Pseudo-Hermitian physics from dynamically coupled macrospins

TL;DR

This paper explores the spectral properties of coupled macrospins with frequency-dependent interactions, revealing pseudo-Hermitian dynamics and phenomena like level attraction and $ ext{PT}$-symmetry breaking, influenced by damping effects.

Contribution

It introduces a generalized Landau-Lifshitz-Gilbert model showing pseudo-Hermitian behavior in coupled macrospins with nonlocal interactions, connecting spectral phenomena to $ ext{PT}$-symmetry concepts.

Findings

Hybridization leads to anticrossing or level attraction depending on interactions.

Dissipative effects can induce $ ext{PT}$-symmetry breaking.

Spectral properties persist approximately even with local damping.

Abstract

We consider two classical macrospins with dynamical (frequency-dependent) coupling, modeled by a generalized Landau-Lifshitz-Gilbert equation. We show that, in the absence of local damping, the resulting dynamics are pseudo-Hermitian. When two precessional modes hybridize near a crossing, the spectral behavior takes the form either of an anticrossing or level attraction, with the latter formalized in terms of spontaneous $\mathcal{PT}$-symmetry breaking. Near equilibrium, mixing due to nondissipative interactions results in repulsion, while dissipative mixing results in attraction. In contrast, when the fluctuating degrees of freedom form a free-energy saddle point, we find that nondissipative interactions result in level attraction, while dissipative interactions produce level repulsion. Accounting for the effects of local Gilbert damping, we examine the cases in which approximate $\mathcal{PT}$-symmetry breaking is still possible and determine the degree to which the qualitative spectral properties still persist.