Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1612.00761 · Physical review. B./Physical review. B

Unveiling magnetic interactions of ruthenium trichloride via constraining direction of orbital moments: Potential routes to realize a quantum spin liquid

Yusheng Hou, Hongjun Xiang, X. G. Gong

Published Aug 7, 2017• 74 citations
arXivHTMLPDF

Abstract

Recent experiments reveal that the honeycomb ruthenium trichloride $\ensuremath{\alpha}\ensuremath{-}\mathrm{RuC}{\mathrm{l}}_{3}$ is a prime candidate of the Kitaev quantum spin liquid (QSL). However, there is no theoretical model which can properly describe its experimental dynamical response due to the lack of a full understanding of its magnetic interactions. Here, we propose a general scheme to calculate the magnetic interactions in systems (e.g., $\ensuremath{\alpha}\ensuremath{-}\mathrm{RuC}{\mathrm{l}}_{3}$) with nonnegligible orbital moments by constraining the directions of orbital moments. With this scheme, we put forward a minimal ${J}_{1}\ensuremath{-}{K}_{1}\ensuremath{-}{\mathrm{\ensuremath{\Gamma}}}_{1}\ensuremath{-}{J}_{3}\ensuremath{-}{K}_{3}$ model for $\ensuremath{\alpha}\ensuremath{-}\mathrm{RuC}{\mathrm{l}}_{3}$ and find that: (I) The third nearest neighbor (NN) antiferromagnetic Heisenberg interaction ${J}_{3}$ stabilizes the zigzag antiferromagnetic order; (II) The NN symmetric off-diagonal exchange ${\mathrm{\ensuremath{\Gamma}}}_{1}$ plays a pivotal role in determining the preferred direction of magnetic moments and generating the spin wave gap. An exact diagonalization study on this model shows that the Kitaev QSL can be realized by suppressing the NN symmetric off-diagonal exchange ${\mathrm{\ensuremath{\Gamma}}}_{1}$ and the third NN Heisenberg interaction ${J}_{3}$. Thus, we not only propose a powerful general scheme for investigating the intriguing magnetism of ${J}_{\mathrm{eff}}=1/2$ magnets, but also point out future directions for realizing the Kitaev QSL in the honeycomb ruthenium trichloride $\ensuremath{\alpha}\ensuremath{-}\mathrm{RuC}{\mathrm{l}}_{3}$.

DOI
10.1103/physrevb.96.054410

Related papers

Proximate Dirac spin liquid in the honeycomb lattice J1−J3 XXZ model: Numerical study and application to cobaltates

Anjishnu Bose, Manodip Routh, Sreekar Voleti +4 more

Recent theoretical and experimental work suggests that the honeycomb cobaltates, initially proposed as candidate Kitaev quantum magnets, are in fact described by a pseudospin-$1/2$ easy-plane spin Hamiltonian with nearest-neighbor ferromagnetic (FM) exchange ${J}_{1}$ being frustrated by antiferromagnetic third-neighbor exchange ${J}_{3}$ and weaker compass anisotropies. Using exact diagonalization and density-matrix renormalization group (DMRG) calculations, we show that this model exhibits FM order at small ${J}_{3}/{J}_{1}$ and zigzag (ZZ) order at large ${J}_{3}/{J}_{1}$, separated by an intermediate phase, which we label as $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\mathrm{SL}}$. This $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\mathrm{SL}}$ phase is shown to exhibit spin-liquid-like correlations in DMRG, although we cannot preclude weak broken symmetries, e.g., weak Ising type N\'eel order, given the limits on our explored system sizes. Using a modified parton mean field theory and variational Monte Carlo on Gutzwiller projected wave functions, we show that the optimal FM and ZZ orders as well as the intermediate $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\mathrm{SL}}$ state are proximate to a ``parent'' Dirac spin liquid (SL). This Dirac SL is shown to capture the broad continuum in the temperature and magnetic field dependent terahertz spectroscopy of ${\mathrm{BaCo}}_{2}{({\mathrm{AsO}}_{4})}_{2}$, and the reported low-temperature metallic thermal conductivity in ${\mathrm{Na}}_{2}{\mathrm{Co}}_{2}{\mathrm{TeO}}_{6}$ and ${\mathrm{BaCo}}_{2}{({\mathrm{AsO}}_{4})}_{2}$ upon incorporating disorder-induced broadening.

arXiv:2212.13271•Physical review. B./Physical review. B•Nov 16, 2023•17 citations

Clues and criteria for designing a Kitaev spin liquid revealed by thermal and spin excitations of the honeycomb iridate Na2IrO3

