Non-Adiabatic Spin Transfer Torque in Real Materials

TL;DR

This paper derives an explicit expression for the non-adiabatic spin-transfer torque parameter  in magnetic materials, showing that intrinsic spin-orbit interactions often dominate and can be estimated reliably, impacting magnetic texture dynamics.

Contribution

The paper provides a new, simple formula relating  to band structure and Bloch state lifetimes, clarifying the role of spin-orbit interactions in spin-transfer torques.

Findings

Intrinsic spin-orbit interactions dominate  contributions.

Derived  expression relates to band structure and Bloch state lifetimes.

 can be estimated with confidence using the model.

Abstract

The motion of simple domain walls and of more complex magnetic textures in the presence of a transport current is described by the Landau-Lifshitz-Slonczewski (LLS) equations. Predictions of the LLS equations depend sensitively on the ratio between the dimensionless material parameter $\beta$ which characterizes non-adiabatic spin-transfer torques and the Gilbert damping parameter $\alpha$. This ratio has been variously estimated to be close to 0, close to 1, and large compared to 1. By identifying $\beta$ as the influence of a transport current on $\alpha$, we derive a concise, explicit and relatively simple expression which relates $\beta$ to the band structure and Bloch state lifetimes of a magnetic metal. Using this expression we demonstrate that intrinsic spin-orbit interactions lead to intra-band contributions to $\beta$ which are often dominant and can be (i) estimated with some confidence and (ii) interpreted using the "breathing Fermi surface" model.