α-RuCl 3 is drawing much attention as a promising candidate Kitaev quantum spin liquid [1][2][3][4][5][6][7][8]. However, despite intensive research efforts, controversy remains about the form of the basic interactions governing the physics of this material. Even the sign of the Kitaev interaction (the bonddependent anisotropic interaction responsible for Kitaev physics) is still under debate, with conflicting results from theoretical and experimental studies [5,6,[9][10][11][12][13][14][15]. The significance of the symmetric off-diagonal exchange interaction (referred to as the Γ term) is another contentious question [16][17][18]. Here, we present resonant elastic x-ray scattering data that provides unambiguous experimental constraints to the two leading terms in the magnetic interaction Hamiltonian. We show that the Kitaev interaction (K) is ferromagnetic, and that the Γ term is antiferromagnetic and comparable in size to the Kitaev interaction. Our findings also provide a natural explanation for the large anisotropy of the magnetic susceptibility in α-RuCl 3 as arising from the large Γ term. We therefore provide a crucial foundation for understanding the interactions underpinning the exotic magnetic behaviours observed in α-RuCl 3 .
Recent discovery of the half-quantized thermal Hall conductivity in α-RuCl3, a candidate material for the Kitaev spin liquid, suggests the presence of a highly-entangled quantum state in external magnetic fields. This field-induced phase appears between the low-field zig-zag magnetic order and the high-field polarized state. Motivated by this experiment, we study possible field-induced quantum phases in theoretical models of the Kitaev magnets, using the two-dimensional tensor network approach or infinite tensor product states (iTPS). More specifically, we map out the magnetic-field phase diagram of the K-Γ-Γ model, where K is the ferromagnetic Kitaev interaction and Γ, Γ are additional bond-dependent anisotropic interactions between spin-1/2 moments. We find various novel quantum ground states in addition to the chiral Kitaev spin liquid occupying a small area in the phase diagram. They form a band of emergent quantum phases in an intermediate window of external magnetic fields, somewhat reminiscent of the experiment. We discuss the implications of these results in view of the experiment and previous theoretical studies. arXiv:1908.07671v1 [cond-mat.str-el]
There has been a great interest in magnetic field induced quantum spin liquids in Kitaev magnets after the discovery of neutron scattering continuum and half-quantized thermal Hall conductivity in the material α-RuCl 3. In this work, we provide a semiclassical analysis of the relevant theoretical models, which enable us to treat large system sizes approximating the thermodynamic limit. We find a series of competing magnetic orders with fairly large unit cells at intermediate magnetic fields, which are mostly missed by previous studies. We show that quantum fluctuations are typically strong in these large unit cell orders, while the magnetic excitations, magnons, have a dispersion that resembles a scattering continuum. The huge quantity of magnon bands with finite Chern numbers also gives rise to an unusually large thermal Hall conductivity. Given the highly frustrated nature of the spin model, the large unit cell orders are likely to melt into the putative spin liquid in the quantum limit. Our work provides an important basis for a thorough investigation of emergent spin liquids and competing phases in Kitaev magnets.
We propose a theoretical model for a gapless spin liquid phase that may have been observed in a recent experiment on H3LiIr2O6 [1,2]. Despite the insulating and non-magnetic nature of the material, the specific heat coefficient C/T ∼ 1/ √ T in zero magnetic field and C/T ∼ T /B 3/2 with finite magnetic field B have been observed. In addition, the NMR relaxation rate shows 1/(T1T ) ∼ (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, 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 ∼ 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.
The appearance of nontrivial phases in Kitaev materials exposed to an external magnetic field has recently been a subject of intensive studies. Here, we elucidate the relation between the field-induced ground states of the classical and quantum spin models proposed for such materials, by using the infinite density matrix renormalization group (iDMRG) and the linear spin wave theory (LSWT). We consider the K model, where and are off-diagonal spin exchanges on top of the dominant Kitaev interaction K. Focusing on the magnetic field along the [111] direction, we explain the origin of the nematic paramagnet, which breaks the lattice-rotational symmetry and exists in an extended window of magnetic field, in the quantum model. This phenomenon can be understood as the effect of quantum order-by-disorder in the frustrated ferromagnet with a continuous manifold of degenerate ground states discovered in the corresponding classical model. We compute the dynamical spin structure factors using a matrix operator based time evolution and compare them with the predictions from LSWT. We, thus, provide predictions for future inelastic neutron scattering experiments on Kitaev materials in an external magnetic field along the [111] direction. In particular, the nematic paramagnet exhibits a characteristic pseudo-Goldstone mode, which results from the lifting of a continuous degeneracy via quantum fluctuations.
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