Symmetry rules and strain/order-parameter relationships for coupling between octahedral tilting and cooperative Jahn–Teller transitions in ABX 3 perovskites. I. Theory

Abstract

Space groups, order-parameter and strain/order-parameter coupling relationships in ABX 3 perovskite structures which combine cooperative Jahn–Teller distortions and octahedral tilting have been investigated from the perspective of group theory using the computer program ISOTROPY. Two common Jahn–Teller ordering schemes are associated with the irreducible representations {M}_2^+ and {R}_3^ + of the space group Pm\overline 3m. A third, less-common ordering scheme is associated with \Gamma _3^ +. These combine with tilting instabilities associated with {M}_3^ + and {R}_4^ + to generate a predicted suite of Jahn–Teller structure types that includes many of the known structures of manganites, vanadates, Cu and Cr halides. Order-parameter coupling and possible phase transitions are described using Landau free-energy expansions, and general expressions for the relationships between symmetry-adapted spontaneous strains and particular order-parameter components are presented. These provide a general formal framework for determining structural evolution across multi-component order-parameter space and for characterizing the influence of tilting instabilities on Jahn–Teller instabilities or of Jahn–Teller ordering on octahedral tilting.