In 1842, the British mathematician Samuel Earnshaw proved that it is not possible to achieve static levitation using any combination of fixed magnets and electric charges. In this case, static levitation means stable suspension of an object against gravity. However, it exists in a few ways to levitate by getting around the assumptions of the theorem. One of them consists of a rotating object with fixed magnets. This is called “The levitron”, a toy first invented by Roy Harrison in 1983. The spinning top can levitate delicately above a base with a careful arrangement of magnets so long as its rotation speed and height remain within certain limits. This phenomenon could become very interesting when applied to nanoparticles.

In fact, according to the Einstein–de Haas and Barnett effects, a change in the magnetization of an object is accompanied by a change in its rotational motion. Specifically, if the magnetic moment of a magnet is varied by a single Bohr magneton, it must rotate about the magnetic moment axis to conserve angular momentum. This clear manifestation of the quantum spin origin of magnetization, as prescribed by the gyromagnetic relation, is hence boosted at the nanoscale and could have been used to make a nanoscale “levitron”.

Physicists from Austria recently explored the role of the quantum spin origin of magnetization in magnetic levitation. While the earnshaw’s theorem is preventing any magnetic levitation of a nonrotating ferromagnet in a static magnetic field, they showed that levitation can be achieved by mechanically spinning the magnet. At the single atom level, magnetic trapping with static fields is also possible by exploiting the fast Larmor precession of its quantum spin. In this case, the atom is, from the mechanics point of view, a point particle without rotational degrees of freedom. A magnetic nanoparticle lies between the Levitron and the atom, as both its rotational degrees of freedom and the quantum spin origin of magnetization have to be accounted for. Can a nonrotating magnetic nanoparticle, despite Earnshaw’s theorem, be stably levitated with static magnetic fields?

In their last paper, the team lead by O. Romero-Isart theoretically demonstrated the viability of a nonrotating single magnetic domain nanoparticle can be stably levitated in an external static magnetic field. The stabilization relies on the quantum spin origin of magnetization acting as a gyromagnetic effect. They predicted a stable point, and showed that, in the absence of thermal fluctuations, the quantum state of the nanomagnet at the equilibrium point contains entanglement and squeezing.

In the quantum world, tiny non-gyrating nanoparticles can stably levitate in a magnetic field. Quantum mechanical properties that are not noticeable in the macroscopic world but strongly influence nano objects are accountable for this phenomenon.

Oriol Romero-Isart, Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences

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