Scaling and data collapse from local moments in frustrated disordered quantum spin systems

Abstract Recently measurements on various spin–1/2 quantum magnets such as H 3 LiIr 2 O 6, LiZn 2 Mo 3 O 8, ZnCu 3 (OH) 6 Cl 2 and 1T-TaS 2 —all described by magnetic frustration and quenched disorder but with no other common relation—nevertheless showed apparently universal scaling features at low temperature. In particular the heat capacity C H, T in temperature T and magnetic field H exhibits T / H data collapse reminiscent of scaling near a critical point. Here we propose a theory for this scaling collapse based on an emergent random-singlet regime extended to include spin-orbit coupling and antisymmetric Dzyaloshinskii-Moriya (DM) interactions. We derive the scaling C H, T / T ~ H − γ F q T / H with F q x = x q at small x, with q ∈ 0, 1, 2 an integer exponent whose value depends on spatial symmetries. The agreement with experiments indicates that a fraction of spins form random valence bonds and that these are surrounded by a quantum paramagnetic phase. We also discuss distinct scaling for magnetization with a q -dependent subdominant term enforced by Maxwell’s relations.