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arXiv:2407.14663

The Role of Quantum Metastability and the Perspective of Quantum Glassiness in Kitaev Fractional Spin Dynamics: An NMR Study

Wassilios Papawassiliou, Nicolas Lazaridis, Eunice Mumba Mpanga, Jonas Koppe, Nikolaos Panopoulos, Marina Karagianni, Lydia Gkoura, Romain Berthelot, Michael Fardis, Andrew J. Pell, G. C. Papavassiliou

Published Jul 19, 2024• 0 citations
arXivHTMLPDF

Abstract

The suppression of magnetic order and the detection of a half-quantized thermal Hall effect in α-RuCl3 under an external magnetic field have sparked significant debate, whether these phenomena point to spin fractionalization, as posited by the Kitaev quantum spin liquid (QSL) model, or if they arise from a more conventional mechanism in an antiferromagnetically ordered spin state. Here, through 23Na NMR relaxation measurements on the layered cobaltate Na2Co2TeO6 at two distinct magnetic fields (4.7 and 9.4 Tesla), we provide compelling evidence supporting a variant interpretation. While upon cooling, the NMR relaxation times align with the temperature dependence predicted by Kitaev fractional spin excitations, below 10 K, a dynamically heterogeneous state is detected with Quantum Spin Glass (QSG) characteristics. In this state, the spin fractionalization dynamics unfold over markedly different time scales, and are characterized by quantum metastability, inducing prolonged equilibration as T->0. This observation challenges the prevailing view of a primarily homogeneous QSL state, as the ground state of tangible Kitaev systems.

DOI
10.48550/arxiv.2407.14663

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Quantum spin liquid is a disordered but highly entangled magnetic state with fractional spin excitations1. The ground state of an exactly solved Kitaev honeycomb model is perhaps its clearest example2. Under a magnetic field, a spin flip in this model fractionalizes into two types of anyon, a quasiparticle with more complex exchange statistics than standard fermions or bosons: a pair of gauge fluxes and a Majorana fermion2,3. Here, we demonstrate this kind of fractionalization in the Kitaev paramagnetic state of the honeycomb magnet α-RuCl3. The spin excitation gap determined by nuclear magnetic resonance consists of the predicted Majorana fermion contribution following the cube of the applied magnetic field2,4,5, and a finite zero-field contribution matching the predicted size of the gauge flux gap2,6. The observed fractionalization into gapped anyons survives in a broad range of temperatures and magnetic fields, which establishes α-RuCl3 as a unique platform for future investigations of anyons.

