The hidden energy scale and spin-glass freezing in geometrically frustrated magnets

High-purity geometrically frustrated (GF) magnetic systems are the most-studied material platforms in which the coveted quantum spin-liquid (QSL) phase could be realized. This picture is complicated by the fact that some such materials have been shown to undergo spin-glass freezing at the “hidden energy scale” T^*, which might be incompatible with a QSL. In the present work, we propose a microscopic origin of the hidden energy scale based on the observation that in GF systems for which data are available over a sufficiently large temperature range, the heat capacity C(T) displays two readily distinguishable peaks, the lower of which is of the order of T^*. We argue that for a given lattice, the states that give rise to the lower and higher peaks consist of sets of excitations adiabatically connected to, respectively, the ground and excited states of the Ising model on the same lattice. We further illustrate this scenario of the hidden energy scale by numerical simulations of small clusters of spins on the kagome lattice. Lastly, we demonstrate via a microscopic calculation that our proposal is consistent with spin-glass freezing at temperatures ~T^* in a broad range of quenched disorder strengths.