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:1902.07451 · Physical review. B./Physical review. B

Kitaev-like honeycomb magnets: Global phase behavior and emergent effective models

Juraj Rusnačko, Dorota Gotfryd, Jiří Chaloupka

Published Feb 19, 2019• 55 citations
arXivHTMLPDF

Abstract

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 ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$ 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.

DOI
10.1103/physrevb.99.064425

Related papers

Heisenberg-Kitaev model in a magnetic field: 1 / S expansion

Pedro M. Cônsoli, Lukas Janssen, Matthias Vojta C +1 more

The exact solution of Kitaev's spin-$1/2$ honeycomb spin-liquid model has sparked an intense search for Mott insulators hosting bond-dependent Kitaev interactions, of which ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$ and $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Ru}{\mathrm{Cl}}_{3}$ are prime examples. Subsequently, it has been proposed that also spin-1 and spin-$3/2$ analogs of Kitaev interactions may occur in materials with strong spin-orbit coupling. As a minimal model to describe these Kitaev materials, we study the Heisenberg-Kitaev Hamiltonian in a consistent $1/S$ expansion, with $S$ being the spin size. We present a comprehensive study of this model in the presence of an external magnetic field applied along two different directions, [001] and [111], for which an intricate classical phase diagram has been reported. In both settings, we employ spin-wave theory in a number of ordered phases to compute phase boundaries at the next-to-leading order in $1/S$ and show that quantum corrections substantially modify the classical phase diagram. More broadly, our work presents a consistent route to investigate the leading quantum corrections in spin models that break spin-rotational symmetry.

arXiv:2007.03717•Physical review. B./Physical review. B•Oct 22, 2020•47 citations

Global Phase Diagram of the Extended Kitaev-Heisenberg Model on Honeycomb Lattice

Jie Lou, Long Liang, Yue Yu +1 more

We study the extended Kitaev-Heisenberg (EKH) quantum spin model by adding bond-dependent off-diagonal Heisenberg term into the original KH model, which was recently proposed to describe the honeycomb Iridates. A rigorous mathematical mapping of spin operators reveals the intrinsic symmetry of the model Hamiltonian. By employing an unbiased numerical entanglement renormalization method based on tensor network ansatz, we obtain the global phase diagram containing eight distinct quantum phases. By using the dual mapping of spin operators, each of the individual magnetic phase in the global phase diagram can be clearly understood. At last, we show that a valence solid state emerges as the ground state in the quadro-critical region where multiple magnetic phases compete most intensively.

arXiv:1501.06990•Jan 28, 2015•3 citations

Kitaev-Heisenberg Model on a Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides A2IrO3

Jiří Chaloupka, George Jackeli, Giniyat Khaliullin

We derive and study a spin one-half Hamiltonian on a honeycomb lattice describing the exchange interactions between Ir4+ ions in a family of layered iridates A2IrO3 (A=Li,Na). Depending on the microscopic parameters, the Hamiltonian interpolates between the Heisenberg and exactly solvable Kitaev models. Exact diagonalization and a complementary spin-wave analysis reveal the presence of an extended spin-liquid phase near the Kitaev limit and a conventional Néel state close to the Heisenberg limit. The two phases are separated by an unusual stripy antiferromagnetic state, which is the exact ground state of the model at the midpoint between two limits.

arXiv:1004.2964•Physical Review Letters•Jul 9, 2010•1,055 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

Can we realize Kitaev quantum spin liquids in the $J_\text{eff}=1/2$ honeycomb cobaltates?

