Electronic ordering in perovskites and the effects on the symmetry of crystal structures

The symmetry of a crystal structure plays a crucial role for the physical properties of a crystalline material. For instance the electronic properties such as pyroelectric, piezoelectric or ferroelectric properties are either allowed or prohibited by symmetry. In other cases the symmetry has to obey the electronic properties of the crystal, for example when a temperature or pressure induced charge ordering or charge disproportionation occurs. When the crystal undergoes a phase transition from an electronically unordered to an electronically ordered state the symmetry is usually lowered at the transition point.

In order to study more systematically the physical properties of materials where the symmetry is determined by the electronic properties, it is reasonable to look for model systems where the chemical composition can be easily varied. Such model systems are for example given by solids with perovskite crystal structure where most of the simple perovskites with chemical formula ABO₃ are rather well understood and the chemical composition for the A and B ions can be easily modified.

Recently, the crystal structure class of A-site ordered quadruple perovskites with chemical formula AA’₃B₄O₁₂ (with A’, B = metallic ions) gained a lot of attention. For this special class of perovskites, usually synthesized under high pressure, a zoo of different temperature-driven electronic properties can be found.

For instance in quadruple perovskites with Cu on the A’-site and Fe on the B-site, either an inter-site charge transfer (ISCT) or a charge disproportion (CD) can be found depending on the size of the lanthanide atom on the A-site. The ISCT is observed for lanthanide ions A = La, Pr, Nd, Sm, Eu, Gd and Tb, whereas the CD in these quadruple perovskites is observed for heavier lanthanide ions A = Dy, Ho, Er, TM, Yb, Lu [1]. Interestingly both electronic transitions are accompanied by many other physical effects. At the transition point a metal-to-insulator and an antiferromagnetic phase transition accompanies the ISCT effect, whereas the CD effect is accompanied by a metal-to-semiconductor and a ferrimagnetic phase transition. Additionally both effects are accompanied by structural changes. For the ISCT an isostructural phase transition with negative-thermal-expansion-like volume change upon heating occurs, whereas for the CD no volume change at the transition point can be found, although the rock-salt ordering of the B-site oxidation state forces the symmetry to be lowered. From this example of a chemical series of a quadruple perovskite, it is obvious that the type of the electronic change at the transition point can induce a change of symmetry of the crystal structure.

Intriguingly, the whole picture can change, if the atoms on the A’- and B-site are replaced by other metals. Apparently, this occurs for quadruple perovskites where the Fe ion on the B-site is replaced by Cr. Although a similar ISCT effect with accompanying antiferromagnetic and isostructural phase transition as for the iron containing quadruple perovskites is observed, the volume change behaves differently [2]. In these compounds the negative-thermal-expansion-like volume change upon heating changes into a positive-thermal-expansion-like volume change, which impressively shows the influence of the interplay between the cations on the A-site and the cations on the A’- and B-sites. In order to investigate the connection between electronic and structural transition for other quadruple perovskites, we focused our research on the A-site ordered quadruple perovskite BiCu₃Cr₄O₁₂ with the Bi ion being a much heavier cation on the A-site compared to lanthanide cations.

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Fig. 1: Projection of the monoclinic crystal structure of BiCu₃Cr₄O₁₂ (BCCO) at 100 K along the b-axis (a) and along the ... [more]

Fig. 1: Projection of the monoclinic crystal structure of BiCu₃Cr₄O₁₂ (BCCO) at 100 K along the b-axis (a) and along the [101] direction (b). Similar to the room temperature structure BCCO builds a corner-sharing framework of CrO₆ octahedra with Bi icosahedra and square-planar coordinated CuO₄ configurations. The charge disproportionation of the Cr ions in columns is indicated by the different colors of the CrO₆ octahedra.
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Fig. 1: Projection of the monoclinic crystal structure of BiCu₃Cr₄O₁₂ (BCCO) at 100 K along the b-axis (a) and along the [101] direction (b). Similar to the room temperature structure BCCO builds a corner-sharing framework of CrO₆ octahedra with Bi icosahedra and square-planar coordinated CuO₄ configurations. The charge disproportionation of the Cr ions in columns is indicated by the different colors of the CrO₆ octahedra.

