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arXiv:2608.18530

High-field fate of the Kitaev quantum spin liquid in $α$-RuCl$_3$

K. Imamura, R. Ohno, Y. C. Tsuzuki, Y. Akui, Ryuichi Namba, K. Ishihara, M. Akaki, M. Kimata, N. Kurita, H. Tanaka, N. Kimura, S. Imajo, A. Matsuo, K. Kindo, Y. Matsuda, K. Hashimoto, Y. Mizukami, T. Shibauchi

Published Aug 19, 2026• 0 citations
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Abstract

Kitaev quantum spin liquids (KQSLs) host fractionalized excitations described by itinerant Majorana quasiparticles and gapped $Z_2$ fluxes (visons), providing a platform for emergent topological matter. Whether such a state survives under strong magnetic fields, however, remains an open question. The layered honeycomb magnet $α$-RuCl$_3$ is a leading candidate material: an in-plane field of $\sim$ 7 T suppresses antiferromagnetic order and induces a quantum-disordered phase exhibiting signatures consistent with Majorana excitations, including an anomalous thermal Hall effect and field-angle-dependent specific heat. At higher fields, the magnetization approaches saturation, suggesting a transition to a spin-polarized state, yet the microscopic evolution between these limits remains unresolved. Here we report high-field specific heat measurements up to 24 T that reveal a distinct crossover at $μ_0H^*\approx$15 T, beyond which the perturbative Kitaev description breaks down. Above $H^*$, the characteristic six-fold angular modulation of the specific heat collapses and the excitation gap deviates from the predicted $H^3$ scaling. Meanwhile, the gap decreases with increasing field and the in-plane magnetization anisotropy persists up to $\sim$ 24 T, both in sharp contrast to a trivial spin-polarized state, indicating that KQSL signatures are preserved even at $\sim$ 90 % of magnetization saturation. These results reveal that the KQSL in $α$-RuCl$_3$ extends well beyond the perturbative window, persisting as a nonperturbative regime in which the Majorana and vison energy scales merge, before eventually giving way to spin polarization. This thermodynamic roadmap provides a basis for understanding how fractionalized phases evolve under strong magnetic fields.

DOI
10.48550/arxiv.2608.18530

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High-field fate of the Kitaev quantum spin liquid in ααα-RuCl3_33​
Kitaev quantum spin liquids (KQSLs) host fractionalized excitations described by itinerant Majorana quasiparticles and gapped Z2Z_2Z2​ fluxes (visons), providing a platform for emergent topological matter. Whether such a state survives under strong magnetic fields, however, remains an open question. The layered honeycomb magnet ααα-RuCl3_33​ is a leading candidate material: an in-plane field of ∼\sim∼ 7 T suppresses antiferromagnetic order and induces a quantum-disordered phase exhibiting signatures consistent with Majorana excitations, including an anomalous thermal Hall effect and field-angle-dependent specific heat. At higher fields, the magnetization approaches saturation, suggesting a transition to a spin-polarized state, yet the microscopic evolution between these limits remains unresolved. Here we report high-field specific heat measurements up to 24 T that reveal a distinct crossover at μ0H∗≈μ_0H^*\approxμ0​H∗≈15 T, beyond which the perturbative Kitaev description breaks down. Above H∗H^*H∗, the characteristic six-fold angular modulation of the specific heat collapses and the excitation gap deviates from the predicted H3H^3H3 scaling. Meanwhile, the gap decreases with increasing field and the in-plane magnetization anisotropy persists up to ∼\sim∼ 24 T, both in sharp contrast to a trivial spin-polarized state, indicating that KQSL signatures are preserved even at ∼\sim∼ 90 % of magnetization saturation. These results reveal that the KQSL in ααα-RuCl3_33​ extends well beyond the perturbative window, persisting as a nonperturbative regime in which the Majorana and vison energy scales merge, before eventually giving way to spin polarization. This thermodynamic roadmap provides a basis for understanding how fractionalized phases evolve under strong magnetic fields.
A Kitaev quantum spin liquid involves fractionalized quasiparticles called itinerant Majorana fermions and localized gauge fluxes. The topological character with chiral excitations under a magnetic field is currently in an active debate. For a candidate spin liquid $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$, we report low-energy spin excitations through nuclear magnetic and quadrupole resonance measurements down to temperatures three orders of magnitude lower than the exchange energy. In a field-driven disordered state, we found the evolution of two kinds of gapped spin excitations with distinct field dependences. The result is indicative of a field-induced hybridization between fractionalized quasiparticles, as inferred by the perturbation theory for the Kitaev model. The detailed field dependence of spin dynamics across the quantum critical region shows the emergence of a gapless intermediate phase between the gapped zigzag order phase and spin-disordered phases.
Intermediate Field Spin(on) Dynamics in ααα-RuCl3_33​
We present comprehensive inelastic neutron spectroscopic maps of the magnetic field-induced disordered phase of the Kitaev quantum spin liquid candidate material ααα-RuCl3_33​. For fields along both in-plane high-symmetry directions we observe that the spin excitation spectrum at and above a magnetic field of 8~T is gapped. Excitation modes then sharpen for increasing field but are consistently broader than experimental resolution even at 13.5~T. The out-of-plane dispersion diminishes in the 7-10~T regime, signifying enhanced two-dimensional behavior as the in-plane liquid correlations are established. In this regime, excitations are very broad and largely flat for all accessible energy-momenta, which is kinematically at odds with a magnon-decay picture. By contrast, a continuum of fractionalized excitations naturally yields a broad continuum response, which crucially may be accompanied by sharper modes of bound states of fractionalized excitations. Their damping by the continuum accounts for the observed spectral broadening and field dependence. Our results provide strong evidence for the existence of fractionalized excitations in ααα-RuCl3_33​ in a magnetic field.
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.
Abstract We present comprehensive inelastic neutron spectroscopic maps of the magnetic field-induced disordered phase of the Kitaev quantum spin liquid candidate material α-RuCl 3 . For fields along both in-plane high symmetry directions we observe that the spin excitation spectrum at and above a magnetic field of 8 T is gapped. Excitation modes then sharpen for increasing field but are consistently broader than experimental resolution even at 13.5 T. The out-of-plane dispersion diminishes in the 7-10 T regime, signifying enhanced two-dimensional behavior as the in-plane liquid correlations are established. In this regime, excitations are very broad and largely flat for all accessible energy-momenta, which is kinematically at odds with a magnon-decay picture. By contrast, a continuum of fractionalized excitations naturally yields a broad continuum response, which crucially may be accompanied by sharper modes of bound states of fractionalized excitations. Their damping by the continuum accounts for the observed spectral broadening and field dependence. Our results provide strong evidence for the existence of fractionalized excitations in α-RuCl 3 in a magnetic field.
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.
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.