  We theoretically study the levitation of a single magnetic domain nanosphere
in an external static magnetic field. We show that apart from the stability
provided by the mechanical rotation of the nanomagnet (as in the classical
Levitron), the quantum spin origin of its magnetization provides two additional
mechanisms to stably levitate the system. Despite of the Earnshaw theorem, such
stable phases are present even in the absence of mechanical rotation. For large
magnetic fields, the Larmor precession of the quantum magnetic moment
stabilizes the system in full analogy with magnetic trapping of a neutral atom.
For low magnetic fields, the magnetic anisotropy stabilizes the system via the
Einstein-de Haas effect. These results are obtained with a linear stability
analysis of a single magnetic domain rigid nanosphere with uniaxial anisotropy
in a Ioffe-Pritchard magnetic field.
