Spin kinetics in $n$-type InAs quantum wells under intense terahertz laser fields is investigated by developing fully microscopic kinetic spin Bloch equations via the Floquet-Markov theory and the nonequilibrium Greens function approach, with all the relevant scattering, such as the electron-impurity, electron-phonon, and electron-electron Coulomb scattering explicitly included. We find that a {em finite} steady-state terahertz spin polarization induced by the terahertz laser field, first predicted by Cheng and Wu [Appl. Phys. Lett. {bf 86}, 032107 (2005)] in the absence of dissipation, exists even in the presence of all the scattering. We further discuss the effects of the terahertz laser fields on the spin relaxation and the steady-state spin polarization. It is found that the terahertz laser fields can {em strongly} affect the spin relaxation via hot-electron effect and the terahertz-field-induced effective magnetic field in the presence of spin-orbit coupling. The two effects compete with each other, giving rise to {em non-monotonic} dependence of the spin relaxation time as well as the amplitude of the steady state spin polarization on the terahertz field strength and frequency. The terahertz field dependences of these quantities are investigated for various impurity densities, lattice temperatures, and strengths of the spin-orbit coupling. Finally, the importance of the electron-electron Coulomb scattering on spin kinetics is also addressed.
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