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arXiv:1706.09908 · Physical review. B./Physical review. B

Quantum spin liquid signatures in Kitaev-like frustrated magnets

Matthias Gohlke, Gideon Wachtel, Youhei Yamaji, Frank Pollmann, Yong Baek Kim

Published Feb 13, 2018• 128 citations
arXivHTMLPDF

Abstract

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 $K$ 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.

DOI
10.1103/physrevb.97.075126

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Motivated by recent experiments on \ensuremathα\ensuremath−RuCl3\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}\ensuremathα\ensuremath−RuCl3​, we investigate a possible quantum spin liquid ground state of the honeycomb-lattice spin model with bond-dependent interactions. We consider the K\ensuremath−\ensuremathΓK\ensuremath{-}\mathrm{\ensuremath{\Gamma}}K\ensuremath−\ensuremathΓ model, where KKK and \ensuremathΓ\mathrm{\ensuremath{\Gamma}}\ensuremathΓ 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 \ensuremathα\ensuremath−RuCl3\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}\ensuremathα\ensuremath−RuCl3​. We discuss these results in light of recent and future experiments.
Abstract The spin liquid phase is one of the prominent strongly interacting topological phases of matter whose unambiguous confirmation is yet to be reached despite intensive experimental efforts on numerous candidate materials. Recently, a new family of correlated honeycomb materials, in which strong spin-orbit coupling allows for various bond-dependent spin interactions, have been promising candidates to realize the Kitaev spin liquid. Here we study a model with bond-dependent spin interactions and show numerical evidence for the existence of an extended quantum spin liquid region, which is possibly connected to the Kitaev spin liquid state. These results are used to provide an explanation of the scattering continuum seen in neutron scattering on α-RuCl3.
Abstract Large anisotropic exchange in 5 d and 4 d oxides and halides open the door to new types of magnetic ground states and excitations, inconceivable a decade ago. A prominent case is the Kitaev spin liquid, host of remarkable properties such as protection of quantum information and the emergence of Majorana fermions. Here we discuss the promise for spin-liquid behavior in the 4 d 5 honeycomb halide α -RuCl 3 . From advanced electronic-structure calculations, we find that the Kitaev interaction is ferromagnetic, as in 5 d 5 iridium honeycomb oxides, and indeed defines the largest superexchange energy scale. A ferromagnetic Kitaev coupling is also supported by a detailed analysis of the field-dependent magnetization. Using exact diagonalization and density-matrix renormalization group techniques for extended Kitaev-Heisenberg spin Hamiltonians, we find indications for a transition from zigzag order to a gapped spin liquid when applying magnetic field. Our results offer a unified picture on recent magnetic and spectroscopic measurements on this material and open new perspectives on the prospect of realizing quantum spin liquids in d 5 halides and oxides in general.
Compounds of transition metal ions with strong spin-orbit coupling recently attracted attention due to the possibility to host frustrated bond-dependent anisotropic magnetic interactions. In general, such interactions lead to complex phase diagrams that may include exotic phases, e.g., the Kitaev spin liquid. Here we report on our comprehensive analysis of the global phase diagram of the extended Kitaev-Heisenberg model relevant to honeycomb lattice compounds Na2IrO3{\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}Na2​IrO3​ and $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$. We have utilized recently developed method based on spin coherent states that enabled us to resolve arbitrary spin patterns in the cluster ground states obtained by exact diagonalization. Global trends in the phase diagram are understood in combination with the analytical mappings of the Hamiltonian that uncover peculiar links to known models---Heisenberg, Ising, Kitaev, or compass models on the honeycomb lattice---or reveal entire manifolds of exact fluctuation-free ground states. Finally, our study can serve as a methodological example that can be applied to other spin models with complex bond-dependent non-Heisenberg interactions.
Motivated by the recent synthesis of two insulating Li2IrO3{\mathrm{Li}}_{2}{\mathrm{IrO}}_{3}Li2​IrO3​ polymorphs, where Ir4+{\mathrm{Ir}}^{4+}Ir4+ Seff=1/2{S}_{\mathrm{eff}}=1/2Seff​=1/2 moments form 3D (``harmonic'') honeycomb structures with threefold coordination, we study magnetic Hamiltonians on the resulting $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Li}}_{2}{\mathrm{IrO}}_{3}$ hyperhoneycomb lattice and $\ensuremath{\gamma}\text{\ensuremath{-}}{\mathrm{Li}}_{2}{\mathrm{IrO}}_{3}$ stripyhoneycomb lattice. Experimentally measured magnetic susceptibilities suggest that Kitaev interactions, predicted for the ideal ${90}^{\ensuremath{\circ}}$ Ir-O-Ir bonds, are sizable in these materials. We first consider pure Kitaev interactions, which lead to an exactly soluble 3D quantum spin liquid (QSL) with emergent Majorana fermions and Z2{\mathrm{Z}}_{2}Z2​ flux loops. Unlike 2D QSLs, the 3D QSL is stable to finite temperature, with ${T}_{c}\ensuremath{\approx}|K|/100$. On including Heisenberg couplings, exact solubility is lost. However, by noting that the shortest closed loop $\ensuremath{\ell}$ is relatively large in these structures, we construct an $\ensuremath{\ell}\ensuremath{\rightarrow}\ensuremath{\infty}$ approximation by defining the model on the Bethe lattice. The phase diagram of the Kitaev-Heisenberg model on this lattice is obtained directly in the thermodynamic limit, using tensor network states and the infinite-system time-evolving-block-decimation (iTEBD) algorithm. Both magnetically ordered and gapped QSL phases are found, the latter being identified by an entanglement fingerprint.
We provide an exact study of dynamical correlations for the quantum spin-orbital liquid phases of an SU(2)-symmetric Kitaev honeycomb lattice model. We show that the spin dynamics in this Kugel-Khomskii type model is exactly the density-density correlation function of S=1 fermionic magnons, which could be probed in resonant inelastic x-ray scattering experiments. We predict the characteristic signatures of spin-orbital fractionalization in inelastic scattering experiments and compare them to the ones of the spin-anisotropic Kitaev honeycomb spin liquid. In particular, the resonant inelastic x-ray scattering response shows a characteristic momentum dependence directly related to the dispersion of fermionic excitations. The neutron scattering cross section displays a mixed response of fermionic magnons as well as spin-orbital excitations. The latter has a bandwidth of broad excitations and a vison gap that is three times larger than that of the spin-1=2 Kitaev model.
We present an augmented parton mean-field theory which (i) reproduces the exact ground state, spectrum, and dynamics of the quantum spin-liquid phase of Kitaev's honeycomb model, and (ii) is amenable to the inclusion of integrability breaking terms, allowing a perturbation theory from a controlled starting point. Thus, we exemplarily study dynamical spin correlations of the honeycomb Kitaev quantum spin liquid within the $K\ensuremath{-}J\ensuremath{-}\mathrm{\ensuremath{\Gamma}}$ model, which includes Heisenberg and symmetric-anisotropic (pseudodipolar) interactions. This allows us to trace changes of the correlations in the regime of slowly moving fluxes, where the theory captures the dominant deviations when integrability is lost. These include an asymmetric shift together with a broadening of the dominant peak in the response as a function of frequency, the generation of further-neighbor correlations and their structure in real and spin space, and a resulting loss of an approximate rotational symmetry of the structure factor in reciprocal space. We discuss the limitations of this approach and also view the neutron-scattering experiments on the putative proximate quantum spin-liquid material $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ in the light of the results from this extended parton theory.