Instability analysis of spin-electron-acoustic waves and the appearance of separated spin electron cyclotron mode in spin-polarized magnetized quantum plasma.

Linear and nonlinear characteristics of electrostatic waves are studied in a magnetized plasma consisting of spin-up (n_{↑}) and spin-down (n_{↓}) state populations with uniformly distributed static ions in the background. The linear analysis shows the existence of four modes. One of these modes, termed the separated spin electron cyclotron wave, is found to be due to the separated spin populations. The Zakharov-Kuznetsov equation is derived by the reductive perturbation technique. The instability growth rate γ is obtained from the same equation. It is observed that the magnetized spin quantum plasma admits rarefactive soliton with constant amplitude but increasing width with the increasing strength of the applied magnetic field. It has also been observed that the amplitude of soliton decreases and its width increases with the increasing values of polarization ratio κ. The unstable region expands with the increase in polarization ratio and contracts with the increased plasma number density and magnetic-field strength. The (growth rate) γ of instability reduces by increasing the κ and is increasing when the density of the plasma and the strength of the magnetic field increasing. The model developed in this work finds its scope in studying degenerate electron gas and astrophysical systems such as pulsar magnetosphere and neutron stars.