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Physical review. B./Physical review. B

Ferrimagnetic Kitaev spin liquids in mixed spin- 1 2 and spin- 3 2 honeycomb magnets

W. M. H. Natori, Yang Yang, Hui-Ke Jin, Johannes Knolle, Natalia Borisovna Perkins

Published Jun 4, 2025• 1 citation
Publisher

Abstract

We explore the phase diagram of a mixed-spin Kitaev model, where spin-1/2 and spin-3/2 ions form a staggered pattern on a honeycomb lattice. Enabled by an exact mapping of local conserved flux operators onto ${Z}_{2}$ gauge fields, we perform a parton mean-field theory for the model with a single-ion anisotropy. The phase diagram contains four types of quantum spin liquids distinguished by quadrupolar parameters. These analytical results are quantitatively confirmed by state-of-the-art DMRG simulations. We also explore the potential experimental realization of the mixed-spin Kitaev model in materials such as ${\mathrm{Zr}}_{0.5}{\mathrm{Ru}}_{0.5}{\mathrm{Cl}}_{3}$. By developing a superexchange theory specifically for this mixed-spin system, we identify the conditions under which dominant Kitaev-like interactions emerge. Our findings highlight the importance of spin-orbital couplings and quadrupolar order parameters in stabilizing exotic phases, providing a foundation for exploring mixed-spin Kitaev magnets.

DOI
10.1103/physrevb.111.214411

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We explore the phase diagram of a mixed-spin Kitaev model, where spin-1/2 and spin-3/2 ions form a staggered pattern on a honeycomb lattice. Enabled by an exact mapping of local conserved flux operators onto Z2{Z}_{2}Z2​ gauge fields, we perform a parton mean-field theory for the model with a single-ion anisotropy. The phase diagram contains four types of quantum spin liquids distinguished by quadrupolar parameters. These analytical results are quantitatively confirmed by state-of-the-art DMRG simulations. We also explore the potential experimental realization of the mixed-spin Kitaev model in materials such as Zr0.5Ru0.5Cl3{\mathrm{Zr}}_{0.5}{\mathrm{Ru}}_{0.5}{\mathrm{Cl}}_{3}Zr0.5​Ru0.5​Cl3​. By developing a superexchange theory specifically for this mixed-spin system, we identify the conditions under which dominant Kitaev-like interactions emerge. Our findings highlight the importance of spin-orbital couplings and quadrupolar order parameters in stabilizing exotic phases, providing a foundation for exploring mixed-spin Kitaev magnets.
We explore the potential experimental realization of the mixed-spin Kitaev model in materials such as Zr0.5_{0.5}0.5​Ru0.5_{0.5}0.5​Cl3_33​, where spin-1/2 and spin-3/2 ions occupy distinct sublattices of a honeycomb lattice. By developing a superexchange theory specifically for this mixed-spin system, we identify the conditions under which dominant Kitaev-like interactions emerge. Focusing on the limiting case of pure Kitaev coupling with single-ion anisotropy, we employ a combination of superexchange theory, parton mean-field theory, and density matrix renormalization group (DMRG) simulations. We establish a comprehensive ground-state phase diagram identifying four distinct quantum spin liquid phases. Our findings highlight the importance of spin-orbital couplings and quadrupolar order parameters in stabilizing exotic phases, providing a foundation for exploring mixed-spin Kitaev magnets.
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.
Abstract The S=3/2 Kitaev honeycomb model (KHM) is a quantum spin liquid (QSL) state coupled to a static Z2 gauge field. Employing an SO(6) Majorana representation of spin3/2’s, we find an exact representation of the conserved plaquette fluxes in terms of static Z2 gauge fields akin to the S=1/2 KHM which enables us to treat the remaining interacting matter fermion sector in a parton mean-field theory. We uncover a ground-state phase diagram consisting of gapped and gapless QSLs. Our parton description is in quantitative agreement with numerical simulations, and is furthermore corroborated by the addition of a [001] single ion anisotropy (SIA) which continuously connects the gapless Dirac QSL of our model with that of the S=1/2 KHM. In the presence of a weak [111] SIA, we discuss an emergent chiral QSL within a perturbation theory.
In the field of quantum magnetism, the exactly solvable Kitaev honeycomb model serves as a paradigm for the fractionalization of spin degrees of freedom and the formation of [Formula: see text] quantum spin liquids. An intense experimental search has led to the discovery of a number of spin-orbit entangled Mott insulators that realize its characteristic bond-directional interactions and, in the presence of magnetic fields, exhibit no indications of long-range order. Here, we map out the complete phase diagram of the Kitaev model in tilted magnetic fields and report the emergence of a distinct gapless quantum spin liquid at intermediate field strengths. Analyzing a number of static, dynamical, and finite temperature quantities using numerical exact diagonalization techniques, we find strong evidence that this phase exhibits gapless fermions coupled to a massless U(1) gauge field. We discuss its stability in the presence of perturbations that naturally arise in spin-orbit entangled candidate materials.
The Kitaev model, which hosts a quantum spin liquid (QSL) in the ground state, was originally defined on a two-dimensional honeycomb lattice, but can be straightforwardly extended to any tricoordinate lattices in any spatial dimensions. In particular, the three-dimensional (3D) extensions are of interest as a realization of 3D QSLs, and some materials like βββ-Li2_{2}2​IrO3_{3}3​, γγγ-Li2_22​IrO3_33​, and βββ-ZnIrO3_{3}3​ were proposed for the candidates. However, the phase diagrams of the models for those candidates have not been fully elucidated, mainly due to the limitation of numerical methods for 3D frustrated quantum spin systems. Here we study the Kitaev-Heisenberg model defined on a 3D hyperhoneycomb lattice, by using the pseudofermion functional renormalization group method. We show that the ground-state phase diagram contains the QSL phases in the vicinities of the pristine ferromagnetic and antiferromagnetic Kitaev models, in addition to four magnetically ordered phases, similar to the two-dimensional honeycomb case. Our results respect the four-sublattice symmetry inherent in the model, which was violated in the previous study. Moreover, we also show how the phase diagram changes with the anisotropy in the interactions. The results provide a reference for the search of the hyperhoneycomb Kitaev materials.
The S=32S=\frac{3}{2}S=23​ Kitaev honeycomb model (KHM) is unique among the spin-SSS Kitaev models due to a massive ground-state quasidegeneracy that hampered previous numerical and analytical studies. In a recent work [Jin et al., Nat. Commun. 13, 3813 (2022)], we showed how an SO(6) Majorana parton mean-field theory of the S=32S=\frac{3}{2}S=23​ isotropic KHM explains the anomalous features of this Kitaev spin liquid (KSL) in terms of an emergent low-energy Majorana flat band. Away from the isotropic limit, the S=32S=\frac{3}{2}S=23​ KSL generally displays a quadrupolar order with gapped or gapless Majorana excitations, features that were quantitatively confirmed by density-matrix renormalization group simulations. In this paper, we explore the connection between the S=32S=\frac{3}{2}S=23​ KHM with Kugel-Khomskii models and discover exactly soluble examples for the latter. We perform a symmetry analysis for the variational parton mean-field Ans\"atze in the spin and orbital basis for different quantum liquid phases of the S=32S=\frac{3}{2}S=23​ KHM. Finally, we investigate a proposed time-reversal symmetry-breaking spin liquid induced by [111] single-ion anisotropy and elucidate its topological properties as well as experimental signatures, e.g., an unquantized thermal Hall response.