Control of magnetic domain wall motion by electric fields has recently attracted scientific attention because of its potential for magnetic logic and memory devices. Here, we report on a new driving mechanism that allows for magnetic domain wall motion in an applied electric field without the concurrent use of a magnetic field or spin-polarized electric current. The mechanism is based on elastic coupling between magnetic and ferroelectric domain walls in multiferroic heterostructures. Pure electric-field driven magnetic domain wall motion is demonstrated for epitaxial Fe films on BaTiO$_3$ with in-plane and out-of-plane polarized domains. In this system, magnetic domain wall motion is fully reversible and the velocity of the walls varies exponentially as a function of out-of-plane electric field strength.
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