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 $C[H,T]/T\sim H^{-\gamma }{F}_q[T/H]$ with $F_q[x]=x^q$ at small $x$, 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.

v2. Expanded argument in Appendix 2 and revised for clarity. v3. Fixed typo in Fig 3 caption. Main text 4 pages 4 figures, Appendix 6 pages 1 figure

References in corpus (8)

• Spin Dynamics of the Spin-1/2 Kagome Lattice Antiferromagnet ZnCu_3(OH)_6Cl_2
• Spin-glass ground state in a triangular-lattice compound YbZnGaO${}_4$
• Possible valence-bond condensation in the frustrated cluster magnet LiZn2Mo3O8
• Absence of magnetic thermal conductivity in the quantum spin liquid candidate YbMgGaO4
• Dynamic Scaling in the Susceptibility of the Spin-1\2 Kagome Lattice Antiferromagnet Herbertsmithite
• Gapless excitations in the ground state of 1T-TaS${}_2$
• Emergent orbitals in the cluster Mott insulator on a breathing Kagome lattice
• Strong-disorder renormalization for interacting non-Abelian anyon systems in two dimensions

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