  D'yakonov-Perel' (DP) mechanism describes the dynamics of non-equilibrium
spin distribution in a two-dimensional (2D) system in the presence of Rashba
spin-orbit coupling. In this paper, we study the anisotropy of spin relaxation
via the DP mechanism for a 2D semiconductor with an elliptic band structure.
Within the effective-mass approximation, the low-energy band structure is
described using anisotropic in-plane effective mass of free carriers. Spin
relaxation time of free carriers is calculated theoretically using the time
evolution equation of the density matrix of a polarized spin ensemble in the
strong momentum scattering regime. Results are obtained for scattering
potential due to both Coulomb interaction and neutral defects in the sample. We
show that the ratio of spin relaxation time in the y- and x-direction within
the 2D plane displays a power-law dependence on the effective mass ratio, while
the exponent captures the details of the scattering potential. The model is
applied to study electron spin relaxation in monolayer black phosphorus, which
is known to exhibit significant band structure ellipticity. The model can also
predict spin relaxation anisotropy in mechanically strained 2D materials in
which elliptic band structure emerges as a consequence of the modification of
the lattice constants.