Shreya Das, Sreekar Voleti, Tanusri Saha‐Dasgupta +1 more

The quest for Kitaev quantum spin liquids has led to great interest in honeycomb quantum magnets with strong spin-orbit coupling. It has been recently proposed that even Mott insulators with $3d$ transition metal ions, having nominally weak spin-orbit coupling, can realize such exotic physics. Motivated by this, we study the rhombohedral honeycomb cobaltates CoTiO$_3$, BaCo$_2$(PO$_4$)$_2$, and BaCo$_2$(AsO$_4$)$_2$, using $\textit{ab initio}$ density functional theory, which takes into account realistic crystal field distortions and chemical information, in conjunction with exact diagonalization numerics. We show that these Co$^{2+}$ magnets host $j_\text{eff}=1/2$ local moments with highly anisotropic $g$-factors, and we extract their full spin Hamiltonians including longer-range and anisotropic exchange couplings. For CoTiO$_3$, we find a nearest-neighbor easy-plane ferromagnetic $XXZ$ model with additional bond-dependent anisotropies and interlayer exchange, which supports three-dimensional (3D) Dirac nodal line magnons. In contrast, for BaCo$_2$(PO$_4$)$_2$ and BaCo$_2$(AsO$_4$)$_2$, we find a strongly suppressed interlayer coupling, and significant frustration from additional third-neighbor antiferromagnetic exchange mediated by P/As. Such bond-anisotropic $J_1$-$J_3$ spin models can support collinear zig-zag or coplanar spiral ground states; we discuss their dynamical spin correlations which reveal a gapped Goldstone mode, and argue that the effective parameters of these pseudospin-$1/2$ models may be strongly renormalized by coupling to a low energy spin-exciton. Our results call for re-examining proposals for realizing Kitaev spin liquids in the honeycomb cobaltates.

arXiv:2106.11982•Jun 22, 2021•0 citations

Spin interaction and magnetism in cobaltate Kitaev candidate materials: An ab initio and model Hamiltonian approach

Shishir Kumar Pandey, Ji Feng

In the quest for materials hosting Kitaev spin liquids, much of the efforts have been focused on the fourth- and fifth-row transition metal compounds, which are spin-orbit coupling--assisted Mott insulators. Here we study the structural and magnetic properties of $3d$ transition metal oxides, ${\mathrm{Na}}_{2}{\mathrm{Co}}_{2}{\mathrm{TeO}}_{6}$ and ${\mathrm{Na}}_{3}{\mathrm{Co}}_{2}{\mathrm{SbO}}_{6}$. The partial occupancy of sodium in former compound is addressed using a cluster expansion, and a honeycomb lattice of sodiums is found to be energetically favored. Starting from the ab initio band structures, a many-body second-order perturbation theory leads to a pseudospin-$\frac{1}{2}$ Hamiltonian with estimated magnetic interactions. We show that the experimentally observed zigzag magnetic state is stabilized only when the first-neighbor Kitaev coupling dominates over the Heisenberg term, both of which are highly suppressed due to presence of ${e}_{g}$ orbitals. A third-neighbor Heisenberg interaction is found dominant in both these compounds. We also present a phase diagram for ${\mathrm{Na}}_{2}{\mathrm{Co}}_{2}{\mathrm{TeO}}_{6}$ by varying the electron-electron and spin-orbit interactions. The computed spin excitation spectra are found to capture essential features of recent experimental magnon spectrum, lending support to our results.

