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We theoretically study the levitation of a single magnetic domain nanospherein an external static magnetic field. We show that apart from the stabilityprovided by the mechanical rotation of the nanomagnet (as in the classicalLevitron), the quantum spin origin of its magnetization provides two additionalmechanisms to stably levitate the system. Despite of the Earnshaw theorem, suchstable phases are present even in the absence of mechanical rotation. For largemagnetic fields, the Larmor precession of the quantum magnetic momentstabilizes the system in full analogy with magnetic trapping of a neutral atom.For low magnetic fields, the magnetic anisotropy stabilizes the system via theEinstein-de Haas effect. These results are obtained with a linear stabilityanalysis of a single magnetic domain rigid nanosphere with uniaxial anisotropyin a Ioffe-Pritchard magnetic field.

Linear Stability Analysis of a Levitated Nanomagnet in a Static Magnetic Field: Quantum Spin Stabilized Magnetic Levitation