+ could be enhanced in CaMnTi 2 O 6 resulting in higher T N similar to a higher magnetic transition temperature in CaCu 3 Ti 4 O 12 in comparison with CaCu 3 Ge 4 O 12 and CaCu 3 Sn 4 O 12 . 3 No cooperative long-range magnetic order of the parent compound, CaFeTi 2 O 6 , was found down to 4.2 K. 27 The presence of magnetic cations at the B sites significantly enriched magnetic behaviours. First, the ordering temperature of Mn 2+ at the A′ and A″ sites can reach T A,N = 70 K in CaMnFeReO 6 24 and T A,C = 100 K in CaMnMnReO 6 . 24 Second, the magnetic ordering of Mn 2+ at the A′ and A″ sites can be either antiferromagnetic (T A,N in CaMnFeReO 6 ) 24 or ferromagnetic (T A,C in CaMnMnReO 6 24 and T C = 76 K in NdMnMnSbO 6 ). 22 Magnetic cations at the B sublattice can order first as in CaMnMnReO 6 at T B,C = 120 K (a ferrimagnetic structure), 24 can order first with much higher temperatures as in CaMnFeReO 6 at T B,C = 500 K and in Ca 2 CuMnFe 2 Re 2 O 12 at T B,C = 560 K (a ferrimagnetic structure of Fe 3+ and Re 5+ ) 24 or can order at the same temperature with the A′ and A″ sites as in NdMnMnSbO 6 . 22 There is a spin reorientation transition in NdMnMnSbO 6 at 42 K driven by order of the Nd moments. 22 RMnMn 2 O 6 compounds also show complex magnetic behaviours at several transition temperatures (two or three magnetic transitions depending of R and stoichiometry); 23 30 Significant magnetoresistance was found in CaMnFeReO 6 and magnetoresistance switching was observed in Ca 2 CuMnFe 2 Re 2 O 12 . 24 Therefore, A 2 A′A″B 4 O 12 perovskites show complex magnetic properties.
It was found that RMnMn 2 O 6 (uRMn 3 O 6 ) compounds are prone to non-stoichiometry, R 1−δ Mn 3 O 6−1.5δ , with δ = −(0.059-0.071) for R = Gd, δ = 0 for R = Dy, δ = 0.05-0.1 for R = Ho and Y, and δ = 0.12 for R = Er and Tm, and their magnetic properties are highly sensitive to the δ values. 23 The real rare-earth cation deficiency was formed in the case of Er 0.88 Mn 3  Neutron diffraction showed that Fe 3+ cations occupy the A′ site (8%) and the A″ site (16%) in CaMnFeReO 6 . 24 This fact shows that Fe 3+ can in principle be at the tetrahedral A″ site (Fig. 3). The location of a very small amount of Fe 3+ cations at the square-planar A′ site was also observed in AA′ 3 B 4 O 12 by Mössbauer spectroscopy, but the concentration never reaches a few percent. 38 A very small antisite disorder at the B sites was found in CaMnFeReO 6 (3% Fe/Re) and CaMnMnReO 6 (4% Mn/Re); CaMnMnReO 6 also had about 5% of Mn at the Ca site, 24 and small amounts of Mn were found at the Nd and Sb sites of NdMnMnSbO 6 . 22 Different atoms (e.g., Cu 2+ and Mn 2+ ) that can occupy both tetrahedral and square-planar sites (Fig. 3) order poorly between the A′ and A″ sites as found by neutron diffraction in the case of Ca 2 CuMnFe 2 Re 2 O 12 (60% Cu and 40% Mn at A′ and 23-36% Cu and 64-77% Mn at A″); 24 and the degree of ordering can depend on synthesis conditions. 24 (Fig. 3). Another interesting observation is that when the B site is solely occupied by Mn with the average oxidation state higher than +3, there seems to be a tendency for a layered B-site ordering with the appearance of one layer consisting of highly distorted (by the Jahn-Teller effect) Mn 3+ O 6 octahedra.
Very few compositions of AA′ 3 B 4 O 12 can be prepared at ambient pressure (for example, ( 23 and 10 GPa-1670 K for CaMnFeReO 6 (and others). 24 The symmetry of A 2 A′A″B 4 O 12 under synthesis conditions is crucial for the realization of ordering of different cations between the A′ and A″ sites. In general, three situations are possible for compounds with the A 2 A′A″B 4 O 12 stoichiometry. First, the structure can have one crystallographic A site (e.g., with the maximum symmetry of Pm3m and a p × a p × a p ). In this case, we will probably have GdFeO 3 -type structures (simple ABO 3 perovskites) with random distribution of all A cations at one site after quenching and pressure release. 22 Second, the structure can have two crystallographic A sites with the 1 : 1 ratio (e.g., with P4/mmm symmetry and √2a p × √2a p × a p considered in ref. 29). In this case, it is difficult to expect noticeable ordering of different cations between the A′ and A″ sites. Third, the structure can have three A sites with the 2 : 1 : 1 ratio (e.g., with I4/mmm symmetry and 2a p × 2a p × 2a p ). In this case, the ordering of different cations between the A′ and A″ sites can be realized. If the second case takes place (for some compositions), a modification of synthesis conditions could help to increase the ordering. In most cases, samples are quenched after the synthesis, but slow cooling could drive ( partial) ordering. We are not aware of any in situ HP and HT studies of either AA′ 3 B 4 O 12 or A 2 A′A″B 4 O 12 .

