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arXiv:2604.03099

Proximate quantum spin liquids and Majorana continua in magnetically ordered Kitaev magnets

Peng Rao, Roderich Moessner, Johannes Knolle

Published Apr 3, 2026• 0 citations
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Abstract

We study the spin excitation spectra in magnetically ordered phases proximate to the Kitaev quantum spin liquid (KQSL). Although the low-energy universal features should be governed by the magnetic orders, the $\textit{non-universal}$ high-energy features of the KQSL and adjacent phases can be remarkably similar. Therefore, we study the extended Kitaev model within a Stoner-like theory using Majorana partons, and compute the inelastic neutron scattering (INS) intensities in the random phase approximation. First, we benchmark against the antiferromagnetic (AFM) Heisenberg model and recover the AFM order with linear Goldstone modes. We then explore the phase diagram which agrees qualitatively with previous numerical results. In particular, the Majorana parton theory accurately captures Order-by-Disorder effects in the Kitaev-Heisenberg limit. We also find large INS intensities near the associated high-symmetry Brillouin zone (BZ) points of the magnetic orders. At intermediate and high energies, broad multi-spinon continua emerge across the BZ, providing a distinct mechanism for magnon decay and spectral broadening beyond the conventional multi-magnon decay scenario. Finally, we study the model Hamiltonian of candidate Kitaev material $α$-RuCl$_3$. The zigzag ground state agrees qualitatively with experiments, its stability under external magnetic field also exhibits strong anisotropy in the field directions, and broad scattering continua are recovered similar to those observed experimentally.

DOI
10.48550/arxiv.2604.03099

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We study the spin excitation spectra in magnetically ordered phases proximate to the Kitaev quantum spin liquid (KQSL). Although the low-energy universal features should be governed by the magnetic orders, the non-universal\textit{non-universal}non-universal high-energy features of the KQSL and adjacent phases can be remarkably similar. Therefore, we study the extended Kitaev model within a Stoner-like theory using Majorana partons, and compute the inelastic neutron scattering (INS) intensities in the random phase approximation. First, we benchmark against the antiferromagnetic (AFM) Heisenberg model and recover the AFM order with linear Goldstone modes. We then explore the phase diagram which agrees qualitatively with previous numerical results. In particular, the Majorana parton theory accurately captures Order-by-Disorder effects in the Kitaev-Heisenberg limit. We also find large INS intensities near the associated high-symmetry Brillouin zone (BZ) points of the magnetic orders. At intermediate and high energies, broad multi-spinon continua emerge across the BZ, providing a distinct mechanism for magnon decay and spectral broadening beyond the conventional multi-magnon decay scenario. Finally, we study the model Hamiltonian of candidate Kitaev material ααα-RuCl3_33​. The zigzag ground state agrees qualitatively with experiments, its stability under external magnetic field also exhibits strong anisotropy in the field directions, and broad scattering continua are recovered similar to those observed experimentally.
The Kitaev quantum spin liquid (KQSL) is an exotic emergent state of matter exhibiting Majorana fermion and gauge flux excitations. The magnetic insulator alpha-RuCl3 is thought to realize a proximate KQSL. We used neutron scattering on single crystals of alpha-RuCl3 to reconstruct dynamical correlations in energy-momentum space. We discovered highly unusual signals, including a column of scattering over a large energy interval around the Brillouin zone center, which is very stable with temperature. This finding is consistent with scattering from the Majorana excitations of a KQSL. Other, more delicate experimental features can be transparently associated with perturbations to an ideal model. Our results encourage further study of this prototypical material and may open a window into investigating emergent magnetic Majorana fermions in correlated materials.
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Motivated by the appearance of Majorana fermions in a broad range of correlated and topological electronic systems, we develop a general method to compute the dynamical response of interacting Majorana fermions in the random-phase approximation (RPA). This can be applied self-consistently on top of Majorana mean-field theory backgrounds, thereby in particular providing a powerful tool to analyze behavior in the vicinity of (various heavily studied) exactly soluble models. Prime examples are quantum spin liquids (QSL) with emergent Majorana excitations, with the celebrated exact solution of Kitaev. We employ the RPA to study in considerable detail phase structure and dynamics of the extended Kitaev honeycomb K J Γ model, with and without an applied field. First, we benchmark our method with Kitaev's exactly soluble model, finding a remarkable agreement. The interactions between Majorana fermions even turn out to mimic the effect of local Z 2 flux excitations, which we explain analytically. Second, we show how small non-Kitaev couplings J and Γ induce Majorana bound states, resulting in sharp features in the dynamical structure factor in the presence of fractionalization: such “spinon excitons” naturally appear, and can coexist and interact with the broad Majorana continuum. Third, for increasing couplings or field, our theory predicts instabilities of the Kitaev QSL (KQSL) triggered by the condensation of the sharp modes. From the high-symmetry momenta of the condensation we can deduce which magnetically ordered phases surround the KQSL, in good agreement with previous finite-size numerics. We discuss implications for experiments and the broad range of applicability of our method to other QSL and Majorana systems.
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.
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