Non-Hermitian and Liouvillian skin effects in magnetic systems

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.