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

Extraordinary SEAWs under influence of the spin-spin interaction and the quantum Bohm potential