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 ${90}^{\circ }$ 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 ${90}^{\circ }$ 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.

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• Domain walls
• Geometric & topological phases
• Non-reciprocal propagation
• Optical interferometry
• Polarization of light
• Spin waves
• Antiferromagnets