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 $C[H,T]\mathrm{/}T\sim H^{-\gamma }{F}_q[T\mathrm{/}H]$ with $F_q[x] = x^{q}$atsmall$x$,with$q \in$ (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.