Dynamical couplings in ferroelectrics and multiferroics

First-principle-based molecular dynamics simulations are developed and used to investigate dynamical phenomena in the $\textrm{Pb(Zr,Ti)}\textrm{O}_{3}$ (PZT) ferroelectric solid solutions and in the multiferroic BiFeO$_3$ system\footnote{D. Wang, J. Weerasinghe,and L. Bellaiche, Phys. Rev. B {\bf 83},020301(R) (2011).}$^,$\footnote{D. Wang, E. Buixaderas, J. \'I\~niguez, J. Weerasinghe,H. Wang, and L. Bellaiche,Phys. Rev. Lett. {\bf 107}, 175502 (2011). }. Several interesting effects are reported, including: (1) the existence of \emph{two} $E$ modes in PZT in the 50--75\quad cm$^{-1}$ range for temperatures smaller than $\simeq 200$\quad K when the system is in its $R3c$ phase. Such existence originates from a {\it linear} coupling between ferroelectric (FE) motions and tiltings of oxygen octahedra; (2) a Fermi resonance (FR) emerging from a {\it nonlinear} coupling between FE distortions and oxygen octahedra tilts. This FR manifests itself as the doubling of a nominally-single FE mode in a purely FE phase, when the resonant frequency of the FE mode is close to the first overtone of the oxygen octahedra tiltings; and (3) the prediction of an electromagnon peak, that results from specific interactions between magnetic dipoles, FE motions and oxygen octahedra tiltings, in BiFeO$_3$. Some of these results have been confirmed by recent Raman scattering experiments, and analytical models are also developed to better understand such effects.\footnote{This work is done in collaboration with L. Bellaiche (University of Arkansas), J. Hlinka (Institute of Physics, Czech Republic), E. Buxiaderas (Institute of Physics, Czech Republic), J. \'I\~niguez (Institut de Ci\`encia de Materials de Barcelona, Spain) and J. Weerasinghe (University of Arkansas)}