Faculty Sponsor's Department:
Ferroelectric materials are materials having a phase in which they exhibit spontaneous polarization – polarization is acquired in an electric field, but when the field is switched off the material retains its polarization. Using theoretical studies, the simple binary oxides BaO and SrO have previously been shown, contrary to expectations, to undergo a ferroelectric phase transition when grown as a film on a suitably lattice-mismatched substrate. The mismatch leads to a biaxial strain, the critical value of which is known from ab initio calculations for zero temperature, but this reference is of little practical value for guiding experimental fabrication efforts. The aim of this project is to construct a temperature-strain phase diagram, extending the theoretical information to non-zero temperatures, by simulating the effects of thermal fluctuations using an effective Hamiltonian approach. Predictions can then be made regarding the more general conditions under which each material will undergo the phase transition into a ferroelectric state. Our approach involves mapping zero-temperature information from ab initio studies to a low-energy Hamiltonian for the microscopic degrees of freedom and solving for the thermal properties using classical Monte Carlo simulations. We first demonstrate the properties and features of the Monte Carlo simulations by exactly solving the well-known Ising ferromagnet, before discussing the related low-energy Hamiltonian for describing ferroelectric materials.