Magnetic levitation and harmonic trapping of a milligram-scale Yttrium Iron Garnet sphere

We report passive magnetic levitation and three-dimensional harmonic trapping of a 0.3 milligram, 0.5 millimeter diameter Yttrium Iron Garnet sphere at 4 K. The gradient of an external magnetic field is used for vertical trapping, while the finite size effect of the diamagnetic effect is used for horizontal trapping. The dynamics of the levitated sphere was optically measured to have trapping frequencies of up to around 600 Hz and mechanical $Q$-factors in the order of $Q \sim 10^3$. These results were quantitatively reproduced by three-dimensional finite element method simulations. Our results can provide a novel system where magnetism, rigid body motions, microwaves, and optics interact.