Dipole-dipole interactions and incommensurate order in perovskite structures

Dipole-dipole (DD) interactions are known to play an important role in conditioning ferroelectricity in ABO(3) perovskite crystals. Their possible role in conditioning nonferroelectric (inhomogeneous) cation ordering is presently unexplored. I analyze the energy of DD interactions in perovskite structure for different inhomogeneous spatial patterns of electric dipoles localized at the lattice sites. I show that DD interactions can favor inhomogeneous ordering when other terms of the Hamiltonian allow large total polarizability of A sites, comparably large total polarizability of oxygen sites in A-O planes, and relatively weak total polarizability of oxygen sites in the B-O direction. These conditions are naturally expected in PbZrO3 crystals, for which the reason behind antiferroelectric and incommensurate inhomogeneous ordering is currently being debated.