Broadband optomechanical transduction of nanomagnetic spin modes.

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.