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D'yakonov-Perel' (DP) mechanism describes the dynamics of non-equilibriumspin distribution in a two-dimensional (2D) system in the presence of Rashbaspin-orbit coupling. In this paper, we study the anisotropy of spin relaxationvia the DP mechanism for a 2D semiconductor with an elliptic band structure.Within the effective-mass approximation, the low-energy band structure isdescribed using anisotropic in-plane effective mass of free carriers. Spinrelaxation time of free carriers is calculated theoretically using the timeevolution equation of the density matrix of a polarized spin ensemble in thestrong momentum scattering regime. Results are obtained for scatteringpotential due to both Coulomb interaction and neutral defects in the sample. Weshow that the ratio of spin relaxation time in the y- and x-direction withinthe 2D plane displays a power-law dependence on the effective mass ratio, whilethe exponent captures the details of the scattering potential. The model isapplied to study electron spin relaxation in monolayer black phosphorus, whichis known to exhibit significant band structure ellipticity. The model can alsopredict spin relaxation anisotropy in mechanically strained 2D materials inwhich elliptic band structure emerges as a consequence of the modification ofthe lattice constants.

Spin relaxation due to the D'yakonov-Perel' mechanism in 2D semiconductors with an elliptic band structure