  Diamagnetic levitation can provide a completely passive method to support
materials against the pull of gravity, and researchers have levitated both
solids and fluids. Such levitation can be assisted by increasing the magnetic
susceptibility contrast by using a surrounding paramagnetic medium and through
buoyancy forces, known as magneto-Archimedean levitation. The
magneto-Archimedean levitation of solids has proved useful in chemistry and
biology. However, the levitation of fluid droplets has an additional interest
because the fluid droplet's shape can deform. We perform experiments and
simulations to gauge the squashing or eccentricity of the static magnetically
levitated fluid droplet. By carefully characterizing all the parameters
affecting the droplet's levitation, using image analysis to estimate the
droplet's eccentricity, and using finite element adaptive simulations to find
the lowest energy droplet shape, we find good agreement between the simulations
and experimental results. As a potential application, we show that the
droplet's eccentricity can be used to perform magnetic gradiometry with a
potential resolution of $S\sim 8\,{\rm nT/cm}$, over a volume of 10 mm$^3$,
which is competitive with other room-temperature magnetic gradiometer
techniques.
