Hidden energy scale in geometrically frustrated magnets

We study the effect of quenched disorder on geometrically frustrated (GF) magnets, a class of systems in which spin liquids are widely sought. We analyse the available data on the spin-glass freezing transition in GF system and show that its phenomenology is qualitatively different from that of conventional (non-GF) glasses. Whereas conventional systems have a glass-transition temperature that increases with increasing disorder, GF systems have a glass temperature that increases with decreasing disorder, approaching, in the clean limit, a finite value. This behaviour implies the existence of a hidden energy scale (far smaller than the Weiss constant) which is independent of disorder and drives the glass transition in the presence of disorder. Motivated by these observations, we propose a scenario in which the interplay of interactions and entropy in the disorder-free system yields a temperature-dependent magnetic permeability with a crossover temperature that determines the hidden energy scale. The relevance of this scale for quantum spin liquids is discussed.