Spin current evolution in the separated spin-up and spin-down quantum hydrodynamics

• We derive the spin current equation for particles with different projection of spin.
• We predict the contribution of Bohm potential to the dynamics of spin current.
• We derive the spin-current wave in the system of spin-polarized particles.
• We study the propagation of spin-acoustic wave in magnetized dielectrics.

We have developed a method of quantum hydrodynamics (QHD) that describes particles with spin-up and with spin-down in separate. We have derived the equation of the spin current evolution as a part of the set of the quantum hydrodynamics equations that treat particles with different projection of spin on the preferable direction as two different species. We have studied orthogonal propagation of waves in the external magnetic field and determined the contribution of quantum corrections due to the Bohm potential and to magnetization energy of particles with different projections of spin in the spin-current wave dispersion. We have analyzed the limits of weak and strong magnetic fields.