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

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.