Dynamical multiferroicity

An appealing mechanism for inducing multiferroicity in materials is the generation of electric polarization by a spatially varying magnetization that is coupled to the lattice through the spin-orbit interaction. Here we describe the reciprocal effect, in which a time-dependent electric polarization induces magnetization even in materials with no existing spin structure. We develop a formalism for this dynamical multiferroic effect in the case for which the polarization derives from optical phonons, and compute the strength of the phonon Zeeman effect, which is the solid-state equivalent of the well-established vibrational Zeeman effect in molecules, using density functional theory. We further show that a recently observed behavior - the resonant excitation of a magnon by optically driven phonons - is described by the formalism. Finally, we discuss examples of scenarios that are not driven by lattice dynamics and interpret the excitation of Dzyaloshinskii-Moriya-type electromagnons and the inverse Faraday effect from the viewpoint of dynamical multiferroicity.