© Max Planck Institute for Solid State Research / Etter

© Max Planck Institute for Solid State Research / Etter

Detailed synchrotron powder X-ray diffraction measurements revealed that BiCu₃Cr₄O₁₂ exhibits a different structural behavior at the transition point of approximately 188 K, compared to the so far known quadruple perovskite compounds. Upon cooling, the temperature-dependent diffraction patterns show a slowly increasing emergence of Bragg peaks until at T = 160 K the intensity of the new Bragg peaks is saturated. Crystallographic investigations indicated that this is not a simple transition from an electronically unordered cubic crystal structure to a cubic ordered one. In fact the new symmetry is much lower and the new crystal structure can be described using a C-centered monoclinic symmetry with perovskite lattice parameters of  (2 √2 a_p × 2 a_p × 2 √2 a_p (a_p = cubic perovskite lattice parameter (≈3.6514 Å)) (Fig. 1). Due to the fact that a group-subgroup relation exists, an approach of using symmetry modes was used in order to carry out detailed Rietveld refinements for every diffraction pattern. Careful inspection of the lattice parameters revealed that the monoclinic β angle does not show a continuous behavior over temperature, although all other lattice parameters behave rather smoothly and show no obvious jump (Fig. 2). This applies likewise for the shift of the relative atomic coordinates (or equivalent to the amplitudes of the corresponding symmetry modes) of the Bi ion which also show no definite jump in their behavior. Therefore the type of the phase transition can be regarded as a weakly first order phase transition.

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Fig. 2: Pseudo-cubic lattice parameters (a+b) for BiCu₃Cr₄O₁₂ as well as the monoclinic volume (c) over temperature upon ... [more]

Fig. 2: Pseudo-cubic lattice parameters (a+b) for BiCu₃Cr₄O₁₂ as well as the monoclinic volume (c) over temperature upon cooling and heating. At 188.3 K a weak first order phase transition from cubic to monoclinic symmetry can be observed. [less]

Fig. 2: Pseudo-cubic lattice parameters (a+b) for BiCu₃Cr₄O₁₂ as well as the monoclinic volume (c) over temperature upon cooling and heating. At 188.3 K a weak first order phase transition from cubic to monoclinic symmetry can be observed.

© Max Planck Institute for Solid State Research / Etter

© Max Planck Institute for Solid State Research / Etter

Interestingly the behavior of the volume (Fig. 2(c)) is different than for other ACu₃Cr₄O₁₂ (A = La, Y) quadruple perovskites [2]. Instead of showing a positive-thermal-expansion-like volume change upon heating, a negative-thermal-expansion-like volume change can be observed which is very similar to the behavior of the ACu₃Fe₄O₁₂ quadruple perovskites with ISCT effect. Detailed investigations of the bond valence sums of the Cr and Cu atoms revealed that there exists a huge splitting in the environment of the different Cr ions. Although no definite oxidation states for the individual Cr atoms can be given yet, it is clear that the distinguishable Cr ions show a columnar ordering (Fig. 1), which is similar to a CD behavior.

Taking a look to the Fe analogue of this Bi quadruple perovskite, a similar behavior for the volume can be found but at a much higher temperature of 428 K [3]. Otherwise the Fe analogue has an isostructural phase transition with an unambiguous ISCT effect towards higher temperatures. This clearly evidences that the replacement of the metallic B-site cation can lead to an entirely different behavior with regard to temperature-dependent electronic effects.

Although not all electronic properties of these quadruple perovskites are fully understood yet, it is fascinating how the symmetry is influenced by solely the change of the electronic ordering.