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Intermediate-field spin(on) dynamics in α-RuCl₃

Arnab Banerjee, Colin L. Sarkis, Kiranmayi D. Dixit, Peng Rao, Guga Khundzakishvili, Christian Balz, Jiaqiang Yan, Barry Winn, Travis J. Williams, Unnikrishnan Arjun, Roderich Moessner, Johannes Knolle, S. E. Nagler, D. M. Tennant

Published Feb 20, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.21203/rs.3.rs-8824928/v1

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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.
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.
It is known that α-RuCl3 has been studied extensively because of its proximity to the Kitaev quantum-spin-liquid (QSL) phase and the possibility of approaching it by tuning the competing interactions. Here we present the first polarized inelastic neutron scattering study on α-RuCl3 single crystals to explore the scattering continuum around the Γ point at the Brillouin zone center, which was hypothesized to be resulting from the Kitaev QSL state but without concrete evidence. With polarization analyses, we find that, while the spin-wave excitations around the M point vanish above the transition temperature T N, the pure magnetic continuous excitations around the Γ point are robust against temperature. Furthermore, by calculating the dynamical spin-spin correlation function using the cluster perturbation theory, we derive magnetic dispersion spectra based on the K–Γ model, which involves with a ferromagnetic Kitaev interaction of –7.2 meV and an off-diagonal interaction of 5.6 meV. We find this model can reproduce not only the spin-wave excitation spectra around the M point, but also the non-spin-wave continuous magnetic excitations around the Γ point. These results provide evidence for the existence of fractional excitations around the Γ point originating from the Kitaev QSL state, and further support the validity of the K–Γ model as the effective minimal spin model to describe α-RuCl3.
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.
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 $μ_0H^*\approx$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.
We report on terahertz spectroscopy of quantum spin dynamics in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$, a system proximate to the Kitaev honeycomb model, as a function of temperature and magnetic field. We follow the evolution of an extended magnetic continuum below the structural phase transition at Ts2=62  K{T}_{s2}=62\text{ }\text{ }\mathrm{K}Ts2​=62  K. With the onset of a long-range magnetic order at TN=6.5  K{T}_{N}=6.5\text{ }\text{ }\mathrm{K}TN​=6.5  K, spectral weight is transferred to a well-defined magnetic excitation at $\ensuremath{\hbar}{\ensuremath{\omega}}_{1}=2.48\text{ }\text{ }\mathrm{meV}$, which is accompanied by a higher-energy band at $\ensuremath{\hbar}{\ensuremath{\omega}}_{2}=6.48\text{ }\text{ }\mathrm{meV}$. Both excitations soften in a magnetic field, signaling a quantum phase transition close to Bc=7  T{B}_{c}=7\text{ }\text{ }\mathrm{T}Bc​=7  T, where a broad continuum dominates the dynamical response. Above Bc{B}_{c}Bc​, the long-range order is suppressed, and on top of the continuum, emergent magnetic excitations evolve. These excitations follow clear selection rules and exhibit distinct field dependencies, characterizing the dynamical properties of a possibly field-induced quantum spin liquid.
Raman and terahertz spectroscopy, combined with exact diagonalization studies, reveal the nature of the high-field phase of the proximate Kitaev material $\ensuremath{\alpha}$-RuCl3{}_{3}3​ as a partially polarized quantum disordered state. The state is characterized by a gapped multiparticle continuum, out of which a two-particle bound state emerges, together with a well-defined single-particle excitation at low energy. The results underline the unusual nature of the high-field phase, and the important role of Kitaev and off-diagonal interactions in $\ensuremath{\alpha}$-RuCl3{}_{3}3​.