  We show how to measure a steady-state magnon population in a magnetostatic
mode of a ferromagnet or ferrimagnet, such as yttrium iron garnet. We adopt an
optomechanical approach and utilize the magnetoelasticity of the ferromagnet.
The magnetostrictive force dispersively couples magnons to the deformation
displacement of the ferromagnet, which is proportional to the magnon
population. By further coupling the mechanical displacement to an optical
cavity that is resonantly driven by a weak laser, the magnetostrictively
induced displacement can be sensed by measuring the phase quadrature of the
optical field. The phase shows an excellent linear dependence on the magnon
population for a not very large population, and can thus be used as a
`magnometer' to measure the magnon population. We further study the effect of
thermal noises, and find a high signal-to-noise ratio even at room temperature.
At cryogenic temperatures, the resolution of magnon excitation numbers is
essentially limited by the vacuum fluctuations of the phase, which can be
significantly improved by using a squeezed light.

Quantum Physics;Mesoscale and Nanoscale Physics;Optics