Origin of the hidden energy scale and the $f$-ratio in geometrically frustrated magnets

TL;DR

This paper explores the origin of the hidden energy scale in geometrically frustrated magnets, linking it to non-magnetic excitations and showing its influence on spin-glass freezing and the frustration ratio.

Contribution

It proposes that the hidden energy scale arises from non-magnetic excitations and relates it to the entropy of ground states, providing a new understanding of frustration and spin-glass behavior.

Findings

GF magnets exhibit two temperature scales in specific heat.

The hidden energy scale $T^*$ is linked to non-magnetic excitations.

Spin-glass freezing occurs at temperatures around $T^*$ in disordered materials.

Abstract

Sufficiently clean geometrically frustrated (GF) magnets are the largest class of candidate materials that may host quantum spin liquids (QSLs). Some of them have been shown to exhibit spin-glass freezing, potentially precluding QSLs, at the "hidden energy scale", which is significantly lower than the microscopic energy scale of spin interactions. Here, we investigate the origin of the hidden energy scale and its relationship to the $f$-ratio, the figure of merit for the degree of frustration in GF magnetic materials. The available experimental and numerical data provide evidence that GF magnets display, universally, two distinct temperature scales in the specific heat, the lowest of which is of the order of the hidden energy scale $T^*$. We argue that this scale is determined by non-magnetic excitations, similar to spin exchanges in chains of spins. The collective entropy of such excitations matches the entropy of the ground states of the Ising model on the same lattice, which provides a way to verify the proposed scenario in experiment. We demonstrate that in the presence of quenched disorder, a broad class of materials exhibits spin-glass freezing at temperatures of order $T^*$, in accordance with experimental observations. As $T^*$ is a property of the clean GF medium, it leads to a constraint on the $f$-ratio.