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 and of the space group . A third, less-common ordering scheme is associated with . These combine with tilting instabilities associated with and 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.