  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
non-trivial temperature dependence for all the coefficients in the expansion,
including the quadratic one, which is shown to behave non-linearly. 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 fourth order.
