  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.
