Topological excitations and the dynamic structure factor of spin liquids on the kagome lattice

Abstract

Recent neutron scattering experiments on the spin-1/2 kagome lattice antiferromagnet ZnCu 3 (OH) 6 Cl 2 (Herbertsmithite) provide the first evidence of fractionalized excitations in a quantum spin liquid state in two spatial dimensions 1 . In contrast to existing theoretical models of both gapped and gapless spin liquids 2-8 , which give rise to sharp dispersing features in the dynamic structure factor 9,10 , the measured dynamic structure factor reveals an excitation continuum that is remarkably flat as a function of frequency. Here we show that many experimentally observed features can be explained by the presence of topological vison excitations in a Z 2 spin liquid 11 . These visons form flat bands on the kagome lattice, and thus act as a momentum sink for spin-carrying excitations that are probed by neutron scattering. We compute the dynamic structure factor for two di erent Z 2 spin liquids 2 and find that our results for one of them are in qualitative agreement with the neutron scattering experiments above a very low energy cuto , below which the structure factor is probably dominated by impurities.Herbertsmithite, a layered spin-1/2 kagome lattice antiferromagnet 12 , is one of the strongest contenders for an experimental realization of a spin liquid state 13 . Indeed, no sign of magnetic ordering is observed down to temperatures around 50 mK, whereas the natural energy scale set by the magnetic exchange coupling J ∼ 200 K is four orders of magnitude larger 14 . Neutron scattering experiments 1 on single crystals of this material are consistent with a continuum of fractionalized spinon excitations as expected in a quantum spin liquid state. However, mean-field theories predict a vanishing structure factor below the onset of the two-spinon continuum, which is at a finite energy even for gapless spin liquids, apart from the small set of crystal momenta where the spinon gap closes. This is in stark contrast to experiments, where the measured structure factor is finite and almost constant as a function of frequency down to energies of the order of ∼ J /10 (ref. 1).Here we propose an explanation for the lack of a momentumdependent spinon continuum threshold via the interaction of spinons with another set of excitations which form a (nearly) flat band. Such localized excitations act as a momentum sink for the spinons, thereby flattening the dynamic structure factor. So far, the only theoretical model for a spin liquid state on the kagome lattice which naturally gives rise to a flat excitation band at low energies consists of the Z 2 spin liquids 2-4 . Besides spinons, these states exhibit gapped vortex excitations 15,16 of an emergent Z 2 gauge field 17,18 , socalled visons 11 , which indeed have a lowest energy band that is nearly flat 19,20 . Because the visons carry neither charge nor spin, they do not couple directly to neutrons. They interact with spinons, however, and we show that this coupling is responsible for flattening the dynamic structure factor and removing the sharp onset at the twospinon contin...

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“…Due to enhanced quantum fluctuations and reduced dimensionality, the low-dimensional quantum magnets host very often exotic quantum states of matter [1][2][3][4][5][6][7][8][9][10][11][12][13] . Especially for the one-dimensional (1D) spin systems, realization of novel quantum spin states is not only of lively experimental interest [7][8][9][10]12,13 but also a constant focus of theoretical study 1,2,[14][15][16][17] , since quantitative description of the elementary excitations can be provided by rigorous theoretical approaches and precise comparisons between theoretical predictions and experimental results can be made [7][8][9][10]12,13,15 .…”

Gapped spin liquid with Z2 topological order for the kagome Heisenberg model

“…Fractionalized spin excitations in neutron experiments [42] have been interpreted in terms of bosonic spinons in Ref. [98] and fermionic spinons in Ref. [99].…”

Colloquium : Herbertsmithite and the search for the quantum spin liquid

“…3, right). A major thrust has been to attempt to find evidence for these excitations in the spin excitation spectrum measured by inelastic neutron scattering (Han, Helton et al, 2012;Punk et al, 2014). A clever experiment was also proposed to search for visons by putting magnetic flux through a loop of the material and looking for a novel type of flux quantization (Senthil and Fisher, 2001).…”