Modelling of cavity optomechanical magnetometers

Cavity optomechanical magnetic field sensors, constructed by coupling a magnetostrictive material to a micro-toroidal optical cavity, act as ultra-sensitive room temperature magnetometers with tens of micrometre size and broad bandwidth, combined with a simple operating scheme. Here, we develop a general recipe for predicting the field sensitivity of these devices. Several geometries are analysed, with a highest predicted sensitivity of 180~p$\textrm{T}/\sqrt{\textrm{Hz}}$ at 28~$\mu$m resolution limited by thermal noise in good agreement with previous experimental observations. Furthermore, by adjusting the composition of the magnetostrictive material and its annealing process, a sensitivity as good as 20~p$\textrm{T}/\sqrt{\textrm{Hz}}$ may be possible at the same resolution. This method paves a way for future design of magnetostrictive material based optomechanical magnetometers, possibly allowing both scalar and vectorial magnetometers.