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arXiv:2003.02529 · npj Quantum Materials

Observation of plaquette fluctuations in the spin-1/2 honeycomb lattice

Christian Wessler, B. Roessli, Karl W. Krämer, B. Delley, O. Waldmann, L. Keller, Denis V. Sheptyakov, Hans B. Braun, M. Kenzelmann

Published Nov 13, 2020• 28 citations
arXivHTMLPDF

Abstract

Abstract Quantum spin liquids are materials that feature quantum entangled spin correlations and avoid magnetic long-range order atT = 0 K. Particularly interesting are two-dimensional honeycomb spin lattices where a plethora of exotic quantum spin liquids have been predicted. Here, we experimentally study an effectiveS = 1/2 Heisenberg honeycomb lattice with competing nearest and next-nearest-neighbour interactions. We demonstrate that YbBr3avoids order down to at leastT = 100 mK and features a dynamic spin–spin correlation function with broad continuum scattering typical of quantum spin liquids near a quantum critical point. The continuum in the spin spectrum is consistent with plaquette type fluctuations predicted by theory. Our study is the experimental demonstration that strong quantum fluctuations can exist on the honeycomb lattice even in the absence of Kitaev-type interactions, and opens a new perspective on quantum spin liquids.

DOI
10.1038/s41535-020-00287-1

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Abstract Quantum spin liquids are materials that feature quantum entangled spin correlations and avoid magnetic long-range order atT = 0 K. Particularly interesting are two-dimensional honeycomb spin lattices where a plethora of exotic quantum spin liquids have been predicted. Here, we experimentally study an effectiveS = 1/2 Heisenberg honeycomb lattice with competing nearest and next-nearest-neighbour interactions. We demonstrate that YbBr3avoids order down to at leastT = 100 mK and features a dynamic spin–spin correlation function with broad continuum scattering typical of quantum spin liquids near a quantum critical point. The continuum in the spin spectrum is consistent with plaquette type fluctuations predicted by theory. Our study is the experimental demonstration that strong quantum fluctuations can exist on the honeycomb lattice even in the absence of Kitaev-type interactions, and opens a new perspective on quantum spin liquids.
Quantum spin liquids are materials that feature quantum entangled spin correlations and avoid magnetic long-range order at T = 0 K. Particularly interesting are two-dimensional honeycomb spin lattices where a plethora of exotic quantum spin liquids have been predicted. Here, we experimentally study an effective S = 1/2 Heisenberg honeycomb lattice with competing nearest and next-nearest-neighbour interactions. We demonstrate that YbBr3 avoids order down to at least T = 100 mK and features a dynamic spin–spin correlation function with broad continuum scattering typical of quantum spin liquids near a quantum critical point. The continuum in the spin spectrum is consistent with plaquette type fluctuations predicted by theory. Our study is the experimental demonstration that strong quantum fluctuations can exist on the honeycomb lattice even in the absence of Kitaev-type interactions, and opens a new perspective on quantum spin liquids.
Quantum spin liquids are materials that feature quantum entangled spin correlations and avoid magnetic long-range order at T = 0 K. Particularly interesting are two-dimensional honeycomb spin lattices where a plethora of exotic quantum spin liquids have been predicted. Here, we experimentally study an effective S=1/2 Heisenberg honeycomb lattice with competing nearest and next-nearest neighbor interactions. We demonstrate that YbBr3_33​ avoids order down to at least T=100 mK and features a dynamic spin-spin correlation function with broad continuum scattering typical of quantum spin liquids near a quantum critical point. The continuum in the spin spectrum is consistent with plaquette type fluctuations predicted by theory. Our study is the experimental demonstration that strong quantum fluctuations can exist on the honeycomb lattice even in the absence of Kitaev-type interactions, and opens a new perspective on quantum spin liquids.
