Quantum physicists in Oriol Romero-Isart’s research group in Innsbruck show in two current publications that, despite Earnshaw’s theorem, nanomagnets can be stably levitated in an external static magnetic field owing to quantum mechanical principles. The quantum angular momentum of electrons, which also causes magnetism, is accountable for this mechanism.

In 1842, British mathematician Samuel Earnshaw proved that there is no stable configuration of levitating permanent magnets. If one magnet is levitated above another, the smallest disturbance will cause the system to crash. The magnetic top, a popular toy, circumvents the Earnshaw theorem: When it is disturbed, the gyrating motion of the top causes a system correction and stability is maintained. In collaboration with researchers from the Max Planck Institute for Quantum Optics, Munich, physicists in Oriol Romero-Isart’s research group at the Institute for Theoretical Physics, Innsbruck University, and the Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, have now shown that: “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,” says Oriol Romero-Isart.

The theoretical physicists carried out comprehensive stability analyses depending on the object’s radius and the strength of the external magnetic field. The results showed that, in the absence of dissipation, a state of equilibrium appears. This mechanism relies on the gyromagnetic effect: Upon a change in direction of the magnetic field, an angular momentum occurs because the magnetic moment couples with the spin of the electrons. “This stabilizes the magnetic levitation of the nanomagnet,” explains first author Cosimo Rusconi. In addition, the researchers showed that the equilibrium state of magnetically levitated nanomagnets exhibits entanglement of its degrees of freedom.

**New field of research**

Oriol Romero-Isart and his team are optimistic that these levitated nanomagnets can soon be observed experimentally. They have made suggestions on how this could be achieved under realistic conditions. Levitated nanomagnets are a new experimental research field for physicists. Studies of nanomagnets under unstable condition could lead to the discovery of exotic quantum phenomena. In addition, after coupling several nanomagnets, quantum nano magnetism could be simulated and studied experimentally. Levitated nanomagnets are also of high interest for technical applications, for example for developing high precision sensors.

Physical Review Letters – Quantum Spin Stabilized Magnetic Levitation

We theoretically show that, despite Earnshaw’s theorem, 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, namely, the gyromagnetic effect. We predict the existence of two stable phases related to the Einstein–de Haas effect and the Larmor precession. At a stable point, we derive a quadratic Hamiltonian that describes the quantum fluctuations of the degrees of freedom of the system. We show that, in the absence of thermal fluctuations, the quantum state of the nanomagnet at the equilibrium point contains entanglement and squeezing.

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 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.

Brian Wang is a Futurist Thought Leader and a popular Science blogger with 1 million readers per month. His blog Nextbigfuture.com is ranked #1 Science News Blog. It covers many disruptive technology and trends including Space, Robotics, Artificial Intelligence, Medicine, Anti-aging Biotechnology, and Nanotechnology.

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You can stably levitate superconducting magnets, thanks to flux vortex pinning. I’ve done it myself.