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We report passive magnetic levitation and three-dimensional harmonic trappingof 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, whilethe finite size effect of the diamagnetic effect is used for horizontaltrapping. The dynamics of the levitated sphere was optically measured to havetrapping frequencies of up to around 600 Hz and mechanical $Q$-factors in theorder of $Q \sim 10^3$. These results were quantitatively reproduced bythree-dimensional finite element method simulations. Our results can provide anovel system where magnetism, rigid body motions, microwaves, and opticsinteract.

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