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Disorder Induced Quantum Griffiths Phase in the Proximate Kitaev Quantum Spin Liquid Na2Co2TeO6

Wassilios Papawassiliou, Nicolas Lazardis, Eunice Mumba Mpanga, Jonas Koppe, Nikolaos Panopoulos, Lydia Gkoura, Romain Berthelot, Michael Fardis, Gaël De Paëpe, Andrew J. Pell, G. C. Papavassiliou

Published Aug 12, 2026• 0 citations

Abstract

Abstract Disorder is generally expected to destabilize a Kitaev quantum spin liquid, yet it can also generate new quantum phases. Na2Co2TeO6, which contains substantial intrinsic Na-site disorder, provides a promising platform to examine how randomness reshapes spin dynamics. Here, by employing 23Na NMR, we reveal a disorder induced softening of the spin excitations. Between 10 K and 100 K, the temperature dependence of the NMR relaxation times is consistent with the presence of gapped fractional spin excitations. Below 10 K, however, they bifurcate into two distinct channels: a slow-relaxing channel, preserving the gapped excitations character, and a fast-relaxing channel that follows a Korringa-like law, indicating the emergence of nearly gapless spin excitations. This two-channels regime is accompanied by ultraslow, microsecond scale spin fluctuations following an Arrhenius activation law. Besides, ab initio NMR lineshape calculations show that a quantum spin liquid-like model reproduces the low-temperature NMR spectra sufficiently better than magnetically ordered models. Together, our findings indicate transition upon cooling to a disorder-driven quantum spin liquid Griffiths phase, comprising slowly fluctuating gapped regions within a matrix of nearly gapless low-energy spin excitations.

DOI: 10.21203/rs.3.rs-10266479/v1

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A quantum spin liquid is a magnetic phase of matter that is remarkable for its ground state long-range entanglement and fractional excitations. A quantum spin liquid appears in the well-known Kitaev honeycomb spin-half model. In a magnetic field, there is a phase transition to a topological phase with an energy gap in the bulk and chiral Majorana fermions at the edge. However, recent nuclear magnetic resonance experiments suggest excitations without a gap in this phase, signalled by the cubic temperature dependence of the spin-lattice relaxation rate at low temperatures. In this work, I propose a mechanism to account for this experimental result. I use the localization of chiral Majorana modes in defects to explain the presence of gapless modes in the bulk. Treating the weak interaction between the chiral modes in the defects within a mean-field approximation, I find that these modes remain gapless when the interaction is below a critical value that depends on the magnetic field strength. I used the effective low-energy theory to calculate the spin-lattice relaxation rate and found a behavior that agrees with the experimental result.

The Kitaev quantum spin liquid provides an ideal playground for the spin fractionalization to Majorana and vison excitations. The fingerprints manifest themselves in spin dynamics, which are accessible via many experimental techniques. However, extrinsic disorder effects are inevitable in real materials. Here, the authors compute finite-temperature spin dynamics in disordered Kitaev spin liquids and clarify that disorder seriously affects the vison excitations rather than Majorana quasiparticles. Furthermore, the softening of the vison excitations and Majorana zero modes emerge due to disorder, which will help identify Kitaev magnets.

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.

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-

{\Gamma }^{{\prime} }

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.