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

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 arc calculated for two regimes: propagation parallel and perpendicular to the direction of the equilibrium spin polarization.