Emergent Gauge Flux and Spin Ordering in Magnetized Triangular Spin Liquids: Applications to Hofstadter-Hubbard Model

Abstract

Motivated by recent progress in moiré superlattices and spin-1/2 triangular-lattice antiferromagnets, we study how orbital magnetic flux and Zeeman coupling compete or cooperate in generating internal U(1) gauge flux in a triangular spin liquid. We show that orbital flux favors a chiral spin liquid with staggered internal flux, whereas Zeeman coupling destabilizes the spinon Fermi-pocket state toward a Landau-level state with spontaneous uniform internal flux and conical spin order. We demonstrate this mechanism in a spin-$1/2$ $J_1$-$J_2$-$J_{\chi }$ model, and further identify thermal Hall and magnetic signatures that distinguish these regimes, with potential applications to moiré Hofstadter-Hubbard systems and triangular-lattice antiferromagnets.

arXiv comment16 pages, 9 figures