arXiv:2502.08698 · Physical review. B./Physical review. B

Rethinking α − RuCl 3 : Parameters, models, and phase diagram

Marius Möller, P. A. Maksimov, Shengtao Jiang, Steven R. White, Roser Valentí, A. L. Chernyshev

Published Aug 13, 2025• 15 citations

Abstract

$\ensuremath{\alpha}$-RuCl${}_{3}$ promises to harbor an exotic Kitaev spin liquid that could shape the fortunes of the fields of quantum materials and quantum computing. Here, the authors offer a Rosetta Stone for this and other anisotropic-exchange Kitaev materials. The key message is the approach for constraining parameters of their low-energy spin models using experimental observables. This work clears the path to a consistent interpretation of experiments and gives important new insights into the fundamental properties of quantum magnets with spin-orbit coupling.

DOI: 10.1103/hflp-41lj

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Dynamical and thermal magnetic properties of the Kitaev spin liquid candidate α-RuCl3

Pontus Laurell, Satoshi Okamoto

Abstract What is the correct low-energy spin Hamiltonian description of $$\alpha$$ α -RuCl $$_{3}$$ 3 ? The material is a promising Kitaev spin liquid candidate, but is also known to order magnetically, the description of which necessitates additional interaction terms. The nature of these interactions, their magnitudes and even signs, remain an open question. In this work we systematically investigate dynamical and thermodynamic magnetic properties of proposed effective Hamiltonians. We calculate zero-temperature inelastic neutron scattering (INS) intensities using exact diagonalization, and magnetic specific heat using a thermal pure quantum states method. We find that no single current model satisfactorily explains all observed phenomena of $$\alpha$$ α -RuCl $$_{3}$$ 3 . In particular, we find that Hamiltonians derived from first principles can capture the experimentally observed high-temperature peak in the magnetic specific heat, while overestimating the magnon energy at the zone center. In contrast, other models reproduce important features of the INS data, but do not adequately describe the magnetic specific heat. To address this discrepancy we propose a modified ab initio model that is consistent with both magnetic specific heat and low-energy features of INS data.

arXiv:1906.07579npj Quantum MaterialsJan 10, 202092 citations

Kitaev exchange and field-induced quantum spin-liquid states in honeycomb α-RuCl3

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

Scientific ReportsNov 30, 2016275 citations

Probing α−RuCl3 Beyond Magnetic Order: Effects of Temperature and Magnetic Field

Stephen M. Winter, Kira Riedl, David A. S. Kaib +2 more

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Quantum spin liquid phases in Kitaev materials

Po-Hao Chou, Chung‐Yu Mou, Chung‐Hou Chung +1 more

arXiv:2503.10226npj Quantum MaterialsAug 16, 20254 citations

NMR Evidence for Majorana Gap in the Kitaev Quantum Spin Liquid

Junya Yamamoto, Yuya Nagai, Takaaki Jin-no +6 more

International Conference on Low Temperature Physics (LT)May 22, 20230 citations

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

Han Li, Wei Li, Gang Su

arXiv:2211.01360Physical review. B./Physical review. BMar 10, 20235 citations

arXiv:2502.08698 · Physical review. B./Physical review. B

Rethinking α − RuCl 3 : Parameters, models, and phase diagram

Marius Möller, P. A. Maksimov, Shengtao Jiang, Steven R. White, Roser Valentí, A. L. Chernyshev

Published Aug 13, 2025• 15 citations

arXiv HTML PDF

Abstract

\ensuremath{\alpha}

-RuCl

{}_{3}

promises to harbor an exotic Kitaev spin liquid that could shape the fortunes of the fields of quantum materials and quantum computing. Here, the authors offer a Rosetta Stone for this and other anisotropic-exchange Kitaev materials. The key message is the approach for constraining parameters of their low-energy spin models using experimental observables. This work clears the path to a consistent interpretation of experiments and gives important new insights into the fundamental properties of quantum magnets with spin-orbit coupling.

