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An effective Hamiltonian is derived to describe the conduction band ofmonolayer black phosphorus (phosphorene) in the presence of spin-orbit couplingand external electric field. Envelope function approximation along withsymmetry arguments and Lowdin partitioning are utilized to derive extrinsicspin-orbit coupling. The resulting spin splitting appears in fourth orderperturbation terms and is shown to be linear in both the magnitude of theexternal electric field and the strength of the atomic spin-orbit coupling,similar to the Bychkov-Rashba expression but with an in-plane anisotropy. Theanisotropy depends on the coupling between conduction band and other bands bothclose and distant in energy. The spin relaxation of conduction electrons isthen calculated within the Dyakonov-Perel mechanism where momentum scatteringrandomizes the polarization of a spin ensemble. We show how the anisotropicFermi contour and the anisotropic extrinsic spin splitting contribute to theanisotropy of spin-relaxation time. Scattering centers in the substrate areconsidered to be charged impurities with screened Coulomb potential.

Extrinsic Spin-Orbit Coupling and Spin Relaxation in Phosphorene