Spin current contribution in the spectrum of collective excitations of degenerate partially polarized spin-1/2 fermions at separate dynamics of spin-up and spin-down fermions

TL;DR

This paper develops a two-fluid hydrodynamic model for degenerate partially polarized spin-1/2 fermions, revealing three collective excitation modes including a spin wave influenced by spin current contributions.

Contribution

It introduces a novel two-fluid hydrodynamic framework consistent with a non-linear Pauli equation, incorporating a new equation of state for spin current in degenerate fermions.

Findings

Identified three collective excitation modes: two sound waves and one spin wave.

Calculated the spectra of these waves for different propagation directions.

Demonstrated the influence of spin current on collective excitations.

Abstract

The spectrum of collective excitations of degenerate partially polarized spin-1/2 fermions is considered. The spin-up fermions and the spin-down fermions are considered as different fluids. Corresponding two-fluid hydrodynamics consistent with a non-linear Pauli equation is suggested. An equation of state for the spin current caused by the distribution of particles on different energy levels is suggested for the degenerate regime, where the spin current is caused by the Pauli blocking. Spectrum of three waves is found as a solution of the hydrodynamic equations: two sound waves and one spin wave. Their spectrums are calculated for two regimes: propagation parallel and perpendicular to the direction of the equilibrium spin polarization.