  We have developed the quantum hydrodynamic model 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
(QHD) 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.
