  In order to detect high frequency gravitational waves, we need a new
detection method. In this paper, we develop a formalism for a gravitational
wave detector using magnons in a cavity. Using Fermi normal coordinates and
taking the non-relativistic limit, we obtain a Hamiltonian for magnons in
gravitational wave backgrounds. Given the Hamiltonian, we show how to use the
magnons for detecting high frequency gravitational waves. Furthermore, as a
demonstration of the magnon gravitational wave detector, we give upper limits
on GHz gravitational waves by utilizing known results of magnon experiments for
an axion dark matter search.
