  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 towards 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.