Youhei Yamaji, Takafumi J. Suzuki, Takuto Yamada +3 more

Contrary to the original expectation, ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$ is not a Kitaev's quantum spin liquid (QSL) but shows a zigzag-type antiferromagnetic order in experiments. Here, we propose experimental clues and criteria to measure how a material in hand is close to the Kitaev's QSL state. For this purpose, we systematically study thermal and spin excitations of a generalized Kitaev-Heisenberg model studied by Chaloupka et al., Phys. Rev. Lett. 110, 097204 (2013) and an effective ab initio Hamiltonian for ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$ proposed by Yamaji et al., Phys. Rev. Lett. 113, 107201 (2014), by employing a numerical diagonalization method. We reveal that closeness to the Kitaev's QSL is characterized by the following properties, besides trivial criteria such as reduction of magnetic ordered moments and N\'eel temperatures. (1) Two peaks in the temperature dependence of specific heat at ${T}_{\ensuremath{\ell}}$ and ${T}_{h}$ caused by the fractionalization of spin to two types of Majorana fermions. (2) In between the double peak, a prominent plateau or shoulder pinned at $\frac{R}{2}ln2$ in the temperature dependence of entropy, where $R$ is the gas constant. (3) Failure of the linear spin wave approximation at the low-lying excitations of dynamical structure factors. (4) Small ratio ${T}_{\ensuremath{\ell}}/{T}_{h}$ close to or less than 0.03. According to the proposed criteria, ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$ is categorized to a compound close to the Kitaev's QSL, and is proven to be a promising candidate for the realization of the QSL if the relevant material parameters can further be tuned by making thin film of ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$ on various substrates or applying axial pressure perpendicular to the honeycomb networks of iridium ions. Applications of these characterization to ${({\mathrm{Na}}_{1\ensuremath{-}x}{\mathrm{Li}}_{x})}_{2}{\mathrm{IrO}}_{3}$ and other related materials are also discussed.

arXiv:1601.05512•Physical review. B./Physical review. B•May 24, 2016•106 citations

Spin-orbit excitation energies, anisotropic exchange, and magnetic phases of honeycomb RuCl3

Ravi Yadav, Nikolay A. Bogdanov, Vamshi M. Katukuri +3 more

Using quantum chemistry calculations we shed fresh light on the electronic structure and magnetic properties of RuCl3, a proposed realization of the honeycomb Kitaev spin model. It is found that the nearest-neighbor Kitaev exchange K is weaker than in 5d5 Ir oxides but still larger than other effective spin couplings. The electronic-structure computations also indicate a ferromagnetic K in the halide, which is supported by a detailed analysis of the field-dependent magnetization. From exact-diagonalization calculations for extended Kitaev-Heisenberg Hamiltonians we additionally find that a transition from zigzag order to a spin-liquid ground state can be induced in RuCl3 with external magnetic field.

arXiv:1604.04755•Apr 16, 2016•104 citations

Phase diagram and spin correlations of the Kitaev-Heisenberg model: Importance of quantum effects

Dorota Gotfryd, Juraj Rusnačko, Krzysztof Wohlfeld +3 more

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.

arXiv:1608.05333•Physical review. B./Physical review. B•Jan 23, 2017•75 citations

Gapless quantum spin liquid in a honeycomb Γ magnet

Qiang Luo, Jize Zhao, Hae-Young Kee +1 more

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.

arXiv:1910.01562•npj Quantum Materials•Jun 4, 2021•38 citations

High-field quantum spin liquid transitions and angle-field phase diagram of the Kitaev magnet α−RuCl3

Han Li, Wei Li, Gang Su

The pursuit of quantum spin liquid (QSL) in the Kitaev honeycomb magnets has drawn intensive attention recently. In particular, $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ has been widely recognized as a promising candidate for the Kitaev QSL. Although the compound exhibits an antiferromagnetic order under zero field, it is believed to be endowed with fractionalized excitations and can be driven to the QSL phase by magnetic fields. Here, based on a realistic $K\text{\ensuremath{-}}J\text{\ensuremath{-}}\mathrm{\ensuremath{\Gamma}}\text{\ensuremath{-}}{\mathrm{\ensuremath{\Gamma}}}^{\ensuremath{'}}$ model for $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$, we exploit the exponential tensor renormalization group approach to explore the phase diagram of the compound under magnetic fields. We calculate the thermodynamic quantities, including the specific heat, Gr\"uneisen parameter, magnetic torque, magnetotropic susceptibility, and so on, under a magnetic field with a tilting angle $\ensuremath{\theta}$ to the ${c}^{*}$-axis perpendicular to the honeycomb plane. We find an extended QSL in the angle-field phase diagram determined with thermodynamic responses. The gapless nature of such field-induced QSL is identified from the specific heat and entropy data computed down to very low temperatures. The present study provides guidance for future high-field experiments for the QSL in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ and other candidate Kitaev magnets.

