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-$1/2$ $J_1\text{−}{J}_2\text{−}{J}_{\chi }$ 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.

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• Fractionalization
• Frustrated magnetism
• Quantum spin liquid
• Moire materials
• Monte Carlo methods