Lattice-based Monte Carlo simulations of the electrocaloric effect in ferroelectrics and relaxor ferroelectrics

Canonical and microcanonical Monte Carlo simulations are carried out to study the electrocaloric effect (ECE) in ferroelectrics and relaxor ferroelectrics (RFEs) by direct computation of field-induced temperature variations at the ferroelectric-to-paraelectric phase transition and the nonergodic-to-ergodic state transformation. A lattice-based Hamiltonian is introduced, which includes a thermal energy, a Landau-type term, a dipole-dipole interaction energy, a gradient term representing the domain-wall energy, and an electrostatic energy contribution describing the coupling to external and random fields. The model is first parametrized and studied for the case of ${\mathrm{BaTiO}}_{3}$. Then, the ECE in RFEs is investigated, with particular focus on the influence of random fields and domain-wall energies. If the strength or the density of the random fields increases, the ECE peak shifts to a lower temperature but the temperature variation is reduced. On the contrary, if the domain-wall energy increases, the peak shifts to a higher temperature and the ECE becomes stronger. In RFEs, the ECE is maximum at the freezing temperature where the nonergodic-to-ergodic transition takes place. Our results imply that the presence of random fields reduces the entropy variation in an ECE cycle by pinning local polarization.