Marginal Metals and Kosterlitz-Thouless Type Phase Transition in Disordered Altermagnets

Altermagnetism, a recently discovered magnetic phase characterized by spin-split bands without net magnetization, has emerged as promising platform for novel physics and potential applications. However, its stability against disorder-ubiquitous in real materials-remains poorly understood. Here, we study the electron localization properties of two-dimensional altermagnets subject to disorder. Remarkably, we discover a disorder-driven phase transition from a marginal metallic phase to an insulator, which falls into the Kosterlitz-Thouless class. We demonstrate this by convincing numerical evidence and propose a vortex-antivortex-like spin pair picture for its interpretation. Moreover, we show that the characteristic spin anisotropy of altermagnets persists but gradually fades away across the transition. These changes directly affect the spin-splitting features that are detectable in angle-resolved photoemission spectroscopy and tunneling magnetoresistance. Our findings provide a new perspective on recent experimental observations of altermagnetism in candidate materials.