Spin-Electromagnetic Hydrodynamics and Magnetization Induced by Spin-Magnetic Interaction

TL;DR

This paper develops a hydrodynamic model incorporating spin and electromagnetic fields, deriving equations for spin-magnetic interactions and magnetization, with implications for understanding spin-electromagnetic phenomena in media.

Contribution

It introduces a novel hydrodynamic framework that integrates spin dynamics with electromagnetic fields, utilizing the Minkowski approach and thermodynamics to derive constitutive equations.

Findings

Derived magnetization from spin-magnetic interactions.

Established a more consistent polarization equation.

Connected spin effects with macroscopic electromagnetic properties.

Abstract

The hydrodynamic model including the spin degree of freedom and the electromagnetic field was discussed. In this derivation, we applied electromagnetism for macroscopic medium proposed by Minkowski. For the equation of motion of spin, we assumed that the hydrodynamic representation of the Pauli equation is reproduced when the many-body effect is neglected. Then the spin-magnetic interaction in the Pauli equation was converted to a part of the magnetization. The fluid and spin stress tensors induced by the many-body effect were obtained by employing the algebraic positivity of the entropy production in the framework of the linear irreversible thermodynamics, including the mixing effect of the irreversible currents. We further constructed the constitutive equation of the polarization and the magnetization. Our polarization equation is more reasonable compared to another result obtained using electromagnetism for macroscopic medium proposed by de Groot-Mazur.