Micromagnetic theory of spin relaxation and ferromagnetic resonance in multilayered metallic films

TL;DR

This paper develops a micromagnetic theory for spin relaxation and ferromagnetic resonance in ultrathin metallic films, linking damping to magnetic anisotropy stress-tensors and deriving analytic expressions for relaxation times and resonance linewidths.

Contribution

It introduces a modified Landau-Lifshitz equation incorporating stress-tensor effects, providing analytical formulas for relaxation and resonance linewidths in multilayered metallic films.

Findings

Analytic expressions for exponential relaxation times.

Derived ferromagnetic resonance linewidth formulas.

Potential application to recent experimental data.

Abstract

Spin relaxation in the ultrathin metallic films of stacked microelectronic devices is investigated on the basis of a modified Landau-Lifshitz equation of micromagnetic dynamics in which the damping torque is treated as originating from the coupling between precessing magnetization-vector and the introduced stress-tensors of intrinsic and extrinsic magnetic anisotropy. Particular attention is given to the time of exponential relaxation and ferromagnetic resonance linewidth which are derived in analytic form from the equation of magnetization energy loss and Gabor uncertainty relation between the full-width-at-half-maximum in resonance-shaped line and lifetime of resonance excitation. The potential of developed theory is briefly discussed in the context of recent measurements.