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

Recently measurements on various spin-1/2 quantum magnets such as H₃LiIr₂O₆, LiZn₂Mo₃O₈, ZnCu₃(OH)₆Cl₂ and 1T-TaS₂-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^-γF_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.