Ferromagnetic Damping/Anti-damping in a Periodic 2D Helical surface; A Non-Equilibrium Keldysh Green Function Approach

TL;DR

This paper presents a theoretical study of spin-orbit torque and Gilbert damping in a 2D helical surface state with ferromagnetic coupling, using a non-equilibrium Green function approach to analyze electronic transport and magnetic damping.

Contribution

It introduces a detailed theoretical framework for calculating spin-orbit torque and Gilbert damping in 2D topological surface states with ferromagnetic exchange, including their dependence on magnetization direction.

Findings

Decomposition of density matrix into Fermi sea and surface components.

Derived expressions for spin-orbit torque contributions.

Predicted damping dependence on magnetization precession axis.

Abstract

In this paper, we investigate theoretically the spin-orbit torque as well as the Gilbert damping for a two band model of a 2D helical surface state with a Ferromagnetic (FM) exchange coupling. We decompose the density matrix into the Fermi sea and Fermi surface components and obtain their contributions to the electronic transport as well as the spin-orbit torque (SOT). Furthermore, we obtain the expression for the Gilbert damping due to the surface state of a 3D Topological Insulator (TI) and predicted its dependence on the direction of the magnetization precession axis.