Exploring High Frequency Gravitational Waves with Magnons

Detecting gravitational waves with frequencies higher than 10 kHz requires new strategies. In previous papers, we proposed magnon gravitational wave detectors and gave the first limit on GHz gravitational waves by reinterpreting the existing data from axion dark matter experiments. In this paper, we show that the sensitivity can be improved by constructing the detector specific to gravitational waves. In particular, we employ an infinite sum of terms in the expansion of Fermi normal coordinates to probe gravitational waves with a wavelength comparable to the detector size. As a consequence, we obtain sensitivity of around $h_c \sim 10^{-20}$.