Pseudo-Hermitian physics from dynamically coupled macrospins
Phys. Rev. B 114, 214420 – Published 19 October, 2026
DOI: https://doi.org/10.1103/7ffq-9cvt
Abstract
We generalize the Landau-Lifshitz-Gilbert equation for classical macrospin precession to include dynamic (frequency-dependent) couplings, which can be either dissipative or nondissipative. Near equilibrium, we find that Onsager reciprocity guarantees quasi-Hermitian dynamics for nondissipatively coupled spins; dissipatively coupled spin systems exhibit the more general pseudo-Hermitian dynamics, provided that the couplings have a bipartite structure. For fixed points away from equilibrium, we find in both cases that fluctuations retain the pseudo-Hermitian property, although the spectral features depend dramatically on the local free energy landscape. When two local precession 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 -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. We present illustrative examples of these phenomena and discuss the systematic construction of higher order exceptional points, with sensing of magnetic field gradients as a potential application. Accounting for the effects of local Gilbert damping, we examine the cases in which approximate -symmetry breaking is still possible and determine the degree to which the qualitative spectral properties still persist.
