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arXiv:2510.11678 · Nature Physics

Spinon mediation of witness spin dynamics in herbertsmithite

H. Takahashi, Jack Murphy, Mitikorn Wood-Thanan, Pascal Puphal, Miguel-Ángel Sánchez-Martínez, Fabian Jerzembeck, Chun-Chih Hsu, Jonathan Ward, Masahiko Isobe, Y. Matsumoto, H. Takagi, Stephen J. Blundell, Michael R. Norman, Felix Flicker, J. C. Davis

Published Jun 10, 2026• 1 citation
arXivHTMLPDF

Abstract

Abstract The kagome lattice of spin-1/2 copper atoms in herbertsmithite is conjectured to sustain a quantum spin liquid state with spinon quasiparticles. Ideally, the kagome crystal planes are each separated by a plane of spinless zinc atoms. However, in real crystals, some spin-1/2 copper atoms substitute randomly onto these inter-kagome zinc sites. Here we reconceptualize such ‘impurity’ atoms as quantum witness spins whose dynamics is designed to probe the spin liquid state. We then introduce spin noise spectroscopy to measure the frequency and temperature dependence of witness spin dynamics, demonstrating that their phenomenology is consistent with extensive interactions between witness spins mediated by propagation of spinons through a quantum spin liquid. Ultimately, a sharp transition occurs at around 260 mK, below which the properties of both spin noise and magnetic susceptibility suggest that the witness spins form a spin glass phase. Among the theoretical models considered, we demonstrate that our observations are only consistent with spinon-mediated interactions between witness spins by either a Z 2 or U(1) quantum spin liquid, with the former model more closely matching the data. Our work demonstrates that quantum mechanical witness spins may now conceivably be used as a widely applicable probe of quantum spin liquid physics.

