Abstract
We analyze the effect of quenched disorder on spin-1/2 quantum magnets in which magnetic frustration promotes the formation of local singlets. Our results include a theory for 2d valence-bond solids subject to weak bond randomness, as well as extensions to stronger disorder regimes where we make connections with quantum spin liquids. We find, on various lattices, that the destruction of a valence-bond solid phase by weak quenched disorder leads inevitably to the nucleation of topological defects carrying spin-1/2 moments. This renormalizes the lattice into a strongly random spin network with interesting low-energy excitations. Similarly when short-ranged valence bonds would be pinned by stronger disorder, we find that this putative glass is unstable to defects that carry spin-1/2 magnetic moments, and whose residual interactions decide the ultimate low energy fate. Motivated by these results we conjecture Lieb-Schultz-Mattis-like restrictions on ground states for disordered magnets with spin-1/2 per statistical unit cell. These conjectures are supported by an argument for 1d spin chains. We apply insights from this study to the phenomenology of YbMgGaO$_4$, a recently discovered triangular lattice spin-1/2 insulator which was proposed to be a quantum spin liquid. We instead explore a description based on the present theory. Experimental signatures, including unusual specific heat, thermal conductivity, and dynamical structure factor, and their behavior in a magnetic field, are predicted from the theory, and compare favorably with existing measurements on YbMgGaO$_4$ and related materials.
Highlights
Magnetic insulators often exhibit quenched disorder from material defects, including randomness in the strengths of magnetic exchanges
III A we discussed a putative valence-bond glass in 2D. This discussion shows that constructible wave functions can be written down, but we argued that they could not be ground states of local Hamiltonians, as they are unstable to the nucleation of spinful defects
Short-ranged valence-bond solid (VBS) order may be observed, through high-order crystalline symmetry-breaking effects which can be seen in sensitive structural probes; for columnar VBS, the lattice modulation would be visible at wave vector M, though we note that the microscopic randomness present in YbMgGaO4 means that shortranged VBS order is not required by the theory
Summary
Magnetic insulators often exhibit quenched disorder from material defects, including randomness in the strengths of magnetic exchanges. Let us focus on the prominent recently discovered material YbMgGaO4 [1,2,3,4,5,6,7,8,9,10,11,12] This is a layered insulator in which the Yb sites yield effective S 1⁄4 1=2 magnetic moments (arising from the strong spin-orbit coupling (SOC) of the heavy Yb3þ ions). Our main concern is the interplay between (1) valence-bond physics and (2) randomness in the exchange couplings
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
