  Magnetic materials are particularly favorable targets for detecting axions
interacting with electrons because the collective excitation of electron spins,
the magnon, can be excited through the axion-magnon conversion process. It is
often assumed that only the zero-momentum uniformly precessing magnetostatic
(Kittel) mode of the magnon is excited. This is justified if the de Broglie
wavelength of the axion is much longer than the size of the target magnetic
material. However, if the de Broglie wavelength is shorter, finite-momentum
magnon modes can also be excited. We systematically analyze the target material
size dependence of the axion-magnon conversion rate. We discuss the importance
of these effects in the detection of relativistic axions as well as in the
detection of axion dark matter of relatively heavy mass with large material
size.
