Microscopic theory of the residual surface resistivity of Rashba electrons

A microscopic expression of the residual electrical resistivity tensor is derived in linear response theory for Rashba electrons scattering at a magnetic impurity with cylindrical or noncylindrical potential. The behavior of the longitudinal and transversal residual resistivity is obtained analytically and computed for an Fe impurity at the Au(111) surface. We studied the evolution of the resistivity tensor elements as a function of the Rashba spin-orbit strength and the magnetization direction of the impurity. We found that the absolute values of longitudinal resistivity reduce with increasing spin-orbit strength of the substrate and that the scattering of the conduction electrons at magnetic impurities with magnetic moments pointing in directions not perpendicular to the surface plane produce a planar Hall effect and an anisotropic magnetoresistance even if the impurity carries no spin-orbit interaction. Functional forms are provided describing the anisotropy of the planar Hall effect and the anisotropic magnetoresistance with respect to the direction of the impurity moment. In the limit of no spin-orbit interaction and a nonmagnetic impurity of cylindrical symmetry, the expression of the residual resistivity of a two-dimensional electron gas has the same simplicity and form as for the three-dimensional electron gas [J. Friedel, J. Nuovo. Cim. 7, 287 (1958)] and can also be expressed in terms of scattering phase shifts.