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The recently proposed dynamical multiferroic effect describes the generationof magnetization from temporally varying electric polarization. Here, we showthat the effect can lead to a magnetic field at moving ferroelectric domainwalls, where the rearrangement of ions corresponds to a rotation offerroelectric polarization in time. We develop an expression for the dynamicalmagnetic field, and calculate the relevant parameters for the example of90$^\circ$ and 180$^\circ$ domain walls in BaTiO$_3$ using a combination ofdensity functional theory and phenomenological modeling. We find that themagnetic field reaches the order of several $\mu$T at the center of the wall,and we propose two experiments to measure the effect with nitrogen-vacancycenter magnetometry.

A dynamical magnetic field accompanying the motion of ferroelectric domain walls