arXiv:2211.01360•Physical review. B./Physical review. B•Mar 10, 2023•5 citations
Recent experiments reveal that the honeycomb ruthenium trichloride \ensuremathα\ensuremath−RuCl3\ensuremath{\alpha}\ensuremath{-}\mathrm{RuC}{\mathrm{l}}_{3}\ensuremathα\ensuremath−RuCl3​ is a prime candidate of the Kitaev quantum spin liquid (QSL). However, there is no theoretical model which can properly describe its experimental dynamical response due to the lack of a full understanding of its magnetic interactions. Here, we propose a general scheme to calculate the magnetic interactions in systems (e.g., \ensuremathα\ensuremath−RuCl3\ensuremath{\alpha}\ensuremath{-}\mathrm{RuC}{\mathrm{l}}_{3}\ensuremathα\ensuremath−RuCl3​) with nonnegligible orbital moments by constraining the directions of orbital moments. With this scheme, we put forward a minimal J1\ensuremath−K1\ensuremath−\ensuremathΓ1\ensuremath−J3\ensuremath−K3{J}_{1}\ensuremath{-}{K}_{1}\ensuremath{-}{\mathrm{\ensuremath{\Gamma}}}_{1}\ensuremath{-}{J}_{3}\ensuremath{-}{K}_{3}J1​\ensuremath−K1​\ensuremath−\ensuremathΓ1​\ensuremath−J3​\ensuremath−K3​ model for \ensuremathα\ensuremath−RuCl3\ensuremath{\alpha}\ensuremath{-}\mathrm{RuC}{\mathrm{l}}_{3}\ensuremathα\ensuremath−RuCl3​ and find that: (I) The third nearest neighbor (NN) antiferromagnetic Heisenberg interaction J3{J}_{3}J3​ stabilizes the zigzag antiferromagnetic order; (II) The NN symmetric off-diagonal exchange \ensuremathΓ1{\mathrm{\ensuremath{\Gamma}}}_{1}\ensuremathΓ1​ plays a pivotal role in determining the preferred direction of magnetic moments and generating the spin wave gap. An exact diagonalization study on this model shows that the Kitaev QSL can be realized by suppressing the NN symmetric off-diagonal exchange \ensuremathΓ1{\mathrm{\ensuremath{\Gamma}}}_{1}\ensuremathΓ1​ and the third NN Heisenberg interaction J3{J}_{3}J3​. Thus, we not only propose a powerful general scheme for investigating the intriguing magnetism of Jeff=1/2{J}_{\mathrm{eff}}=1/2Jeff​=1/2 magnets, but also point out future directions for realizing the Kitaev QSL in the honeycomb ruthenium trichloride \ensuremathα\ensuremath−RuCl3\ensuremath{\alpha}\ensuremath{-}\mathrm{RuC}{\mathrm{l}}_{3}\ensuremathα\ensuremath−RuCl3​.
Recent theoretical and experimental work suggests that the honeycomb cobaltates, initially proposed as candidate Kitaev quantum magnets, are in fact described by a pseudospin-1/21/21/2 easy-plane spin Hamiltonian with nearest-neighbor ferromagnetic (FM) exchange J1{J}_{1}J1​ being frustrated by antiferromagnetic third-neighbor exchange J3{J}_{3}J3​ and weaker compass anisotropies. Using exact diagonalization and density-matrix renormalization group (DMRG) calculations, we show that this model exhibits FM order at small J3/J1{J}_{3}/{J}_{1}J3​/J1​ and zigzag (ZZ) order at large J3/J1{J}_{3}/{J}_{1}J3​/J1​, separated by an intermediate phase, which we label as $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\mathrm{SL}}$. This $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\mathrm{SL}}$ phase is shown to exhibit spin-liquid-like correlations in DMRG, although we cannot preclude weak broken symmetries, e.g., weak Ising type N\'eel order, given the limits on our explored system sizes. Using a modified parton mean field theory and variational Monte Carlo on Gutzwiller projected wave functions, we show that the optimal FM and ZZ orders as well as the intermediate $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\mathrm{SL}}$ state are proximate to a ``parent'' Dirac spin liquid (SL). This Dirac SL is shown to capture the broad continuum in the temperature and magnetic field dependent terahertz spectroscopy of BaCo2(AsO4)2{\mathrm{BaCo}}_{2}{({\mathrm{AsO}}_{4})}_{2}BaCo2​(AsO4​)2​, and the reported low-temperature metallic thermal conductivity in Na2Co2TeO6{\mathrm{Na}}_{2}{\mathrm{Co}}_{2}{\mathrm{TeO}}_{6}Na2​Co2​TeO6​ and BaCo2(AsO4)2{\mathrm{BaCo}}_{2}{({\mathrm{AsO}}_{4})}_{2}BaCo2​(AsO4​)2​ upon incorporating disorder-induced broadening.
