  The separate spin evolution (SSE) of electrons causes the existence of the
spin-electron acoustic wave. Extraordinary spin-electron acoustic waves (SEAWs)
propagating perpendicular to the external magnetic field have large
contribution of the transverse electric field. Its spectrum has been studied in
the quasi-classical limit at the consideration of the separate spin evolution.
The spin-spin interaction and the quantum Bohm potential give contribution in
the spectrum extraordinary SEAW. This contribution is studied in this paper.
Moreover, it is demonstrated that the spin-spin interaction leads to the
existence of the extraordinary SEAWs if the SSE is neglected. The hybridization
of the extraordinary SEAW and the lower extraordinary wave in the regime, where
the cyclotron frequency is larger then the Langmuir frequency is studied
either.
