Valence Bonds in Random Quantum Magnets: Theory and Application to YbMgGaO4

Abstract

We analyze the effect of quenched disorder on spin-1/2quantum 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-1/2moments. 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-1/2magnetic 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 spin1/2per statistical unit cell. These conjectures are supported by an argument for 1D spin chains. We apply insights from this study to the phenomenology ofYbMgGaO4, a recently discovered triangular lattice spin-1/2insulator 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 onYbMgGaO4and related materials.

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Plain Language Summary

Simple models for interacting spins in magnetic solids exhibit a wide range of quantum states and epitomize the counterintuitive nature of quantum correlations. But to explain the behavior of many real materials, the theoretical models must take account of randomness. Understanding the new kinds of correlated quantum states generated by randomness is a venerable theoretical challenge. Here we address this challenge by constructing a theoretical framework using tools from several fields.

Our theoretical analysis of random magnets begins with a surprising result, that applies to a wide range of valence-bond-forming systems: Even when there is initially a large energy barrier to creating any spin-carrying excitation, infinitesimal randomness in the couplings forces zero-energy spin excitations to emerge. We synthesize this and other results, in a variety of limits, into general conjectures (and a proof in one dimension) that limit the possible low-energy behaviors of certain disordered systems to only three types. We trace out the features of various two-dimensional magnets in detail over a succession of energy scales. We use the resulting insights to build a phenomenological theory that accurately predicts the behavior of experimentally measured quantities in several magnetic solids, showing good agreement with experiments thus far.

The theory presented here will help researchers understand the behavior of previously perplexing materials. It provides controlled results that will be valuable points of reference in exploring the treacherous sea of disordered quantum systems.