Emergent Halperin-Saslow mode and Gauge Glass in quantum Ising magnet TmMgGaO$_4$

TL;DR

This paper investigates how quenched disorder and interlayer coupling in a quantum Ising magnet lead to emergent gauge glass phases and Halperin-Saslow modes, providing insights into disordered frustrated magnetic systems.

Contribution

It introduces the concept of a gauge glass and Halperin-Saslow mode arising from quenched disorder in a quantum Ising magnet, extending understanding of disordered frustrated magnets.

Findings

Weak quenched disorder converts BKT phase into a gauge glass.

Emergent Halperin-Saslow mode persists in 3D gauge glass.

Interlayer coupling induces tiny ferromagnetism and suppresses BKT phase.

Abstract

We propose quenched disorders could bring novel quantum excitations and models to certain quantum magnets. Motivated by the recent experiments on the quantum Ising magnet TmMgGaO$_4$, we explore the effects of the quenched disorder and the interlayer coupling in this triangular lattice Ising antiferromagnet. It is pointed out that the weak quenched (non-magnetic) disorder would convert the emergent 2D Berezinskii-Kosterlitz-Thouless (BKT) phase and the critical region into a gauge glass. There will be an emergent Halperin-Saslow mode associated with this gauge glass. Using the Imry-Ma argument, we further explain the fate of the finite-field $C_3$ symmetry breaking transition at the low temperatures. The ferromagnetic interlayer coupling would suppress the BKT phase and generate a tiny ferromagnetism. With the quenched disorders, this interlayer coupling changes the 2D gauge glass into a 3D gauge glass, and the Halperin-Saslow mode persists. This work merely focuses on addressing a phase regime in terms of emergent U(1) gauge glass behaviors and hope to inspire future works and thoughts in weakly disordered frustrated magnets in general.