DOI
10.1038/s41567-026-03303-6

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Abstract The kagome lattice of spin-1/2 copper atoms in herbertsmithite is conjectured to sustain a quantum spin liquid state with spinon quasiparticles. Ideally, the kagome crystal planes are each separated by a plane of spinless zinc atoms. However, in real crystals, some spin-1/2 copper atoms substitute randomly onto these inter-kagome zinc sites. Here we reconceptualize such ‘impurity’ atoms as quantum witness spins whose dynamics is designed to probe the spin liquid state. We then introduce spin noise spectroscopy to measure the frequency and temperature dependence of witness spin dynamics, demonstrating that their phenomenology is consistent with extensive interactions between witness spins mediated by propagation of spinons through a quantum spin liquid. Ultimately, a sharp transition occurs at around 260 mK, below which the properties of both spin noise and magnetic susceptibility suggest that the witness spins form a spin glass phase. Among the theoretical models considered, we demonstrate that our observations are only consistent with spinon-mediated interactions between witness spins by either a Z 2 or U(1) quantum spin liquid, with the former model more closely matching the data. Our work demonstrates that quantum mechanical witness spins may now conceivably be used as a widely applicable probe of quantum spin liquid physics.
A quantum spin liquid (QSL) is an exotic quantum state of matter characterized by fluctuating spins which may exhibit long-range entanglement. Among the possible host candidates for a QSL ground state, the SSS=1/2 kagome lattice antiferromagnet is particularly promising. Using high resolution inelastic neutron scattering measurements on Zn-barlowite (Znx_\mathrm{x}x​Cu4−x_\mathrm{4-x}4−x​(OD)6_\mathrm{6}6​FBr, x≃0.80x\simeq 0.80x≃0.80), we measure a spin excitation spectrum consistent with a QSL ground state. Continuum scattering above $\sim1meVmatchesthatofherbertsmithite(Zn1 meV matches that of herbertsmithite (Zn1meVmatchesthatofherbertsmithite(Zn_\mathrm{x}CuCuCu_\mathrm{4-x}(OD)(OD)(OD)_6ClClCl_2$, x≃0.85x\simeq 0.85x≃0.85), another prominent kagome QSL material, indicating universal spinon excitations. A detailed analysis of the spin-spin correlations, compared with density matrix renormalization group calculations, further indicate a QSL ground state for the physically relevant Hamiltonian parameters. The measured spectra in Zn-barlowite are consistent with gapped behavior with a gap size Δ=1.1(2)Δ= 1.1(2)Δ=1.1(2) meV. Comparison with a simple pair correlation model allows us to clearly distinguish intrinsic kagome correlations from impurity-induced correlations. Our results clarify the behavior that is universal within this important family of QSL candidate materials.
It has been suggested that the nearest-neighbor antiferromagnetic Heisenberg model on the Kagome lattice may be a good starting point for understanding the spin-liquid behavior discovered in herbertsmithite. In this work, we investigate possible quantum spin liquid phases in the presence of spin-rotation symmetry-breaking perturbations such as Dzyaloshinskii-Moriya and Ising interactions, as well as second-neighbor antiferromagnetic Heisenberg interactions. Experiments suggest that such perturbations are likely to be present in herbertsmithite. We use the projective symmetry group analysis within the framework of the slave-fermion construction of quantum spin liquid phases and systematically classify possible spin liquid phases in the presence of perturbations mentioned above. The dynamical spin-structure factor for relevant spin liquid phases is computed and the effect of those perturbations are studied. Our calculations reveal dispersive features in the spin structure factor embedded in a generally diffuse background due to the existence of fractionalized spin-1/21/21/2 excitations called spinons. For two of the previously proposed Z2{Z}_{2}Z2​ states, the dispersive features are almost absent, and diffuse scattering dominates over a large energy window throughout the Brillouin zone. This resembles the structure factor observed in recent inelastic neutron-scattering experiments on singlet crystals of herbertsmithite. Furthermore, one of the Z2{Z}_{2}Z2​ states with the spin structure factor with mostly diffuse scattering is gapped, and it may be adiabatically connected to the gapped spin liquid state observed in recent density-matrix renormalization group calculations for the nearest-neighbor antiferromagnetic Heisenberg model. The perturbations mentioned above are found to enhance the diffuse nature of the spin structure factor and reduce the momentum dependencies of the spin gap. We also calculate the electron spin resonance (ESR) absorption spectra that further characterize the role of spin-rotation symmetry-breaking perturbations in these states. We suggest that the measurement of ESR spectra can shed more light into the nature of the ground state in herbertsmithite.
Copper hydroxyhalide materials herbertsmithite ZnCu3(OH)6Cl2{\mathrm{ZnCu}}_{3}{(\mathrm{OH})}_{6}{\mathrm{Cl}}_{2}ZnCu3​(OH)6​Cl2​ and Zn-barlowite ZnCu3(OH)6FrBr{\mathrm{ZnCu}}_{3}{(\mathrm{OH})}_{6}\mathrm{FrBr}ZnCu3​(OH)6​FrBr are thought to be the best realizations of the spin-1/2 kagome quantum antiferromagnetic Heisenberg model and are widely believed to host a spin liquid ground state. However, the exact nature of such a novel state of matter is still under strong debate, partly due to the complication related to the occupation disorder between the zinc and the copper ions in these systems. More specifically, some nonmagnetic Zn2+{\mathrm{Zn}}^{2+}Zn2+ ions in the system may occupy the Cu2+{\mathrm{Cu}}^{2+}Cu2+ site within the kagome plane and some spin-1/2Cu2+1/2\phantom{\rule{4pt}{0ex}}{\mathrm{Cu}}^{2+}1/2Cu2+ ions may occupy the Zn2+{\mathrm{Zn}}^{2+}Zn2+ site between the kagome planes. Both types of impurity can have a nontrivial effect on the dynamical behavior of the antiferromagnetically coupled Cu2+{\mathrm{Cu}}^{2+}Cu2+ spins on the kagome planes. Recent nuclear magnetic resonance measurements indicate that the magnetic response of the kagome plane is significantly spatial inhomogeneous, even though the content of the misplaced zinc or copper ions is very small. Here we use extensive variational optimization to show that the well-known U(1) Dirac spin liquid state is extremely sensitive to the introduction of the nonmagnetic Zn2+{\mathrm{Zn}}^{2+}Zn2+ impurity in the kagome plane. More specifically, we find that the zinc impurities can significantly reorganize the local spin correlation pattern around them and induce strong spatial oscillation in the magnetic response of the system. We argue that this is a general trend in highly frustrated quantum magnet systems, in which the nonmagnetic impurity may act as a strongly relevant perturbation on the emergent resonating valence bond structure in their spin liquid ground state. We also argue that the strong spatial oscillation in the magnetic response should be attributed to the free moment released by the doped Zn2+{\mathrm{Zn}}^{2+}Zn2+ ions and may serve as the smoking-gun evidence for the Dirac node in the U(1) Dirac spin liquid state on the kagome lattice.
The doping of quantum Heisenberg antiferromagnets on the kagome lattice by nonmagnetic impurities is investigated within the framework of a generalized quantum dimer model (QDM) describing (a) the valence-bond crystal (VBC), (b) the dimer liquid, and (c) the critical region on equal footing. Following the approach by Ralko et al. [Phys. Rev. Lett. 101, 117204 (2008)] for the square and triangular lattices, we introduce the (minimal) extension of the QDM on the kagome lattice to account for spontaneous creation of mobile S=1/2S=1/2S=1/2 spinons at finite magnetic field. Modulations of the dimer density (at zero or finite magnetic field) and of the local field-induced magnetization in the vicinity of impurities are computed using Lanczos exact diagonalization techniques on small clusters (48 and 75 sites). The VBC is clearly revealed from its pinning by impurities, while, in the dimer liquid, crystallization around impurities involves only two neighboring dimers. We also find that a next-nearest-neighbor ferromagnetic coupling favors VBC order. Unexpectedly, a small-size spinon-impurity bound state appears in some region of the dimer-liquid phase. In contrast, in the VBC phase the spinon delocalizes within a large region around the impurity, revealing the weakness of the VBC confining potential. Lastly, we observe that an impurity concentration as small as 4% enhances dimerization substantially. These results are confronted to the valence-bond glass scenario [R. R. P. Singh, Phys. Rev. Lett. 104, 177203 (2010)] and implications to the interpretation of the nuclear magnetic resonance spectra of the Herbertsmithite compound are outlined.
Motivated by recent experimental observations of Kondo resonances in cobalt atoms on single layer 1T-TaSe2_{2}2​, we theoretically investigate the effect of coupling a U(1) quantum spin liquid with a spinon Fermi surface to a lattice of Anderson impurities. Within the slave-rotor formalism, we find that above a critical coupling strength between the spin liquid and impurity lattice, the spinons hybridize to form heavy quasiparticles near the Fermi level, realizing a {\it spinon Kondo lattice phase} analogous to heavy fermion materials. Using the Bethe-Salpeter equation and accounting for emergent gauge fluctuations, we compute the spectral density and density of states, revealing the formation of spinon-chargon bound states in the spinon Kondo lattice phase. We characterize the thermodynamic and spectroscopic signatures of this phase, demonstrating specific heat and neutron scattering responses distinct from a pure quantum spin liquid. Our findings establish the spinon Kondo lattice as a framework to study the rich physics of spin liquids.