DOI: 10.1103/hflp-41lj

Related papers

Dynamical and thermal magnetic properties of the Kitaev spin liquid candidate α-RuCl3

Pontus Laurell, Satoshi Okamoto

Abstract What is the correct low-energy spin Hamiltonian description of $\alpha$ α -RuCl $_{3}$ 3 ? The material is a promising Kitaev spin liquid candidate, but is also known to order magnetically, the description of which necessitates additional interaction terms. The nature of these interactions, their magnitudes and even signs, remain an open question. In this work we systematically investigate dynamical and thermodynamic magnetic properties of proposed effective Hamiltonians. We calculate zero-temperature inelastic neutron scattering (INS) intensities using exact diagonalization, and magnetic specific heat using a thermal pure quantum states method. We find that no single current model satisfactorily explains all observed phenomena of $\alpha$ α -RuCl $_{3}$ 3 . In particular, we find that Hamiltonians derived from first principles can capture the experimentally observed high-temperature peak in the magnetic specific heat, while overestimating the magnon energy at the zone center. In contrast, other models reproduce important features of the INS data, but do not adequately describe the magnetic specific heat. To address this discrepancy we propose a modified ab initio model that is consistent with both magnetic specific heat and low-energy features of INS data.Abstract What is the correct low-energy spin Hamiltonian description of $$\alpha$$ α -RuCl $$_{3}$$ 3 ? The material is a promising Kitaev spin liquid candidate, but is also known to order magnetically, the description of which necessitates additional interaction terms. The nature of these interactions, their magnitudes and even signs, remain an open question. In this work we systematically investigate dynamical and thermodynamic magnetic properties of proposed effective Hamiltonians. We calculate zero-temperature inelastic neutron scattering (INS) intensities using exact diagonalization, and magnetic specific heat using a thermal pure quantum states method. We find that no single current model satisfactorily explains all observed phenomena of $$\alpha$$ α -RuCl $$_{3}$$ 3 . In particular, we find that Hamiltonians derived from first principles can capture the experimentally observed high-temperature peak in the magnetic specific heat, while overestimating the magnon energy at the zone center. In contrast, other models reproduce important features of the INS data, but do not adequately describe the magnetic specific heat. To address this discrepancy we propose a modified ab initio model that is consistent with both magnetic specific heat and low-energy features of INS data.

arXiv:1906.07579npj Quantum MaterialsJan 10, 202092 citations

Kitaev exchange and field-induced quantum spin-liquid states in honeycomb α-RuCl3

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

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.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.

Scientific ReportsNov 30, 2016275 citations

Probing α−RuCl3 Beyond Magnetic Order: Effects of Temperature and Magnetic Field

Stephen M. Winter, Kira Riedl, David A. S. Kaib +2 more

Recent studies have brought α-RuCl_{3} to the forefront of experimental searches for materials realizing Kitaev spin-liquid physics. This material exhibits strongly anisotropic exchange interactions afforded by the spin-orbit coupling of the 4d Ru centers. We investigate the dynamical response at finite temperature and magnetic field for a realistic model of the magnetic interactions in α-RuCl_{3}. These regimes are thought to host unconventional paramagnetic states that emerge from the suppression of magnetic order. Using exact diagonalization calculations of the quantum model complemented by semiclassical analysis, we find a very rich evolution of the spin dynamics as the applied field suppresses the zigzag order and stabilizes a quantum paramagnetic state that is adiabatically connected to the fully polarized state at high fields. At finite temperature, we observe large redistributions of spectral weight that can be attributed to the anisotropic frustration of the model. These results are compared to recent experiments and provide a road map for further studies of these regimes.Recent studies have brought α-RuCl_{3} to the forefront of experimental searches for materials realizing Kitaev spin-liquid physics. This material exhibits strongly anisotropic exchange interactions afforded by the spin-orbit coupling of the 4d Ru centers. We investigate the dynamical response at finite temperature and magnetic field for a realistic model of the magnetic interactions in α-RuCl_{3}. These regimes are thought to host unconventional paramagnetic states that emerge from the suppression of magnetic order. Using exact diagonalization calculations of the quantum model complemented by semiclassical analysis, we find a very rich evolution of the spin dynamics as the applied field suppresses the zigzag order and stabilizes a quantum paramagnetic state that is adiabatically connected to the fully polarized state at high fields. At finite temperature, we observe large redistributions of spectral weight that can be attributed to the anisotropic frustration of the model. These results are compared to recent experiments and provide a road map for further studies of these regimes.

