We investigate the temperature-dependent dynamical properties of ${\mathrm{PbZrO}}_3$ (PZO) using molecular dynamics (MD) simulations with an effective Hamiltonian. As temperature decreases from 1800  to 10 K, PZO is predicted to undergo a sequence of phase transitions. Above 1350 K, it exhibits the cubic paraelectric $Pm\overline{3}m$ phase. Between 1350  and 650 K, an intermediate phase emerges, denoted here as the $\mathrm{\Sigma }$ phase and characterized by antipolar displacements along [110] and complex oxygen octahedral tiltings about [001], both associated with the $\mathrm{\Sigma }$ point and with amplitudes increasing upon cooling. Below 650 K, PZO stabilizes in the $Pbam$ ground state, exhibiting additional $R$- and $S_4$-point order parameters, with all associated condensed degrees of freedom strengthening at lower temperatures. MD results yield a first-order character of the $Pm\overline{3}m$-to-$\mathrm{\Sigma }$ and $\mathrm{\Sigma }$-to-$Pbam$ transitions. Moreover, phonon analysis reveals the predicted temperature evolution of mode frequencies associated with $\mathrm{\Gamma }, R, \mathrm{\Sigma }$, and $S_{4}k$ points. In the cubic phase, $\mathrm{\Sigma }$, mode having both antipolar and octahedral tiltings characteristics is softening on temperature decrease, as consistent with the existence of a bilinear coupling that is often overlooked. In the $\mathrm{\Sigma }$ phase, a mode associated with the $R$-point-induced antiphase octahedral tiltings strongly softens. Within the $Pbam$ phase, multiple resonant frequencies appear for each mode, reflecting complex mode couplings, including bilinear and trilinear ones. These computations agree well with experimental data, including temperature behavior of soft mode and even a higher mode, which calls for testing all present predictions, that may offer new insight into key features of PZOs including its lattice dynamics and phase transitions.

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• Antiferroelectricity
• Critical phenomena
• Dielectric properties
• Dynamical phase transitions
• Ferroelectricity
• Lattice dynamics
• Order parameters
• Phase transitions by order
• Phonons
• Transition temperature
• First-principles calculations
• Symmetries in condensed matter