Extrinsic spin-orbit coupling and spin relaxation in phosphorene

Abstract

An effective Hamiltonian is derived to describe the conduction band of monolayer black phosphorus (phosphorene) in the presence of spin-orbit coupling and external electric field. Envelope function approximation along with symmetry arguments are utilized to derive extrinsic spin-orbit splitting, which is shown to be linear in both the magnitude of the external electric field and the strength of the atomic spin-orbit coupling. The spin splitting is akin to the Bychkov-Rashba expression but demonstrates an in-plane anisotropy. The spin relaxation of conduction electrons is then calculated within the Dyakonov-Perel mechanism where momentum scattering randomizes the polarization of a spin ensemble. We show how the anisotropic Fermi contour and the anisotropic extrinsic spin splitting contribute to the anisotropy of spin-relaxation time. Scattering centers in the substrate are considered to be charged impurities with screened Coulomb potential. We report that spin ensembles with different initial polarization in the plane of phosphorene show an anisotropy of more than an order of magnitude in spin-relaxation time.