Recent experimental evidence for a field-induced quantum spin liquid (QSL) in
α-RuCl
3 calls for an understanding for the ground state of honeycomb Kitaev model under a magnetic field. In this work we address the nature of an enigmatic gapless paramagnetic phase in the antiferromagnetic Kitave model, under an intermediate magnetic field perpendicular to the plane. Combining theoretical and numerical efforts, we identify this gapless phase as a
U(1) QSL with spinon Fermi surfaces. We also reveal the nature of continuous quantum phase transitions involving this
U(1) QSL, and obtain a phase diagram of the Kitaev model as a function of bond anisotropy and perpendicular magnetic field.
Kitaev quantum spin liquids (KQSLs) host fractionalized excitations described by itinerant Majorana quasiparticles and gapped
Z2 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
∼ 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
H3 scaling. Meanwhile, the gap decreases with increasing field and the in-plane magnetization anisotropy persists up to
∼ 24 T, both in sharp contrast to a trivial spin-polarized state, indicating that KQSL signatures are preserved even at
∼ 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.
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.
The frustrated magnet $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ is one of the prime candidates for realizing a Kitaev quantum spin liquid (QSL). However, the existence of a field-induced intermediate QSL phase in this material remains under debate. Here, we employ sign-free numerically exact quantum Monte Carlo simulations to investigate the Kitaev-Heisenberg (KH) model on the honeycomb lattice with $K=\ensuremath{-}2J$ under an applied magnetic field along the
z direction. Our findings reveal that the system undergoes a direct quantum phase transition from a zigzag magnetically ordered phase to a spin-polarized phase at zero temperature, which belongs to the 3D XY universality class. At finite temperatures, a Berezinskii-Kosterlitz-Thouless transition line separates the spin-polarized phase from a quasi-long-range ordered state, eventually terminating at the quantum critical point. Our results convincingly show that there is no intermediate QSL phase in the KH model with a
z-direction magnetic field, which we believe will shed important light on understanding experimental observations in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$.
The possible existence of a quantum spin liquid (QSL) phase, an exotic state of matter with long-range quantum entanglement and fractionalized excitations, in
α-RuCl
3 has sparked widespread interests in exploring QSLs in various Kitaev models under magnetic fields. Recently, a
K-
J-
Γ-
Γ′ model has been proposed to accurately describe the compound by fitting the measured thermodynamic data, where
J is Heisenberg interaction, and
Γ,
Γ′ are off-diagonal exchanges on top of the dominant Kitaev coupling
K. Based on this effective model, an intermediate QSL phase in presence of an out-of-plane fields along the
[111] direction, between the low-field zigzag order and high-field polarized phase, has been predicted. By combining density matrix renormalization group (DMRG), exponential tensor renormalization group (XTRG), and variational Monte Carlo (VMC) calculations, we address the nature of this QSL phase in the honeycomb
K-
J-
Γ-
Γ′ model under the
[111]-direction field. Our DMRG calculations find the algebraic-like decay of spin correlation function, the finite spin scalar chiral order, and lattice nematic order. Together with the XTRG results of power-law specific heat at low temperature, our findings naturally suggest a gapless nematic chiral spin liquid. On the other hand, our VMC study finds a gapped nematic chiral spin liquid with the variational energy very close to that obtained in DMRG. As VMC finds a very small gap that is beyond the current resolution of both ground-state DMRG and finite-temperature XTRG calculations on finite-width cylinders, we resort the full clarification for the nature of the intermediate QSL to future studies. Lastly, we discuss the implications of our results to the recent experiment on
α-RuCl
3 and the QSL-like phase in a similar
K-
Γ-
Γ′ model.
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.