Strain coupling in the PbTiO₃ ferroelectric transition

The construction of a first-principles effective Hamiltonian for the perovskite ferroelectric PbTiO₃ yields independent parameters describing separate contributions from quadratic-order lattice instabilities, anharmonic coupling, long-range dipolar interactions and strain. The origin of the large strain effects in PbTiO₃ is identified through analysis of chemical trends in related perovskite compounds. The generation of long-range interactions by integrating out strain is discussed for these systems, and an analogy with long-range dipolar interactions explored. The effects of strain on the finite-temperature PbTiO₃ ferroelectric transition are investigated by solving the effective Hamiltonian using mean field theory and the Monte Carlo simulation. Strain is found to be responsible for the stabilization of the tetragonal phase below T_c and for the first order character of the transition. The effects of strain in other perovskite transitions are expected to be similar. Finally, the importance of realistic Hamiltonians for future microscopic simulations of microstructure effects is discussed.