Intraband and interband spin-orbit torques in non-centrosymmetric ferromagnets

Abstract

Intraband and interband contributions to the current-driven spin-orbit torque in magnetic materials lacking inversion symmetry are theoretically studied using Kubo formula. In addition to the current-driven field-like torque ${\mathbf{T}}_{\mathrm{FL}}={\tau }_{\mathrm{FL}}\mathbf{m}\times {\mathbf{u}}_{\mathrm{so}}$ (${\mathbf{u}}_{\mathrm{so}}$ 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 ${\mathbf{T}}_{\mathrm{DL}}={\tau }_{\mathrm{DL}}\mathbf{m}\times ({\mathbf{u}}_{\mathrm{so}}\times \mathbf{m})$. 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 exchanged coupled to the Mn moments. Parametric dependences 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.

10 pages, 5 figures

References in corpus (6)

• Dissipationless Quantum Spin Current at Room Temperature
• Spin Transfer Torques
• Theory of ferromagnetic (III,Mn)V semiconductors
• Intrinsic vs. extrinsic anomalous Hall effect in ferromagnets
• Current-induced domain wall motion in Rashba spin-orbit system
• Magneto-gyrotropic effects in semiconductor quantum wells (review)

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• Magnetoelectric effect in band insulator-ferromagnet heterostructures
• Longitudinal optical and spin-Hall conductivities of Rashba conducting strips coupled to ferro- and antiferromagnetic layers
• Transport properties of Rashba conducting strips coupled to magnetic moments with spiral order