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The suppression of magnetic order and the detection of a half-quantized thermal Hall effect in α-RuCl3 under an external magnetic field have sparked significant debate, whether these phenomena point to spin fractionalization, as posited by the Kitaev quantum spin liquid (QSL) model, or if they arise from a more conventional mechanism in an antiferromagnetically ordered spin state. Here, through 23Na NMR relaxation measurements on the layered cobaltate Na2Co2TeO6 at two distinct magnetic fields (4.7 and 9.4 Tesla), we provide compelling evidence supporting a variant interpretation. While upon cooling, the NMR relaxation times align with the temperature dependence predicted by Kitaev fractional spin excitations, below 10 K, a dynamically heterogeneous state is detected with Quantum Spin Glass (QSG) characteristics. In this state, the spin fractionalization dynamics unfold over markedly different time scales, and are characterized by quantum metastability, inducing prolonged equilibration as T->0. This observation challenges the prevailing view of a primarily homogeneous QSL state, as the ground state of tangible Kitaev systems.
Abstract The suppression of magnetic order and the detection of a half-quantized thermal Hall effect in α-RuCl3 under an external magnetic field have sparked significant debate, whether these phenomena point to spin fractionalization, as posited by the Kitaev quantum spin liquid (QSL) model, or if they arise from a more conventional mechanism in an antiferromagnetically ordered spin state. Here, through 23Na NMR relaxation measurements on the layered cobaltate Na2Co2TeO6 at two distinct magnetic fields (4.7 and 9.4 Tesla), we provide compelling evidence supporting a variant interpretation. While upon cooling, the NMR relaxation times align with the temperature dependence predicted by Kitaev’s fractional spin excitations, below 10 K, a dynamically heterogeneous state is detected with Quantum Spin Glass (QSG) characteristics. In this state, the spin fractionalization dynamics unfold over markedly different time scales, and are characterized by quantum metastability, inducing prolonged equilibration as T→0. This observation challenges the prevailing view of a primarily homogeneous QSL state, as the ground state of tangible Kitaev systems.
Abstract Significant efforts have focused on the magnetic excitations of relativistic Mott insulators, predicted to realize the Kitaev quantum spin liquid (QSL). This exactly solvable model involves a highly entangled state resulting from bond-dependent Ising interactions that produce excitations which are non-local in terms of spin flips. A key challenge in real materials is identifying the relative size of the non-Kitaev terms and their role in the emergence or suppression of fractional excitations. Here, we identify the energy and temperature boundaries of non-Kitaev interactions by direct comparison of the Raman susceptibility of α -RuCl 3 with quantum Monte Carlo (QMC) results for the Kitaev QSL. Moreover, we further confirm the fractional nature of the magnetic excitations, which is given by creating a pair of fermionic quasiparticles. Interestingly, this fermionic response remains valid in the non-Kitaev range. Our results and focus on the use of the Raman susceptibility provide a stringent new test for future theoretical and experimental studies of QSLs.
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.
Quantum spin liquids (QSLs) host a variety of fractionalized particles. In Kitaev's paradigmatic honeycomb model a spin-fractionalizes intoflux due to emergentgauge field and matter Majorana fermions. Although these excitations have well-defined dynamics in the integrable limit, their direct experimental identification is notoriously challenging: realistic materials inevitably host additional symmetry-allowed interactions that break integrability and hybridize gauge and matter sectors, while magnetic fields, which are often required to suppress competing order and stabilize a putative QSL regime, further entangle the responses of different fractionalized quasiparticles and may even drive the system into field-induced spin-liquid phases that are not adiabatically connected to the integrable limit. A prominent example is the quantum Majorana metal, in which the distinct dynamics of fractionalized Majorana fermions can become directly visible in scattering. This review highlights recent progress on these related questions: in which field-stabilized QSL regimes and nearby emergent phases, and under what conditions, can the response of a specific fractionalized quasiparticle be isolated and positively understood, thereby clarifying the existence and the experimental scope of putative spin liquids? We review the progress on these questions across Abelian, non-Abelian, and emergent quantum phases under magnetic field that are not perturbatively connected to the integrable limit. We connect these field-induced dynamical phenomena to concrete experimental observables, relevant for neutron scattering, resonant inelastic x-ray scattering, and pump-probe spectroscopy, techniques that are capable of identifying the nature of different magnetic-field-induced phases and resolving specific types of fractionalized particles, including Majoranas andfluxes.
Abstract The pursuit of the quantum spin liquid (QSL) predicted by the Kitaev honeycomb model remains a central yet challenging goal in quantum magnetism. Realistic candidate materials inevitably host non-Kitaev interactions that often lead to antiferromagnetic (AFM) order at low temperature. While magnetic fields can suppress such AFM order and may stabilize a QSL phase, conclusive evidence for a field-induced Kitaev QSL has remained elusive despite a decade of research. Here, we establish an effective K - J -Γ- Γ′{\Gamma }^{{\prime} }Γ′ Γ ′ model with a dominant AFM Kitaev interaction for Na 2 Co 2 TeO 6 , which quantitatively explains its key experimental measurements. Using high-precision tensor-network calculations, we reveal a QSL phase under intermediate [111] magnetic fields, which is possibly gapless, and find it can be adiabatically connected to the intensively studied intermediate-field QSL in the pure AFM Kitaev model. This correspondence confirms that the Kitaev model as the origin of the intermediate-field QSL in cobalt-based magnet Na 2 Co 2 TeO 6 , thus offering a concrete platform for exploring Kitaev-derived QSL in realistic materials.
Quantum spin liquid is a disordered but highly entangled magnetic state with fractional spin excitations1. The ground state of an exactly solved Kitaev honeycomb model is perhaps its clearest example2. Under a magnetic field, a spin flip in this model fractionalizes into two types of anyon, a quasiparticle with more complex exchange statistics than standard fermions or bosons: a pair of gauge fluxes and a Majorana fermion2,3. Here, we demonstrate this kind of fractionalization in the Kitaev paramagnetic state of the honeycomb magnet α-RuCl3. The spin excitation gap determined by nuclear magnetic resonance consists of the predicted Majorana fermion contribution following the cube of the applied magnetic field2,4,5, and a finite zero-field contribution matching the predicted size of the gauge flux gap2,6. The observed fractionalization into gapped anyons survives in a broad range of temperatures and magnetic fields, which establishes α-RuCl3 as a unique platform for future investigations of anyons.