Dynamics of domains switching in epitaxial BaTiO$_3$/SrTiO$_3$ superlattices from first principles*

Superlattices (SL) consisting of alternating layers of perovskite oxides can possess properties that are dramatically different from those of bulk ferroelectrics. [BaTiO$_3$]$_n$/[SrTiO$_3$]$_n$ (BT/ST) SL with relatively large periods exhibit novel nanostripe domains for some specific epitaxial strains and within a particular temperature window [1]. Here, an effective Hamiltonian approach is used within molecular dynamics method to predict the evolution of these nanostripe domains in BT/ST SL under an {\it ac} electric field applied along the SL growth direction. For any investigated frequency, four different regions occur, depending on the magnitude of the electric field: Region I that consists of nanostripe domains in both BT and ST layers; Region II that exhibits nanostripe domains in BT layers while possessing monodomains in ST layers; Region III where bubble domains in BT layers coexist with monodomains in ST layers; and Region IV where monodomains form in both BT and ST layers. The dependency of the domain velocities, activation and critical fields on the field frequency is revealed. [1] Lisenkov et al., {\em Phys. Rev. B}, {\bf 76}, 020102(R) (2007).