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The phase-transition sequence of a ferroelectric perovskite such as BaTiO_3can be simulated by computing the statistical mechanics of a first-principlesderived effective Hamiltonian [Zhong, Vanderbilt and Rabe, Phys. Rev. Lett. 73,1861 (1994)]. Within this method, the effect of an external pressure (ingeneral, of any external field) can be studied by considering the appropriate"enthalpy" instead of the effective Hamiltonian itself. The legitimacy of thisapproach relies on two critical assumptions that, to the best of our knowledge,have not been adequately discussed in the literature to date: (i) that thezero-pressure relevant degrees of freedom are still the only relevant degreesof freedom at finite pressures, and (ii) that the truncation of the Taylorexpansion of the energy considered in the effective Hamiltonian remains a goodapproximation at finite pressures. Here we address these issues in detail andpresent illustrative first-principles results for BaTiO_3. We also discuss howto construct effective Hamiltonians in cases in which these assumptions do nothold.

Effective-Hamiltonian Modeling of External Pressures in Ferroelectric Perovskites