Theory of inertial spin dynamics in anisotropic ferromagnets

TL;DR

This paper develops a theoretical framework for inertial spin dynamics in anisotropic ferromagnets, revealing how inertial effects alter resonance frequencies and providing exact solutions and approximations for these phenomena.

Contribution

It introduces a secular equation for inertial spin systems in ferromagnets, extending the Smit-Beljers formalism to include inertial effects and magnetic anisotropy.

Findings

Precessional resonance frequency decreases with inertia.

Nutation resonance frequency increases due to anisotropy and magnetic field.

Exact solutions and approximations for inertial effects are provided.

Abstract

Recent experimental observation of inertial spin dynamics calls upon holistic reevaluation of the theoretical framework of magnetic resonance in ferromagnets. Here, we derive the secular equation of an inertial spin system in analogy to the ubiquitous Smit-Beljers formalism. We find that the frequency of precessional ferromagnetic resonances is decreased as compared to non-inertial case. We also find that the frequency of nutational resonances is generally increased due to the presence of magnetic anisotropy and applied magnetic field. We obtain exact solutions of the secular equation and approximations that employ the terminology of non-inertial theory and thus allow for convenient estimates of the inertial effects.