Spin Wave Driven Skyrmions in a Bipartite Antiferromagnetic Lattice

We show that a Skyrmion in a classical bipartite antiferromagnetic lattice can be spatially displaced in a controlled manner by externally applied spin waves. We reveal the relation between the Skyrmion motion and the spin wave properties. To this end, we derive a classical spin wave formalism which is tailored to the antiferromagnetic two-dimensional square lattice. The antiferromagnetic spin waves can be classified into two types with respect to their polarization, with two modes each. The circularly polarized spin waves oscillate with different amplitudes in the respective sublattices and induce a Skyrmion Hall effect. The two modes are symmetric under sublattices exchange and determine the overall sign of the Hall angle. Linearly polarized spin waves oscillate elliptically, however, with the same amplitude on each sublattice. These accelerate the Skyrmion solely into their own propagation direction. The two modes are symmetric under component x-y exchange and impact Bloch- or N\'eel Skyrmions differently. Our results indicate possible technical applications of spin-wave driven Skyrmion motion. As one example we propose a racetrack where spin waves pump Skyrmions along the track in antiferromagnets.