Non-Hermitian and Liouvillian skin effects in magnetic systems

TL;DR

The paper addresses whether non-Hermitian skin effects in magnetic systems can be understood from effective non-Hermitian Hamiltonians or require the full Liouvillian treatment. It analyzes a spin chain coupled to a shared reservoir, comparing the conditional non-Hermitian dynamics with the full Liouvillian and linking to Landau-Lifshitz-Gilbert magnetization dynamics in magnetic heterostructures. The key finding is that NHSE and Liouvillian skin effects coincide in the dilute magnon, zero-temperature limit, but the non-Hermitian description misses finite-time transport features and the impact of dissipation outside this regime; the essential ingredients are chiral exchange interactions (DMI) and nonlocal dissipation. The work thus provides a concrete route to realizing NHSE in spintronic platforms by mapping microscopic dynamics to experimentally accessible LLG descriptions in magnetic multilayers, offering guidance for engineering non-Hermitian spin transport in practice.

Abstract

The non-Hermitian skin effect (NHSE) has emerged as a hallmark of non-Hermitian physics, with far-reaching implications for transport, topology, and sensing. While recent works have uncovered the NHSE in magnetic systems, these analyses rely on effective non-Hermitian Hamiltonians, thereby leaving open critical questions regarding their applicability and predictive power in experimentally feasible platforms. Here, we address this gap by exploring both the non-Hermitian and Liouvillian dynamics of a spin chain coupled to a shared bosonic reservoir. We identify the parameter regime in which these frameworks yield congruent predictions, while showing that the non-Hermitian approach fails to capture essential dynamical features -- such as relevant timescales and conditions for experimental observability. Our analysis also reveals that the NHSE stems from the interplay between chiral spin couplings and reciprocal nonlocal dissipation -- two interactions that can naturally occur in magnetic crystals and be easily engineered in magnetic heterostructures. Focusing on a concrete example of such heterostructures, we establish an explicit connection between their Landau-Lifshitz-Gilbert (LLG) dynamics and our microscopic model, providing a tangible route toward realizing the NHSE in an experimentally relevant spintronics setup.

Figures (3)

• Figure 1: (a) A 1d array of spins interacting with a shared reservoir. $\mathbf{s}_{\alpha}$ denotes the spin at the $\alpha$th lattice site and $a$ is the lattice constant. (b) Spatial profile of the density of the first right eigenmode $\psi^{R}_{1,\alpha}$ under open boundary conditions for various sets of system parameters. (c) Corresponding eigenenergy spectra (normalized by $2s$) under periodic boundary conditions.
• Figure 2: (a)-(d) The dynamical evolution of the magnon number $n_{\alpha}$ as a function of time. At time $t=0$, a magnon resides at the site $\alpha=5$. (a) For $J=0$ and $D,\Gamma=1$ the magnonic excitation propagates only towards the left of the array. (b) Nonreciprocal magnon propagation towards the left and right sides of the array for $J,D,\Gamma=1$. (c) For $D=0$ and $\Gamma, J=1$, the propagation is reciprocal. In (a)-(c), the local dissipation is set to $\Gamma_{0}= 2\Gamma$. (d) For a local dissipation $\Gamma_{0} \gg D, \Gamma \neq 0$, magnon decay can suppress the spreading, such that no NHSE is observable.
• Figure 3: (a) Schematic of a multilayer magnetic array. The metallic spacers can mediate an interlayer DM interaction $\propto D$ and a damping-like spin pumping torque $\propto \alpha_{nl}$ between nearest neighbor magnetic layers. (b) Elliptical eigenenergy loop in the complex plane. Small effective next nearest neighbor interactions $\propto \alpha_{nl} D, \alpha_{nl} J$ are induced dynamically and preclude fully circular energy loop, even when the nearest neighbor hoppings become unidirectional. We plot the elliptical eigenenergy loop by choosing the local dissipation as $\alpha_{l}=0.002$ and the nonlocal dissipation as $\alpha_{nl}=0.001$.