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arXiv:2405.06380 · Physical review. B./Physical review. B

( H , Li ) 6 Ru 2 O 6 : A possible zero-field Ru 3 + -based Kitaev quantum spin liquid

Sanjay Bachhar, M. Baenitz, Hubertus Luetkens, John Wilkinson, Sumiran Pujari, A. V. Mahajan

Published Dec 2, 2024• 2 citations
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Abstract

This is a comprehensive study of the Ru${}^{3+}$-based Kitaev honeycomb compound (H,Li)${}_{6}$Ru${}_{2}$O${}_{6}$ (HLRO), combining magnetization ($M$), magnetic specific heat (${C}_{m}$), and local probes (muon spin relaxation and magnetic resonance). There is clear evidence of a Kitaev quantum spin liquid (KQSL) state. $M$, ${C}_{m}$, and magnetic fluctuations (1/${T}_{1}$) exhibit scaling behavior. The ${C}_{m}$ scaling is in good agreement with theory [PRX 11, 011034 (2021)]. A two-step entropy release is taken as a signature of Majorana fermions. HLRO is a realization of a KQSL without magnetic order in zero field, unlike 𝛼-RuCl${}_{3}$.

DOI
10.1103/physrevb.110.l241102

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This is a comprehensive study of the Ru3+{}^{3+}3+-based Kitaev honeycomb compound (H,Li)6{}_{6}6​Ru2{}_{2}2​O6{}_{6}6​ (HLRO), combining magnetization (MMM), magnetic specific heat (Cm{C}_{m}Cm​), and local probes (muon spin relaxation and magnetic resonance). There is clear evidence of a Kitaev quantum spin liquid (KQSL) state. MMM, Cm{C}_{m}Cm​, and magnetic fluctuations (1/T1{T}_{1}T1​) exhibit scaling behavior. The Cm{C}_{m}Cm​ scaling is in good agreement with theory [PRX 11, 011034 (2021)]. A two-step entropy release is taken as a signature of Majorana fermions. HLRO is a realization of a KQSL without magnetic order in zero field, unlike 𝛼-RuCl3{}_{3}3​.
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.
The pursuit of quantum spin liquid (QSL) in the Kitaev honeycomb magnets has drawn intensive attention recently. In particular, $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ has been widely recognized as a promising candidate for the Kitaev QSL. Although the compound exhibits an antiferromagnetic order under zero field, it is believed to be endowed with fractionalized excitations and can be driven to the QSL phase by magnetic fields. Here, based on a realistic $K\text{\ensuremath{-}}J\text{\ensuremath{-}}\mathrm{\ensuremath{\Gamma}}\text{\ensuremath{-}}{\mathrm{\ensuremath{\Gamma}}}^{\ensuremath{'}}$ model for $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$, we exploit the exponential tensor renormalization group approach to explore the phase diagram of the compound under magnetic fields. We calculate the thermodynamic quantities, including the specific heat, Gr\"uneisen parameter, magnetic torque, magnetotropic susceptibility, and so on, under a magnetic field with a tilting angle $\ensuremath{\theta}$ to the c∗{c}^{*}c∗-axis perpendicular to the honeycomb plane. We find an extended QSL in the angle-field phase diagram determined with thermodynamic responses. The gapless nature of such field-induced QSL is identified from the specific heat and entropy data computed down to very low temperatures. The present study provides guidance for future high-field experiments for the QSL in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ and other candidate Kitaev magnets.
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.
We propose a theoretical model for a gapless spin liquid phase that may have been observed in a recent experiment on H3LiIr2O6{\mathrm{H}}_{3}{\mathrm{LiIr}}_{2}{\mathrm{O}}_{6}H3​LiIr2​O6​. Despite the insulating and nonmagnetic nature of the material, the specific heat coefficient $C/T\ensuremath{\sim}1/\sqrt{T}$ in zero magnetic field and $C/T\ensuremath{\sim}T/{B}^{3/2}$ with finite magnetic field BBB have been observed. In addition, the NMR relaxation rate shows $1/({T}_{1}T)\ensuremath{\sim}{(C/T)}^{2}$. Motivated by the fact that the interlayer/in-plane lattice parameters are reduced/elongated by the hydrogen intercalation of the parent compound Li2IrO3{\mathrm{Li}}_{2}{\mathrm{IrO}}_{3}Li2​IrO3​, we consider four layers of the Kitaev honeycomb lattice model with additional interlayer exchange interactions. It is shown that the resulting spin liquid excitations reside mostly in the top and bottom layers of such a layered structure and possess a quartic dispersion. In an applied magnetic field, each quartic mode is split into four Majorana cones with the velocity $v\ensuremath{\sim}{B}^{3/4}$. We suggest that the spin liquid phase in these ``defect'' layers, placed between different stacking patterns of the honeycomb layers, can explain the major phenomenology of the experiment, which can be taken as evidence that the Kitaev interaction plays the primary role in the formation of a quantum spin liquid in this material.
In Kitaev spin liquids, SSS = \textonehalf{} quantum spins on a honeycomb lattice with bond-dependent interactions fractionalize into Majorana fermions. Fingerprints of these fractionalized excitations can be detected via thermodynamic measurements. Here, the authors perform detailed heat capacity experiments on the spin-liquid candidate $\ensuremath{\alpha}$-RuCl3{}_{3}3​ as function of temperature and magnetic field. To estimate the intrinsic phonon contribution, they measure the nonmagnetic reference compound RhCl3{}_{3}3​ and perform $a\phantom{\rule{0}{0ex}}b$ $i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o$ phonon calculations. Measurements and analysis provide experimental evidence of fractionalized excitations in good agreement with theoretical predictions.
Quantum spin liquids, a highly topologically entangled, dynamically correlated state where quantum fluctuations preclude any long-range ordering down to absolute zero. In the search for a topologically robust qubit, the scientific community has been in continuous hunt for real quantum spin liquid systems. Alexei Kitaev in his exactly solvable model for a spin-1/2 two-dimensional honeycomb lattice, presented a system that hosts a topologically protected state (Majorana zero-modes). Under an applied external field, the Kitaev spin liquids turn into a topologically non-trivial chiral spin-liquid state with non-abelian anionic excitations, which is crucial for quantum computing. Earlier theoretical predictions advocated that Kitaev physics can be realized in spin-orbit-coupled Mott insulators such as honeycomb irradiates and ruthenates. However, the experimental findings continuously challenge the theoretical aspects, indicating the presence of non-Kitaev interactions in real materials, where the dimensionality, disorder (vacancy), chemical composition, generalized spin-S, and external perturbations (pressure, magnetic field, temperature) can actively tune the Kitaev interactions and the ground state excitations. In this review article, a comprehensive discussion is included with an updated literature survey in the context of the potential of Raman spectroscopy as a probe for Kitaev quantum spin liquids.