Effective Hamiltonian study of PbSc$_{1/2}$Nb$_{1/2}$O$_3$ under pressure

In general, increasing pressure depresses the transition temperature $T_{FE}$ of ferroelectric transitions, and sufficient pressure yields a FE ~$\rightarrow$~ paraelectric (PE) transition. A more complicated behavior is observed for disordered PbSc$_{1/2}$Nb$_{1/2}$O$_3$ (PSN). At atmospheric pressure, PSN exhibits relaxor ferroelectric (RFE) properties within a small temperature range before transforming to a FE phase at low temperatures. Pressure of approximately 1.5 to 2.5 GPa induces a low-temperature RFE state without a RFE/FE phase boundary.[E. L. Venturini et al.] To investigate the effects of pressure on phase transitions in PSN, we used a first-principles based effective Hamiltonian. Our effective Hamiltonian includes a local field term arising from the charge difference between the Sc$^{3+}$ and Nb$^{5+}$ ions. Under pressure, the local field term changes little, while the FE well depths decrease, increasing the relative importance of the local fields. Molecular dynamics simulations show that $T_{FE}$ decreases with temperature and that the phase transition broadens.