Contrary to the original expectation, Na2IrO3{\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}Na2​IrO3​ is not a Kitaev's quantum spin liquid (QSL) but shows a zigzag-type antiferromagnetic order in experiments. Here, we propose experimental clues and criteria to measure how a material in hand is close to the Kitaev's QSL state. For this purpose, we systematically study thermal and spin excitations of a generalized Kitaev-Heisenberg model studied by Chaloupka et al., Phys. Rev. Lett. 110, 097204 (2013) and an effective ab initio Hamiltonian for Na2IrO3{\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}Na2​IrO3​ proposed by Yamaji et al., Phys. Rev. Lett. 113, 107201 (2014), by employing a numerical diagonalization method. We reveal that closeness to the Kitaev's QSL is characterized by the following properties, besides trivial criteria such as reduction of magnetic ordered moments and N\'eel temperatures. (1) Two peaks in the temperature dependence of specific heat at ${T}_{\ensuremath{\ell}}$ and Th{T}_{h}Th​ caused by the fractionalization of spin to two types of Majorana fermions. (2) In between the double peak, a prominent plateau or shoulder pinned at R2ln2\frac{R}{2}ln22R​ln2 in the temperature dependence of entropy, where RRR is the gas constant. (3) Failure of the linear spin wave approximation at the low-lying excitations of dynamical structure factors. (4) Small ratio ${T}_{\ensuremath{\ell}}/{T}_{h}$ close to or less than 0.03. According to the proposed criteria, Na2IrO3{\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}Na2​IrO3​ is categorized to a compound close to the Kitaev's QSL, and is proven to be a promising candidate for the realization of the QSL if the relevant material parameters can further be tuned by making thin film of Na2IrO3{\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}Na2​IrO3​ on various substrates or applying axial pressure perpendicular to the honeycomb networks of iridium ions. Applications of these characterization to ${({\mathrm{Na}}_{1\ensuremath{-}x}{\mathrm{Li}}_{x})}_{2}{\mathrm{IrO}}_{3}$ and other related materials are also discussed.
Using quantum chemistry calculations we shed fresh light on the electronic structure and magnetic properties of RuCl3, a proposed realization of the honeycomb Kitaev spin model. It is found that the nearest-neighbor Kitaev exchange K is weaker than in 5d5 Ir oxides but still larger than other effective spin couplings. The electronic-structure computations also indicate a ferromagnetic K in the halide, which is supported by a detailed analysis of the field-dependent magnetization. From exact-diagonalization calculations for extended Kitaev-Heisenberg Hamiltonians we additionally find that a transition from zigzag order to a spin-liquid ground state can be induced in RuCl3 with external magnetic field.
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.
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.
The pursuit of quantum spin liquid (QSL) in the Kitaev honeycomb magnets has drawn intensive attention recently. In particular, $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ has been widely recognized as a promising candidate for the Kitaev QSL. Although the compound exhibits an antiferromagnetic order under zero field, it is believed to be endowed with fractionalized excitations and can be driven to the QSL phase by magnetic fields. Here, based on a realistic $K\text{\ensuremath{-}}J\text{\ensuremath{-}}\mathrm{\ensuremath{\Gamma}}\text{\ensuremath{-}}{\mathrm{\ensuremath{\Gamma}}}^{\ensuremath{'}}$ model for $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$, we exploit the exponential tensor renormalization group approach to explore the phase diagram of the compound under magnetic fields. We calculate the thermodynamic quantities, including the specific heat, Gr\"uneisen parameter, magnetic torque, magnetotropic susceptibility, and so on, under a magnetic field with a tilting angle $\ensuremath{\theta}$ to the c∗{c}^{*}c∗-axis perpendicular to the honeycomb plane. We find an extended QSL in the angle-field phase diagram determined with thermodynamic responses. The gapless nature of such field-induced QSL is identified from the specific heat and entropy data computed down to very low temperatures. The present study provides guidance for future high-field experiments for the QSL in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ and other candidate Kitaev magnets.