Emergent gauge flux and spin ordering in magnetized triangular spin liquids: applications to Hofstadter-Hubbard model

TL;DR

This paper explores how magnetic fields influence gauge flux and spin order in triangular spin liquids, revealing mechanisms for chiral spin liquid formation and conical order, with implications for moiré systems and the Hofstadter-Hubbard model.

Contribution

It introduces a detailed analysis of the interplay between orbital flux and Zeeman effects in spin liquids, proposing new pathways for gauge flux generation and magnetic ordering in triangular lattices.

Findings

Orbital flux induces internal U(1) gauge flux via charge fluctuations.

Zeeman coupling can generate a uniform internal gauge flux.

Results have implications for moiré superlattices and the Hofstadter-Hubbard model.

Abstract

Motivated by the recent progress in the moir\'e superlattice systems and spin-1/2 triangular lattice antiferromagnets, we revisit the triangular-lattice spin liquids and study their magnetic responses. While the magnetic responses on the ordered phases can be mundane, the orbital magnetic flux and the Zeeman coupling have synergetic effects on the internal gauge flux generations in the relevant spin liquid phases. The former was known to induce an internal U(1) gauge flux indirectly through the charge fluctuations and ring exchange, and thus could lead to the formation of a chiral spin liquid. The latter could spontaneously generate a uniform field-dependent internal gauge flux, driving a conically-ordered state. The competition and interplay between these two field effects are discussed through a generic spin-1/2 $J_1$-$J_2$-$J_{\chi}$ model and with the experimental consequences. Our results could find applications in the moir\'e superlattice systems with the Hofstadter-Hubbard model as well as the triangular lattice antiferromagnets.