Anomalous Gilbert Damping and Duffing Features of the SFS {\boldmath $\varphi_0$} Josephson Junction

TL;DR

This paper investigates the nonlinear and anomalous magnetic and phase dynamics of the $\

Contribution

It introduces a novel Duffing oscillator model incorporating Gilbert damping to describe the nonlinear behavior of the $\

Findings

Anomalous shift of ferromagnetic resonance frequency with increased Gilbert damping

Duffing oscillator behavior observed in ferromagnetic resonance curves

Proposed a resonance method to measure spin-orbit interaction in noncentrosymmetric materials

Abstract

We demonstrate unusual features of phase dynamics, IV-characteristics and magnetization dynamics of the $\varphi_0$ Josephson junction at small values of spin-orbit interaction, ratio of Josephson to magnetic energy and Gilbert damping. In particular, an anomalous shift of the ferromagnetic resonance frequency with an increase of Gilbert damping is found. The ferromagnetic resonance curves show the Duffing oscillator behaviour, reflecting the nonlinear nature of Landau-Lifshitz-Gilbert (LLG) equation. Based on the numerical analysis of each term in LLG equation we obtained an approximated equation demonstrated both damping effect and Duffing oscillator features. The resulting Duffing equation incorporates the Gilbert damping in a special way across the dissipative term and the restoring force. A resonance method for the determination of spin-orbit interaction in noncentrosymmetric materials which play the role of barrier in $\varphi_0$ junctions is proposed.