Frustration from Localized Zhang-Rice States: A Unified Theory of Doping-Driven Magnetic Transitions in Cuprates

The microscopic mechanism by which doped holes disrupt the antiferromagnetic order is one of the fundamental questions in cuprates. In this work, we propose a unified microscopic theory in which doped holes form spatially localized Zhang-Rice singlets which actively mediate emergent spin exchange. Rather than acting as simple non-magnetic vacancies, these localized states introduce emergent next-nearest $J_2$ and third-nearest $J_3$ neighbor superexchanges. This dopant-induced exchange pathway generates significant magnetic frustration, naturally explaining the rapid collapse of the Néel AFM order and the emergence of a spin-glass phase on the hole-doped side. Our findings provide a comprehensive framework for understanding the complex doping-driven magnetic phase transitions and magnetic electron-hole asymmetry in lightly doped cuprates.