Spin polarization induced by magnetic field and the relativistic Barnett effect

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.