Group-theoretical analysis of 1:3A-site-ordered perovskite formation

Abstract

The quadruple perovskites AA′3 B 4 X 12 are characterized by an extremely wide variety of intriguing physical properties, which makes them attractive candidates for various applications. Using group-theoretical analysis, possible 1:3 A-site-ordered low-symmetry phases have been found. They can be formed from a parent Pm{\bar 3}m perovskite structure (archetype) as a result of real or hypothetical (virtual) phase transitions due to different structural mechanisms (orderings and displacements of atoms, tilts of octahedra). For each type of low-symmetry phase, the full set of order parameters (proper and improper order parameters), the calculated structure, including the space group, the primitive cell multiplication, splitting of the Wyckoff positions and the structural formula were determined. All ordered phases were classified according to the irreducible representations of the space group of the parent phase (archetype) and systematized according to the types of structural mechanisms responsible for their formation. Special attention is paid to the structural mechanisms of formation of the low-symmetry phase of the compounds known from experimental data, such as: CaCu3Ti4O12, CaCu3Ga2Sn2O12, CaMn3Mn4O12, Ce1/2Cu3Ti4O12, LaMn3Mn4O12, BiMn3Mn4O12 and others. For the first time, the phenomenon of variability in the choice of the proper order parameters, which allows one to obtain the same structure by different group-theoretical paths, is established. This phenomenon emphasizes the fundamental importance of considering the full set of order parameters in describing phase transitions. Possible transition paths from the archetype with space group Pm{\bar 3}m to all 1:3 A-site-ordered perovskites are illustrated using the Bärnighausen tree formalism. These results may be used to identify new phases and interpret experimental results, determine the structural mechanisms responsible for the formation of low-symmetry phases as well as to understand the structural genesis of the perovskite-like phases. The obtained non-model group-theoretical results in combination with crystal chemical data and first-principles calculations may be a starting point for the design of new functional materials with a perovskite structure.

Symmetry-based prediction of the type-II multiferroics with pyrochlore structure

“…2) that the final P I 4 3 -and P I 4 1 -phases can be obtained in various symmetry ways from the initial phase. This conclusion corresponds to the so-called variable principle, which was first established in work [48]. From the initial structure with the F d3m space group, this enantiomorphic pair is obtained through intermediate structures (Fig.…”

Energetic Couplings in Ferroics

“…αβγ (α, β, and γ being x, y, or z) is the Levi-Civita symbol whose value is 1 for αβγ being even permutation, −1 for odd permutation and 0 otherwise. Such energies explain why LaMn 3 Cr 4 O 12 has a polarization [90][91][92][93][94][95] . Note that, strictly speaking, LaMn 3 Cr 4 O 12 is not the same as the perovskites ABX 3 .…”

Research progress on quadruple perovskite oxides

“…118,119 As a special case, the magneto-ferroelectricity of LaMn 3-Cr 4 O 12 55 with a cubic quadruple perovskite structure exceeds the framework of the above-mentioned three microscopic mechanisms. Feng and Xiang 56 proposed a new mechanism of symmetric anisotropic exchange to explain the multiferroics in LaMn 3 Cr 4 O 12 with an A-site-ordered quadruple perovskite structure, 20,[120][121][122] in which its B-site Cr 3+ and A-site Mn 3+ ions form a collinear G-type AFM order as the temperature decreases. Although the spin structure of Mn and Cr alone is non-polarized, the magnetic lattice of the two together forms a polarized magnetic dot group, inducing ferroelectricity.…”