In addition to the Kitaev (K) interaction, candidate Kitaev materials also possess Heisenberg (J) and off-diagonal symmetric (Γ) couplings. We investigate the quantum (S = 1/2) K-J-Γ model on the honeycomb lattice by a variational Monte Carlo (VMC) method. In addition to the "generic" Kitaev spin liquid (KSL), we find that there is just one proximate KSL (PKSL) phase, while the rest of the phase diagram contains different magnetically ordered states. The PKSL is a gapless Z2 state with 14 Majorana cones, which in contrast to the KSL has a gapless spin response. In a magnetic field applied normal to the honeycomb plane, it realizes two of Kitaev's gapped chiral spin-liquid phases, of which one is non-Abelian with Chern number ν = 5 and the other is Abelian with ν = 4. These two phases could be distinguished by their thermal Hall conductance.The Kitaev model [1] of bond-dependent Ising-type spin interactions on the honeycomb lattice offers exactly soluble examples of both gapped and gapless quantum spin liquids (QSLs). The magnetically disordered ground states of different QSLs are the consequence of strong intrinsic quantum fluctuations and provide particularly clean realizations of different fundamental phenomena. The gapped Kitaev QSL has Z 2 Abelian topological order, while the quintessential "Kitaev spin liquid" (KSL) is the gapless state whose low-energy excitations form two Majorana cones, whereas its Z 2 flux excitations are gapped. In an applied magnetic field, the Majorana cones become gapped and the resulting state is a chiral spin liquid (CSL) with Ising-type non-Abelian anyonic excitations, which have potential application in fault-tolerant topological quantum computation.Thus the experimental realization of the Kitaev model has moved to the forefront of research in strongly correlated materials. While transition-metal compounds with strong spin-orbit coupling do realize Kitaev-type interactions [2, 3], these "candidate Kitaev" materials typically possess in addition significant non-Kitaev interactions, which lead to Na 2 IrO 3 [4, 5] and α-RuCl 3 [6-9] exhibiting magnetic order at low temperatures. Although H 3 LiIr 2 O 6 [10] is not ordered, it appears to show strong impurity and extrinsic disordering effects. At the same order in a strong-coupling treatment [11], the Kitaev (K) interaction is accompanied by Heisenberg (J) and offdiagonal symmetric (Γ) interactions, and thus the focus of the field has become the understanding of "proximate Kitaev" physics in this class of model, also under applied magnetic fields [12][13][14][15] and pressures [16].In this Letter, we investigate the K-J-Γ extended Kitaev model by variational Monte Carlo (VMC) studies of a spinon representation. Guided by the projective symmetry group (PSG), we obtain the global K-J-Γ phase diagram and show that it contains two distinct QSL phases among several classically ordered phases. One QSL, at small J and Γ, is the generic KSL. At larger Γ we find one proximate KSL (PKSL), a non-Kitaev QSL sharing the same PSG as the KSL but wi...
Spin-orbit coupled honeycomb magnets with the Kitaev interaction have received a lot of attention due to their potential of hosting exotic quantum states including quantum spin liquids. Thus far, the most studied Kitaev systems are 4d/5d-based honeycomb magnets. Recent theoretical studies predicted that 3d-based honeycomb magnets, including Na2Co2TeO6 (NCTO), could also be a potential Kitaev system. Here, we have used a combination of heat capacity, magnetization, electron spin resonance measurements alongside inelastic neutron scattering (INS) to study NCTO’s quantum magnetism, and we have found a field-induced spin disordered state in an applied magnetic field range of 7.5 T < B (⊥ b-axis) < 10.5 T. The INS spectra were also simulated to tentatively extract the exchange interactions. As a 3d-magnet with a field-induced disordered state on an effective spin-1/2 honeycomb lattice, NCTO expands the Kitaev model to 3d compounds, promoting further interests on the spin-orbital effect in quantum magnets.
The frustrated magnet α-RuCl3 constitutes a fascinating quantum material platform that harbors the intriguing Kitaev physics. However, a consensus on its intricate spin interactions and field-induced quantum phases has not been reached yet. Here we exploit multiple state-of-the-art many-body methods and determine the microscopic spin model that quantitatively explains major observations in α-RuCl3, including the zigzag order, double-peak specific heat, magnetic anisotropy, and the characteristic M-star dynamical spin structure, etc. According to our model simulations, the in-plane field drives the system into the polarized phase at about 7 T and a thermal fractionalization occurs at finite temperature, reconciling observations in different experiments. Under out-of-plane fields, the zigzag order is suppressed at 35 T, above which, and below a polarization field of 100 T level, there emerges a field-induced quantum spin liquid. The fractional entropy and algebraic low-temperature specific heat unveil the nature of a gapless spin liquid, which can be explored in high-field measurements on α-RuCl3.
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