Devonshire-Landau free energy of BaTiO₃ from first principles

We have studied the Devonshire-Landau potential underlying the phase transition sequence of BaTiO₃ using the first-principles effective Hamiltonian of Zhong, Vanderbilt, and Rabe [Phys. Rev. Lett. 73, 1861 (1994)], which has been very successful in reproducing the phase transitions and the dielectric and piezoelectric properties of this compound. The configuration space (determined by the polarization P as order parameter) was explored with the help of auxiliary electric fields. We show that the typically assumed form of the potential, a sixth-order expansion in P around the paraelectric cubic phase, properly accounts for the behavior of the system, but we find a nontrivial temperature dependence for all the coefficients in the expansion, including the quadratic one, which is shown to behave nonlinearly. Our results also prove that the sixth-order terms in the free-energy expansion (needed to account for the first-order character of the transitions and the occurrence of an orthorhombic phase) emerge from an interaction model that only includes terms up to the fourth order.