Detection of geometric phases in spin waves using nitrogen vacancy centers

Due to their robustness, the implementation of geometric phases provides a reliable and controllable way to manipulate the phase of a spin wave, thereby paving the way toward functional magnonics-based data processing devices. Moreover, geometric phases in spin waves are interesting from a fundamental perspective as they contain information about spin wave band structures and play an important role in magnon Hall effects. In this paper, we propose to directly measure geometric phases in spin wave systems using the magnetic field sensing capabilities of nitrogen-vacancy (NV) centers. We demonstrate the general principles of this method on two systems in which spin waves acquire a geometric phase, namely, a wire with a magnetic domain wall and a system with position-dependent anisotropy axes, and explicitly show how this phase can be deduced from the NV center signal.