Band Topology and Dynamic Multiferroicity Induced from Dynamical Dzyaloshinskii-Moriya Interactions in Centrosymmetric Lattices

We develop a theory of a dynamical Dzyaloshinskii-Moriya interaction (dDMI) in centrosymmetric crystals by generally considering the vibration of both cations and anions. It gives rise to an antisymmetric spin-lattice coupling, inducing magnon-phonon hybridized topological excitations. Moreover, we find that this dDMI naturally exhibits a magnetoelectric feature, leading to the presence of dynamic multiferroicity with finite toroidal moment distribution in the momentum space. By comparing toroidal moments with band skyrmion structure, we reveal the intrinsic connection between band topology and dynamic multiferroicity through the dDMI.