Unquenched orbital angular momentum as the origin of spin inertia

TL;DR

This paper investigates the physical origin of spin inertia, proposing unquenched orbital angular momentum as a key factor, supported by a theoretical model aligning with experimental observations in cobalt.

Contribution

It introduces a two-sublattice model linking unquenched orbital angular momentum to spin inertia, providing a predictive framework and experimental signatures for verification.

Findings

The inertia parameter matches experimental values in cobalt.

Unquenched orbital angular momentum can explain high-frequency spin modes.

The model distinguishes between nutation and optical modes in ferromagnets.

Abstract

The recent proposal and observation of spin inertia, and the consequent high-frequency spin nutation mode, have raised key questions for our understanding of magnetization dynamics, especially considering its high relevance for magnetic memories and ultrafast switching. Notwithstanding recent progress, a clear identification of spin inertia's physical origin thereby offering predictive power remains to be accomplished. Here, discussing general principles for identifying this physical origin, we examine unquenched orbital angular momentum (OAM) finding it to be a key candidate, despite its typically small value. Treating OAM and spin within a two-sublattice model, we derive the equivalent single-sublattice framework for magnetization dynamics making appropriate approximations. The latter naturally manifests the spin inertia term and parameter, which are otherwise introduced phenomenologically. The inertia parameter evaluated within our model is found to be in good agreement with its experimentally observed value in cobalt. We further delineate key experimental signatures that could verify or rule out the unquenched OAM as the origin of the observed high-frequency mode, and avoid a spurious optical mode in a two-sublattice ferromagnet from being identified as nutation. Our analysis offers a potential link between the recently emerged fields of orbitronics and spin inertia, thereby motivating investigations at their intersection.