Intrinsic spin orbit torque in a single domain nanomagnet

TL;DR

This paper provides a theoretical analysis of intrinsic spin orbit torque in a single domain ferromagnetic layer with Rashba SOC, revealing its field-like symmetry and dependence on material parameters, with implications for different layer configurations.

Contribution

The study introduces a detailed theoretical framework for intrinsic SOT in ferromagnets with Rashba SOC, highlighting its field-like nature and material-dependent sign and magnitude.

Findings

Intrinsic SOT exhibits only field-like torque symmetry.

Sign and magnitude of SOT depend on material parameters.

Different supporting layers can invert SOT sign due to electrostatic doping.

Abstract

We present theoretical studies of the intrinsic spin orbit torque (SOT) in a single domain ferromagnetic layer with Rashba spin-orbit coupling (SOC) using the non-equilibrium Green's function formalism for a model Hamiltonian. We find that, to the first order in SOC, the intrinsic SOT has only the field-like torque symmetry and can be interpreted as the longitudinal spin current induced by the charge current and Rashba field. We analyze the results in terms of the material related parameters of the electronic structure, such as band filling, band width, exchange splitting, as well as the Rashba SOC strength. On the basis of these numerical and analytical results, we discuss the magnitude and sign of SOT. Our results show that the different sign of SOT in identical ferromagnetic layers with different supporting layers, e.g. Co/Pt and Co/Ta, could be attributed to electrostatic doping of the ferromagnetic layer by the support.