Effective Hamiltonian study of ${\mathrm{PbZr}}_{0.95}{\mathrm{Ti}}_{0.05}{\mathrm{O}}_3$

An effective Hamiltonian $H_{\mathrm{eff}}$ is constructed for ${\mathrm{PbZr}}_{0.95}{\mathrm{Ti}}_{0.05}{\mathrm{O}}_3.$ It is parametrized using primarily ab initio results computed in the virtual-crystal approximation. The phase diagram depends sensitively on the energetic competition between the stable orthorhombic antiferroelectric ${(A}_O)$ and the metastable “low temperature” rhombohedral ferroelectric ${(F}_{R\left(\mathrm{LT}\right)})$ structures at 0 K. By incorporating a temperature-dependent thermal-expansion term into $H_{\mathrm{eff}}$ and modifying $H_{\mathrm{eff}}$ to adjust the relative energies of the $A_O$ and $F_{R\left(\mathrm{LT}\right)}$ phases, we obtain a ferroelectric phase intervening between the low-temperature antiferroelectric ground state and the high-temperature paraelectric phase, in qualitative agreement with experiments. We also discuss the temperature-dependent disordering of the oxygen octahedral tilts responsible for the experimentally observed space group of the ferroelectric phase.