arXiv:2205.03836•Physical review. B./Physical review. B•Nov 14, 2022•18 citations
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 \ensuremathα\ensuremath−RuCl3\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}\ensuremathα\ensuremath−RuCl3​. 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.
The exact solution of Kitaev's spin-1/21/21/2 honeycomb spin-liquid model has sparked an intense search for Mott insulators hosting bond-dependent Kitaev interactions, of which Na2IrO3{\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}Na2​IrO3​ and $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Ru}{\mathrm{Cl}}_{3}$ are prime examples. Subsequently, it has been proposed that also spin-1 and spin-3/23/23/2 analogs of Kitaev interactions may occur in materials with strong spin-orbit coupling. As a minimal model to describe these Kitaev materials, we study the Heisenberg-Kitaev Hamiltonian in a consistent 1/S1/S1/S expansion, with SSS being the spin size. We present a comprehensive study of this model in the presence of an external magnetic field applied along two different directions, [001] and [111], for which an intricate classical phase diagram has been reported. In both settings, we employ spin-wave theory in a number of ordered phases to compute phase boundaries at the next-to-leading order in 1/S1/S1/S and show that quantum corrections substantially modify the classical phase diagram. More broadly, our work presents a consistent route to investigate the leading quantum corrections in spin models that break spin-rotational symmetry.
We study the extended Kitaev-Heisenberg (EKH) quantum spin model by adding bond-dependent off-diagonal Heisenberg term into the original KH model, which was recently proposed to describe the honeycomb Iridates. A rigorous mathematical mapping of spin operators reveals the intrinsic symmetry of the model Hamiltonian. By employing an unbiased numerical entanglement renormalization method based on tensor network ansatz, we obtain the global phase diagram containing eight distinct quantum phases. By using the dual mapping of spin operators, each of the individual magnetic phase in the global phase diagram can be clearly understood. At last, we show that a valence solid state emerges as the ground state in the quadro-critical region where multiple magnetic phases compete most intensively.
We derive and study a spin one-half Hamiltonian on a honeycomb lattice describing the exchange interactions between Ir4+ ions in a family of layered iridates A2IrO3 (A=Li,Na). Depending on the microscopic parameters, the Hamiltonian interpolates between the Heisenberg and exactly solvable Kitaev models. Exact diagonalization and a complementary spin-wave analysis reveal the presence of an extended spin-liquid phase near the Kitaev limit and a conventional Néel state close to the Heisenberg limit. The two phases are separated by an unusual stripy antiferromagnetic state, which is the exact ground state of the model at the midpoint between two limits.
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.
Can we realize Kitaev quantum spin liquids in the Jeff=1/2J_\text{eff}=1/2Jeff​=1/2 honeycomb cobaltates?
The quest for Kitaev quantum spin liquids has led to great interest in honeycomb quantum magnets with strong spin-orbit coupling. It has been recently proposed that even Mott insulators with 3d3d3d transition metal ions, having nominally weak spin-orbit coupling, can realize such exotic physics. Motivated by this, we study the rhombohedral honeycomb cobaltates CoTiO3_33​, BaCo2_22​(PO4_44​)2_22​, and BaCo2_22​(AsO4_44​)2_22​, using ab initio\textit{ab initio}ab initio density functional theory, which takes into account realistic crystal field distortions and chemical information, in conjunction with exact diagonalization numerics. We show that these Co2+^{2+}2+ magnets host jeff=1/2j_\text{eff}=1/2jeff​=1/2 local moments with highly anisotropic ggg-factors, and we extract their full spin Hamiltonians including longer-range and anisotropic exchange couplings. For CoTiO3_33​, we find a nearest-neighbor easy-plane ferromagnetic XXZXXZXXZ model with additional bond-dependent anisotropies and interlayer exchange, which supports three-dimensional (3D) Dirac nodal line magnons. In contrast, for BaCo2_22​(PO4_44​)2_22​ and BaCo2_22​(AsO4_44​)2_22​, we find a strongly suppressed interlayer coupling, and significant frustration from additional third-neighbor antiferromagnetic exchange mediated by P/As. Such bond-anisotropic J1J_1J1​-J3J_3J3​ spin models can support collinear zig-zag or coplanar spiral ground states; we discuss their dynamical spin correlations which reveal a gapped Goldstone mode, and argue that the effective parameters of these pseudospin-1/21/21/2 models may be strongly renormalized by coupling to a low energy spin-exciton. Our results call for re-examining proposals for realizing Kitaev spin liquids in the honeycomb cobaltates.
In the quest for materials hosting Kitaev spin liquids, much of the efforts have been focused on the fourth- and fifth-row transition metal compounds, which are spin-orbit coupling--assisted Mott insulators. Here we study the structural and magnetic properties of 3d3d3d transition metal oxides, Na2Co2TeO6{\mathrm{Na}}_{2}{\mathrm{Co}}_{2}{\mathrm{TeO}}_{6}Na2​Co2​TeO6​ and Na3Co2SbO6{\mathrm{Na}}_{3}{\mathrm{Co}}_{2}{\mathrm{SbO}}_{6}Na3​Co2​SbO6​. The partial occupancy of sodium in former compound is addressed using a cluster expansion, and a honeycomb lattice of sodiums is found to be energetically favored. Starting from the ab initio band structures, a many-body second-order perturbation theory leads to a pseudospin-12\frac{1}{2}21​ Hamiltonian with estimated magnetic interactions. We show that the experimentally observed zigzag magnetic state is stabilized only when the first-neighbor Kitaev coupling dominates over the Heisenberg term, both of which are highly suppressed due to presence of eg{e}_{g}eg​ orbitals. A third-neighbor Heisenberg interaction is found dominant in both these compounds. We also present a phase diagram for Na2Co2TeO6{\mathrm{Na}}_{2}{\mathrm{Co}}_{2}{\mathrm{TeO}}_{6}Na2​Co2​TeO6​ by varying the electron-electron and spin-orbit interactions. The computed spin excitation spectra are found to capture essential features of recent experimental magnon spectrum, lending support to our results.