Theory of tensorial magnetic inertia in terahertz spin dynamics

TL;DR

This paper develops a tensorial theory of magnetic inertia in spin dynamics, revealing how anisotropic, chiral, and antisymmetric inertia components influence resonance frequencies and damping in various magnetic materials at THz frequencies.

Contribution

It introduces a tensorial framework for magnetic inertia, decomposes it into three components, and analyzes their distinct effects on spin resonance phenomena.

Findings

Scalar inertia reduces precession and nutation resonance frequencies.

Inertia tensor components further modify nutation resonance frequencies.

Chiral and antisymmetric inertia increase damping of nutation resonances.

Abstract

Magnetic inertia has emerged as a possible way to manipulate ferromagnetic spins at a higher frequency e.g., THz. Theoretical treatments so far have considered the magnetic inertia as a scalar quantity. Here, we explore the magnetic inertial dynamics with a magnetic inertia tensor as macroscopic derivations predicted it to be a tensor. First, the inertia tensor has been decomposed into three terms: (a) scalar and isotropic inertia, (b) anisotropic and symmetric inertia tensor, (c) chiral and antisymmetric tensor. Further, we employ linear response theory to the inertial Landau-Lifshitz-Gilbert equation with the inertia tensor and calculate the effect of chiral and anisotropic inertia on ferromagnets, antiferromagnets, and ferrimagnets. It is established that the precession and nutation resonance frequencies decrease with scalar magnetic inertia. Our results suggest that the nutation resonance frequencies further reduce due to inertia tensor. However, the effective damping of the nutation resonance increases with the chiral and antisymmetric part of the inertia tensor. We show that the precession resonances remain unaffected, while the nutation resonances are modified with the chiral magnetic inertia.