Devonshire-Landau free energy of BaTiO3 from first principles - art. no. 144103

We have studied the Devonshire-Landau potential underlying the phase transi tion 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 dielectri c and piezoelectric properties of this compound. The configuration space (d etermined by the polarization P as order parameter) was explored with the h elp of auxiliary electric fields. We show that the typically assumed form o f 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 non trivial temperature dependence for all the coefficients in the expansion, i ncluding the quadratic one, which is shown to behave nonlinearly. Our resul ts also prove that the sixth-order terms in the free-energy expansion (need ed to account for the first-order character of the transitions and the occu rrence of an orthorhombic phase) emerge from an interaction model that only includes terms up to the fourth order.