The low-frequency ($<80$ cm${}^{-1}$) optical modes appearing in the dielectric spectra at low temperature are determined across the morphotropic phase boundary of disordered $\mathrm{Pb}(\mathrm{Zr},\mathrm{Ti}){\mathrm{O}}_3$ solid solutions from the use of first-principles-based molecular dynamics simulations. In particular, the number of these modes, their resonant frequencies, and dielectric spectral weights are obtained for any Ti composition ranging between 45$\%$ and 56$\%$—which, according to the simulations, allows the existence of three different equilibrium phases all exhibiting both long-range-ordered ferroelectric motions and oxygen octahedral tiltings, that are of rhombohedral $R3c$, monoclinic $Cc$, and tetragonal $I4cm$ space groups. In particular, a compositional-induced anticrossing occurring within the bridging $Cc$ state is revealed, and the difference in frequency between $A^{\prime }$ and $A^{\prime \prime }$ modes in the $Cc$ state is linked to a quantity introduced here and termed the monoclinic depth. Moreover, the coupling between ferroelectric degrees of freedom and oxygen octahedral tiltings is found to play a crucial role on the characteristics of the low-frequency optical modes in the $R3c$, $Cc$, and $I4cm$ phases. Analytical models are further developed to reproduce and better understand such characteristics.

• Received 30 November 2011

DOI:https://doi.org/10.1103/PhysRevB.85.014301