Spin-transfer in an open ferromagnetic layer: from negative damping to effective temperature

TL;DR

This paper investigates spin-transfer effects in ferromagnetic layers, introducing a thermokinetic framework to explain negative damping and effective temperature phenomena observed during spin-injection experiments.

Contribution

It provides a detailed thermokinetic analysis and derivation of Fokker-Planck equations to justify the concepts of negative damping and effective temperature in spin-transfer.

Findings

Identification of current-dependent effective temperature in activation regime

Derivation of Fokker-Planck equations including relaxation effects

Thermokinetic model explaining energy exchange at junctions

Abstract

Spin-transfer is a typical spintronics effect that allows a ferromagnetic layer to be switched by spin-injection. Most of the experimental results about spin transfer are described on the basis of the Landau-Lifshitz-Gilbert equation of the magnetization, in which additional current-dependent damping factors are added, and can be positive or negative. The origin of the damping can be investigated further by performing stochastic experiments, like one shot relaxation experiments under spin-injection in the activation regime of the magnetization. In this regime, the N\'eel-Brown activation law is observed which leads to the introduction of a current-dependent effective temperature. In order to justify the introduction of these counterintuitive parameters (effective temperature and negative damping), a detailed thermokinetic analysis of the different sub-systems involved is performed. We propose a thermokinetic description of the different forms of energy exchanged between the electric and the ferromagnetic sub-systems at a Normal/Ferromagnetic junction. The corresponding Fokker Planck equations, including relaxations, are derived. The damping coefficients are studied in terms of Onsager-Casimir transport coefficients, with the help of the reciprocity relations. The effective temperature is deduced in the activation regime.