Ferroelectric phase transitions: A first-principles approach

Fundamental aspects of the theoretical study of bulk ferroelectric phase transitions through the construction of model Hamiltonians from first-principles calculations are reviewed. It is demonstrated that density-functional-theory linear-response calculations and total-energy calculations with symmetry-constrained ionic relaxation are very useful in the determination of the local mode variable and of the parameters in an explicit expression for the model Hamiltonian. Results of first-principles pseudopotential calculations of the lattice constant, phonon frequencies, and distortion energies for the perovskite ferroelectric PbTiO3 are presented. From this information, the local mode variable is identified, a model Hamiltonian is constructed and its finite-temperature behavior is studied with mean-field theory and Monte Carlo simulation. Very rough agreement with the observed Tc is obtained and various improvements and refinements of the calculation proposed. A well-controlled method for investigation of the intrinsic limitations of the model Hamiltonian approach, based on application to a simple rigid ion model, is outlined and preliminary results described.

Keywords:

• Ferroelectricity
• first principles
• PbTiO₃
• phase transition
• Monte Carlo simulation