Symmetry rules and strain/order-parameter relationships for coupling between octahedral tilting and cooperative Jahn-Teller transitions in ABX3 perovskites. I. Theory.

Space groups, order-parameter and strain/order-parameter coupling relationships in ABX3 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 M2+ and R3+ of the space group Pm3m. A third, less-common ordering scheme is associated with Gamma3+. These combine with tilting instabilities associated with M3+ and R4+ 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.