Geometric phase acquired by spin waves in antiferromagnetic wire with domains of noncoplanar magnetization

We show that a spin wave acquires a polarization-dependent geometric phase along a cyclic trajectory of noncoplanar magnetizations in antiferromagnets. Specifically, we demonstrate that a cyclic set of ${90}^{\ensuremath{\circ}}$ antiferromagnetic domain walls simultaneously introduces geometric and dynamic phases to spin waves, which thus leads to an asymmetric magnitude of the overall phase for left/right circular components. Based on the polarization-dependent phase, we propose theoretically and confirm by micromagnetic simulations that a Mach-Zehnder interferometer with cyclic ${90}^{\ensuremath{\circ}}$ domain walls in one arm and a homogeneous domain in the other arm, naturally acts as a spin-wave circular polarizer. Moreover, the circular polarizer has intrinsic nonreciprocity, which filters opposite polarization in the opposite propagation direction.