Intraband and interband spin-orbit torques in noncentrosymmetric ferromagnets

Abstract

Intraband and interband contributions to the current-driven spin-orbit torque in magnetic materials lacking inversion symmetry are theoretically studied using the Kubo formula. In addition to the current-driven fieldlike torque TFL=τFLm×uso (uso being a unit vector determined by the symmetry of the spin-orbit coupling), we explore the intrinsic contribution arising from impurity-independent interband transitions and producing an anti-damping-like torque of the form TDL=τDLm×(uso×m). Analytical expressions are obtained in the model case of a magnetic Rashba two-dimensional electron gas, while numerical calculations have been performed on a dilute magnetic semiconductor (Ga,Mn)As modeled by the Kohn-Luttinger Hamiltonian exchange coupled to the Mn moments. Parametric dependencies of the different torque components and similarities to the analytical results of the Rashba two-dimensional electron gas in the weak disorder limit are described.