  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.
