Topological electromotive force from domain-wall dynamics in a ferromagnet...

We formulate a local gauge-invariant theory for the electromotive force induced by domain-wall dynamics in a ferromagnet. We demonstrate that this emf generation is a real-space topological pumping effect. The integral of the emf over one pumping period is a quantized topological invariant which does not depend on the details of the domain-wall configuration nor on its detailed dynamics. Based on our theory, the full instanta- neous electric potential distribution can be mapped out by standard electrostatic methods. We also provide further details on our recent experiments which confirmed the emf induced by domain-wall dynamics.