Landau Theory of Tilting of Oxygen Octahedra in Perovskites

The list of possible commensurate phases obtained from the parent tetragonal phase of Ruddlesden-Popper (RP) systems, An+1BnC3n+1 for general n due to a single phase transition involving the reorienting of octahedra of C (oxygen) ions is reexamined using a Landau expansion. This expansion allows for the nonlinearity of the octahedral rotations and the rotation-strain coupling. It is found that most structures allowed by symmetry are inconsistent with the constraint of rigid octahedra, which dictates the form of the quartic terms in the Landau free energy. For A2BC4 our analysis allows only 10 of the 41 structures which satisfy the general symmetry arguments of Hatch et al. [Phys. Rev. B 39, 9282 (1989)]. The symmetry of rotations for RP systems with n > 2 is clarified. Our list of possible structures for general n excludes many structures allowed in previous studies.