AbstractFerroelastic twin boundaries often have properties that do not exist in bulk, such as superconductivity, polarity etc. Designing and optimizing domain walls can hence functionalize ferroelastic materials. Using atomistic simulations, we report that moving domain walls have magnetic properties even when there is no magnetic element in the material. The origin of a robust magnetic signal lies in polar vortex structures induced by moving domain walls, e.g., near the tips of needle domains and near domain wall kinks. These vortices generate displacement currents, which are the origin of magnetic moments perpendicular to the vortex plane. This phenomenon is universal for ionic crystals and holds for all ferroelastic domain boundaries containing dipolar moments. The magnetic moment depends on the speed of the domain boundary, which can reach the speed of sound under strong mechanical forcing. We estimate that the magnetic moment can reach several tens of Bohr magnetons for a collective thin film of 1000 lattice planes and movements of the vortex by the speed of sound. The predicted magnetic fields in thin slabs are much larger than those observed experimentally in SrTiO₃/LaAlO₃ heterostructures, which may be due to weak (accidental) forcing and slow changes of the domain patterns during their experiments. The dynamical multiferroic properties of ferroelastic domain walls may have the potential to be used to construct localized magnetic memory devices in future.