Microscopic Origin Of Spin-Orbit Torque In Ferromagnetic Heterostructures: A First-Principles Approach

We present an ab initio based theoretical framework which elucidates the origin of the spin-orbit torque (SOT) in normal-metal (NM)/ferromagnet (FM) heterostructures. The SOT is decomposed into two contributions, namely, spin-Hall and the spin-orbital components. We find that (i) the fieldlike (FL) SOT is dominated by the spin-orbital component and (ii) both components contribute to the dampinglike (DL) torque with comparable magnitude in the limit of thick Pt film. The contribution of the spin-orbital component to the DL-SOT is present only for NMs with strong SOC coupling strength. We demonstrate that the FL-SOT can be expressed in terms of the nonequilibrium spin-resolved orbital moment accumulation. The calculations reveal that the experimentally reported oxygen-induced sign reversal of the FL-SOT in Pt/Co bilayers is due to the significant reduction of the majority-spin orbital moment accumulation on the interfacial NM atoms.