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

## TL;DR

This paper presents a theoretical analysis demonstrating that quantum spin effects can stabilize the levitation of a nanomagnet in a static magnetic field, even without mechanical rotation, revealing new stabilization mechanisms.

## Contribution

It introduces the concept that quantum spin origins can provide additional stability mechanisms for magnetic levitation beyond classical rotation.

## Key findings

- Quantum spin stabilizes levitation at high magnetic fields via Larmor precession.
- Magnetic anisotropy stabilizes levitation at low magnetic fields through the Einstein-de Haas effect.
- Stable levitation phases exist without mechanical rotation, defying Earnshaw's theorem.

## Abstract

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.