Generation of electric current and electromotive force by an antiferromagnetic domain wall

Dynamic magnetic textures may transfer the angular moment from the varying in time antiferromagnetic order to spins of conduction electrons. Due to the spin orbit coupling (SOC) these spin excitations can induce the electric current of conduction electrons. We calculated the electric current and the electromotive force (EMF) which are produced by a domain wall (DW) moving parallel to the magnetically compensated interface between an antiferromagnetic insulator (AFMI) and a two-dimensional spin orbit coupled metal. Spins of conduction electrons interact with localized spins of a collinear AFMI through the interface exchange interaction. The Keldysh formalism of nonequilibrium Green functions was applied for the analysis of this system. It is shown that a Bloch DW generates the current perpendicular to the DW motion direction. At the same time a N\'{e}el DW creates the electric potential which builds up across the wall. The total charge which is pumped by a Bloch DW can be expressed in terms of a topologically invariant charge quantum. The latter does not depend on variations of DW's velocity and shape. These effects increase dramatically when the Fermi energy approaches the van Hove singularity of the Fermi surface. The obtained results are important for the electrical detection and control of dynamic magnetic textures in antiferromagnets.