Spin polarization induced by magnetic field and the relativistic Barnett effect

TL;DR

This paper explores how magnetic fields and relativistic rotation induce spin polarization in fluids, using classical and quantum models, and discusses implications for heavy-ion collision experiments.

Contribution

It introduces a classical model for spin polarization via the relativistic Barnett effect and derives a quantum field theory formula valid beyond weak fields.

Findings

Spin polarization can be derived classically from the Barnett effect.

The quantum formula for spin polarization accounts for strong magnetic fields.

Spin polarization oscillates with magnetic field strength, similar to de Haas - van Alphen effect.

Abstract

First, I study the analogy between the magnetization of a material and the spin polarization of particles in a fluid. Using the relativistic version of the Barnett effect, i.e. the magnetization of a material induced by mechanical rotation, the spin polarization induced by thermal vorticity is obtained within a purely classical model, where spin is treated as an intrinsic magnetic moment and rotation is included as a non-inertial effect. I argue that since spin polarization induced by thermal vorticity can be obtained in a classical theory, it can not be dominated by quantum anomalies. Second, the spin polarization induced by magnetic field is obtained for a fluid at local thermal equilibrium using statistical quantum field theory. The obtained formula is valid beyond the weak field approximation and when contributions from the non-homogeneity of the magnetic field are small. The exact form of spin polarization is studied for a free Dirac field at global equilibrium, and, like magnetic susceptibility, it oscillates according to the de Haas - van Alphen effect. Finally, I briefly review how magnetic field contributes to the difference between the spin polarization of $\Lambda$ and $\bar{\Lambda}$ observed in heavy-ion collisions.