We explore the phase diagram of the Kitaev-Heisenberg model with nearest neighbor interactions on the honeycomb lattice using the exact diagonalization of finite systems combined with the cluster mean field approximation, and supplemented by the insights from analytic approaches: the linear spin-wave and second-order perturbation theories. This study confirms that by varying the balance between the Heisenberg and Kitaev term, frustrated exchange interactions stabilize in this model either one of four phases with magnetic long range order: N\'eel phase, ferromagnetic phase, and two other phases with coexisting antiferromagnetic and ferromagnetic bonds, zigzag and stripy phase, or one of two distinct spin-liquid phases. Out of these latter disordered phases, the one with ferromagnetic Kitaev interactions has a substantially broader range of stability as the neighboring competing ordered phases, ferromagnetic and stripy, have very weak quantum fluctuations. Focusing on the quantum spin-liquid phases, we study spatial spin correlations and dynamic spin structure factor of the model by the exact diagonalization technique, and discuss the evolution of gapped low-energy spin response across the quantum phase transitions between the disordered spin liquid and phases with long range magnetic order.
We employ the spin cluster perturbation theory to investigate the dynamical properties of the antiferromagnetic ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model on the honeycomb lattice. We obtain the excitation spectra for all possible phases in the phase diagram, including the N\'eel phase, plaquette valence-bond-solid phase, dimer valence-bond-solid phase, and stripe antiferromagnetic phase. In the N\'eel phase, besides the obvious renormalization of the magnon dispersion, we find that the spectrum exhibits a dome-shaped broad continuum around the second Brillouin zone (BZ) and the additional strong continuum close to the corner of the BZ. In the valence-bond-solid phases, the spectra are dominated by a strong broad continuum all the way down to below J1{J}_{1}J1​ coexisting with the lowest-energy triplon modes characterizing the plaquette and dimer phases. We ascribe this strong broad continuum and the additional continuum close to the BZ corner in the N\'eel phase to the contributions of fractionalized spinon excitations. In the stripe phase, a clear difference from the linear-spin-wave approximation is that the spectrum is gapped at the MMM point, while that obtained by the latter is gapless due to the strong quantum fluctuations. We point out that the features observed in the N\'eel phase are consistent with the recent neutron scattering experiments on YbCl3{\mathrm{YbCl}}_{3}YbCl3​ and YbBr3{\mathrm{YbBr}}_{3}YbBr3​.
Abstract A family of spin–orbit coupled honeycomb Mott insulators offers a playground to search for quantum spin liquids (QSLs) via bond-dependent interactions. In candidate materials, a symmetric off-diagonal Γ term, close cousin of Kitaev interaction, has emerged as another source of frustration that is essential for complete understanding of these systems. However, the ground state of honeycomb Γ model remains elusive, with a suggested zigzag magnetic order. Here we attempt to resolve the puzzle by perturbing the Γ region with a staggered Heisenberg interaction which favours the zigzag ordering. Despite such favour, we find a wide disordered region inclusive of the Γ limit in the phase diagram. Further, this phase exhibits a vanishing energy gap, a collapse of excitation spectrum, and a logarithmic entanglement entropy scaling on long cylinders, indicating a gapless QSL. Other quantities such as plaquette-plaquette correlation are also discussed.
Motivated by recent experiments on $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$, we investigate a possible quantum spin liquid ground state of the honeycomb-lattice spin model with bond-dependent interactions. We consider the $K\ensuremath{-}\mathrm{\ensuremath{\Gamma}}$ model, where KKK and $\mathrm{\ensuremath{\Gamma}}$ represent the Kitaev and symmetric-anisotropic interactions between spin-1/2 moments on the honeycomb lattice. Using the infinite density matrix renormalization group, we provide compelling evidence for the existence of quantum spin liquid phases in an extended region of the phase diagram. In particular, we use transfer-matrix spectra to show the evolution of two-particle excitations with well-defined two-dimensional dispersion, which is a strong signature of a quantum spin liquid. These results are compared with predictions from Majorana mean-field theory and used to infer the quasiparticle excitation spectra. Further, we compute the dynamical structure factor using finite-size cluster computations and show that the results resemble the scattering continuum seen in neutron-scattering experiments on $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$. We discuss these results in light of recent and future experiments.