  The stable vortex state that occurs in micron-scale magnetic disks is one of
the most interesting and potentially useful phenomenon in nanomagnetism. A
variety of tools have been applied to study the vortex state, and collective
spin excitations corresponding to harmonic motion of the vortex, but to-date
these tools have measured either strongly driven vortex resonances or have been
unable to simultaneously measure static properties such as the magnetization.
Here we show that by combining the sensitivity of cavity optomechanics with the
technique of torque mixing resonance spectroscopy, we are able to measure the
magnetization, in-plane susceptibility, and spin resonances of individual
vortices in the low-drive limit. These measurements elucidate the complex
behavior of the vortex as it moves through the pinning landscape of the disk.
Furthermore, we observe gyrotropic resonances as high as 1.1 GHz, suggesting
the use of engineering defects for applications such as microwave-to-optical
wavelength conversion.
