  To consider a contribution of the spin-orbit interaction in the extraordinary
wave spectrum we derive a generalization of the separate spin evolution quantum
hydrodynamics. Applying corresponding nonlinear Pauli equation we include Fermi
spin current contribution in the spin evolution. We find that the spectrum of
extraordinary waves consists of three branches: two of them are well-known
extraordinary waves and the third one is the spin-electron acoustic wave
(SEAW). Earlier SEAWs have been considered in the electrostatic limit. Here we
include the electromagnetic effects in their spectrum at the propagation
perpendicular to the external magnetic field. We find that the SEAW spectrum
considerably changes at the account of transverse part of electric field. We
obtain that the separate spin evolution modifies spectrum of the well-known
extraordinary waves either. A change of the extraordinary wave spectrum due to
the spin-orbit interaction is obtained as well.