arXiv:1707.08144Physical Review LettersFeb 15, 2018155 citations

Quantum spin liquid phases in Kitaev materials

Po-Hao Chou, Chung‐Yu Mou, Chung‐Hou Chung +1 more

We develop a gauge-invariant renormalized mean-field theory (RMFT) to reliably find the quantum spin liquid (QSL) states and their field response for realistic Kitaev materials under strong magnetic fields and described by the generalized Kitaev J-K-Γ- ${\Gamma }^{{\prime} }$ model. Remarkably, while our RMFT reproduces previous results based on using more complicated numerical methods, it also predicts several new stable QSL states. In particular, since Kitaev spin liquid (KSL) is no longer a saddle point solution, a new exotic 2-cone state distinct from the KSL is found to describe experimental observations well, and hence should be the candidate state realized in the Kitaev material, α-RuCl3. We further explore the mechanism for the suppression of the observed thermal Hall conductivity at low temperatures within the fermionic framework, and show that the polar-angle dependence of the fermionic gap can distinguish the found 2-cone state from the KSL state in further experiments.We develop a gauge-invariant renormalized mean-field theory (RMFT) to reliably find the quantum spin liquid (QSL) states and their field response for realistic Kitaev materials under strong magnetic fields and described by the generalized Kitaev J-K-Γ- $${\Gamma }^{{\prime} }$$ model. Remarkably, while our RMFT reproduces previous results based on using more complicated numerical methods, it also predicts several new stable QSL states. In particular, since Kitaev spin liquid (KSL) is no longer a saddle point solution, a new exotic 2-cone state distinct from the KSL is found to describe experimental observations well, and hence should be the candidate state realized in the Kitaev material, α-RuCl3. We further explore the mechanism for the suppression of the observed thermal Hall conductivity at low temperatures within the fermionic framework, and show that the polar-angle dependence of the fermionic gap can distinguish the found 2-cone state from the KSL state in further experiments.

arXiv:2503.10226npj Quantum MaterialsAug 16, 20254 citations

NMR Evidence for Majorana Gap in the Kitaev Quantum Spin Liquid

Junya Yamamoto, Yuya Nagai, Takaaki Jin-no +6 more

Low-energy spin excitation can be anisotropic in the Kitaev spin liquid and evolve with magnetic field, as the Majorana fermions acquire the gap.In a candidate material α-RuCl 3 , the spin disordered phase appears under the in-plane magnetic field.We measure the in-plane anisotropy of spin excitation by 35 Cl nuclear magnetic resonance in α-RuCl 3 .The NMR spectrum maintains the three-fold rotational symmetry at low temperatures, as expected for the R 3 lattice.We compare the result with the numerical calculation of the 35 Cl NMR frequency as a function of magnetic field strength and direction.Low-energy spin excitation can be anisotropic in the Kitaev spin liquid and evolve with magnetic field, as the Majorana fermions acquire the gap.In a candidate material α-RuCl 3 , the spin disordered phase appears under the in-plane magnetic field.We measure the in-plane anisotropy of spin excitation by 35 Cl nuclear magnetic resonance in α-RuCl 3 .The NMR spectrum maintains the three-fold rotational symmetry at low temperatures, as expected for the R 3 lattice.We compare the result with the numerical calculation of the 35 Cl NMR frequency as a function of magnetic field strength and direction.

International Conference on Low Temperature Physics (LT)May 22, 20230 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.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:2211.01360Physical review. B./Physical review. BMar 10, 20235 citations

\ensuremath{\alpha}

-RuCl

{}_{3}

Abstract What is the correct low-energy spin Hamiltonian description of

\alpha

α -RuCl

_{3}

3 ? The material is a promising Kitaev spin liquid candidate, but is also known to order magnetically, the description of which necessitates additional interaction terms. The nature of these interactions, their magnitudes and even signs, remain an open question. In this work we systematically investigate dynamical and thermodynamic magnetic properties of proposed effective Hamiltonians. We calculate zero-temperature inelastic neutron scattering (INS) intensities using exact diagonalization, and magnetic specific heat using a thermal pure quantum states method. We find that no single current model satisfactorily explains all observed phenomena of

\alpha

α -RuCl

_{3}

3 . In particular, we find that Hamiltonians derived from first principles can capture the experimentally observed high-temperature peak in the magnetic specific heat, while overestimating the magnon energy at the zone center. In contrast, other models reproduce important features of the INS data, but do not adequately describe the magnetic specific heat. To address this discrepancy we propose a modified ab initio model that is consistent with both magnetic specific heat and low-energy features of INS data.

{\Gamma }^{{\prime} }

model. Remarkably, while our RMFT reproduces previous results based on using more complicated numerical methods, it also predicts several new stable QSL states. In particular, since Kitaev spin liquid (KSL) is no longer a saddle point solution, a new exotic 2-cone state distinct from the KSL is found to describe experimental observations well, and hence should be the candidate state realized in the Kitaev material, α-RuCl3. We further explore the mechanism for the suppression of the observed thermal Hall conductivity at low temperatures within the fermionic framework, and show that the polar-angle dependence of the fermionic gap can distinguish the found 2-cone state from the KSL state in further experiments.

{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.