Some arguments in favor of the terminology
The AA′ 3 B 4 O 12 and A 2 A′A″B 4 O 12 quadruple perovskites have many common structural features ( Fig. 1 and 2). The parent structures of both families have the doubled lattice parameter along all three crystallographic directions, 2a p × 2a p × 2a p , in comparison with a simple ABO 3 perovskite with a p ≈ 3.8 Å resulting in eight ABO 3 formula units in their unit cell. The simplest composition with integer numbers can be written as AA′ 3 B 4 O 12 (Z = 2), corresponding to four ABO 3 units. This is why such perovskites are called quadruple. This formula reflects the presence of the A and A′ cations with quite different coordination environments with the 1 : 3 ratio. Because 1 and 3 are odd numbers (and A and A′ are quite different cations), this formula is retained in the majority of cases. However, there are very few exceptions when A′ = A (for example, CuCu 3 V 4 O 12 and MnMn 3 Mn 4 O 12 ). 33,48 For such cases, the formula can be reduced to simple ABO 3 (Z = 8). However, this formal formula reduction does not eliminate the structural features of such perovskitesthey still belong to the A-site-ordered quadruple perovskite family. Note that perovskites and perovskite-related compounds with the 1 : 3 B-site ordering can also be referred to as (B-site-ordered) quadruple perovskites. 49,50 By analogy, the simplest composition with integer numbers can be written as A 2 A′A″B 4 O 12 (Z = 2), which reflects quite different coordination environments for the A, A′ and A″ sites with the 2 : 1 : 1 ratio. The A 2 A′A″B 4 O 12 formula corresponds to quadruple perovskites. It turns out that A″ = A′ in many cases for perovskites reported so far, and the formula can be reduced to the double perovskite one, AA′B 2 O 6 . However, this formal formula reduction does not reflect the structural features of such perovskites, which still belong to the A-site columnar-ordered quadruple perovskite family, A 2 A′A″B 4 O 12 . Ca 2 CuMnFe 2 Re 2 O 12 , 24 R 2 CuMnMn 2 Mn 2 O 12 (or R 2 CuMn 5 O 12 ) 30 and R 2 MnGaMn 4 O 12 (or R 2 GaMn 5 O 12 ) 30 already require the quadruple formula to write them in integer numbers.

Conclusion
A-site columnar-ordered A 2 A′A″B 4 O 12 quadruple perovskites are in the incipient stage of research. They can be considered as an extended and more complex version of the A-site-ordered AA′ 3 B 4 O 12 quadruple perovskites (with twelve-fold coordinated A and square-planar coordinated A′ sites) because A 2 A′A″B 4 O 12 has ten-fold coordinated A and square-planar coordinated A′ sites plus an additional tetrahedrally coordinated A″ site. This A″ site gives an additional degree of freedom in A 2 A′A″B 4 O 12 because the number of elements that can have a tetrahedral environment is larger than that with a square-planar environment. The A 2 A′A″B 4 O 12 perovskites are the only oxygen-stoichiometric perovskites with tetrahedral sites. This article highlights great potential of A 2 A′A″B 4 O 12 and gives some design principles.

Note added in proof
After this paper was accepted, the synthesis of ferroelectric Ca 2−x Mn x Ti 2 O 6 (x = 0.6) by a spark plasma sintering method was reported. 51

Conflicts of interest
There are no conflicts to declare.