Topological states of matter such as quantum spin liquids (QSLs) are of great interest because of their remarkable predicted properties including protection of quantum information and the emergence of Majorana fermions. Such QSLs, however, have proven difficult to identify experimentally. The most promising approach is to study their exotic nature via the wavevector and intensity dependence of their dynamical response in neutron scattering. A major search has centered on iridate materials which are proposed to realize the celebrated Kitaev model on a honeycomb lattice -a prototypical topological QSL system in two dimensions (2D). The difficulties of iridium for neutron measurements have, however, impeded progress significantly. Here we provide experimental evidence that a material based on ruthenium, α-RuCl 3 realizes the same Kitaev physics but is highly amenable to neutron investigation. Our measurements confirm the requisite strong spin-orbit coupling, and a low temperature 2 magnetic order that matches the predicted phase proximate to the QSL. We also show that stacking faults, inherent to the highly 2D nature of the material, readily explain some puzzling results to date. Measurements of the dynamical response functions, especially at energies and temperatures above that where interlayer effects are manifest, are naturally accounted for in terms of deconfinement physics expected for QSLs. Via a comparison to the recently calculated dynamics from gauge flux excitations and Majorana fermions of the pure Kitaev model we propose α-RuCl 3 as the prime candidate for experimental realization of fractionalized Kitaev physics.Exotic physics associated with frustrated quantum magnets is an enduring theme in condensed matter research. The formation of quantum spin liquids (QSL) The Kitaev model consists of a set of spin-1/2 moments � ���⃗ � arrayed on a honeycomb lattice. The Kitaev couplings, of strength K in eqn.(1) are highly anisotropic with a different spin component interacting for each of the three bonds of the honeycomb lattice. In actual materials a Heisenberg interaction (J) is also generally expected to be present, giving rise to the Heisenberg-Kitaev (H-K) Hamiltonian given by 11 .where, for example, m is the component of the spin directed along the bond connecting spins (i,j). The QSL phase of the pure Kitaev model (J=0), for both ferro and antiferromagnetic K, is stable for relatively small Heisenberg perturbations.Remarkably the Hamiltonian (1) has been proposed to accurately describe octahedrallycoordinated magnetic systems, Fig. 1 21 -27 . Whilst these studies lend support to the material as a potential Kitaev material, conflicting results centering on the low temperature magnetic properties have hindered progress. To resolve this we undertake a comprehensive evaluation of the magnetic and spin orbit properties of α-RuCl 3 , and further measure the dynamical response establishing this as a material proximate to the widely searched for quantum spin liquid.We begin by investigating the crystal and m...

The Kitaev quantum spin liquid (KQSL) is an exotic emergent state of matter exhibiting Majorana fermion and gauge flux excitations. The magnetic insulator α-RuCl is thought to realize a proximate KQSL. We used neutron scattering on single crystals of α-RuCl to reconstruct dynamical correlations in energy-momentum space. We discovered highly unusual signals, including a column of scattering over a large energy interval around the Brillouin zone center, which is very stable with temperature. This finding is consistent with scattering from the Majorana excitations of a KQSL. Other, more delicate experimental features can be transparently associated with perturbations to an ideal model. Our results encourage further study of this prototypical material and may open a window into investigating emergent magnetic Majorana fermions in correlated materials.

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2 The Kitaev model on a honeycomb lattice predicts a paradigmatic quantum spin liquid (QSL) exhibiting Majorana Fermion excitations. The insight that Kitaev physics might be realized in practice has stimulated investigations of candidate materials, recently including α-RuCl3. In all the systems studied to date, significant non-Kitaev interactions induce magnetic order at low temperature. However, inplane magnetic fields of roughly 8 Tesla suppress the long-range magnetic order in α-RuCl3 raising the intriguing possibility of a field-induced QSL exhibiting non-Abelian quasiparticle excitations. Here we present inelastic neutron scattering in α-RuCl3 in an applied magnetic field. At a field of 8 Tesla the spin waves characteristic of the ordered state vanish throughout the Brillouin zone. The remaining single dominant feature of the response is a broad continuum centered at the Γ point, previously identified as a signature of fractionalized excitations. This provides compelling evidence that a field-induced QSL state has been achieved. 3 The Kitaev model on a honeycomb lattice [1] has been exactly solved to reveal a unique quantum spin liquid (QSL) exhibiting itinerant Majorana Fermion and gauge-flux excitations. The Kitaev candidate system α-RuCl3 is an insulating magnetic material comprised of van der Waals coupled honeycomb layers of 4d 5 Ru 3+ cations nearly centered in edge-sharing RuCl6 octahedra. A strong cubic crystal field combined with spin-orbit coupling leads to a Kramer's doublet, nearly perfect J = 1/2 ground state [2][3][4], thus satisfying the conditions necessary for producing Kitaev couplings in the low energy Hamiltonian [5]. Similar to the widely studied honeycomb [6] and hyper-honeycomb [7] Iridates, at low temperatures α-RuCl3 exhibits small-moment antiferromagnetic zigzag order [3,[8][9][10][11] with TN ≈ 7 K for crystals with minimal stacking faults. In the zigzag state the magnetic excitation spectrum shows well-defined low-energy spin waves with minima at the M points (See Supplementary Materials (SM) Fig. S1 for the Brillouin Zone (BZ) definition) as well as a broad continuum that extends to much higher energies centered at the Γ points [12,13]. Above TN the spin waves disappear but the continuum remains, essentially unchanged until high temperatures of the order of 100 K [3,12,13]. In analogy with the situation for coupled spin-½ antiferromagnetic Heisenberg chains [14], the high energy part of the continuum has been interpreted as a signature of fractionalized excitations [3,12,13]. The overall features of the inelastic neutron scattering (INS) response resemble those of the Kitaev QSL [15][16][17] and are consistent with an unusual response seen in Raman scattering [16,18,19], suggesting that the system is proximate to a QSL state exhibiting magnetic Majorana fermion excitations [3,12,13]. Magnetic field offers a clean quantum tuning parameter for Kitaev materials [7][8][9]20] and can be applied on large single crystals facilitating INS studies. It is known to suppress the magnetic ord...

The honeycomb Kitaev-Heisenberg model is a source of a quantum spin liquid with Majorana fermions and gauge flux excitations as fractional quasiparticles. Here we unveil the highly unusual low-temperature heat conductivity κ of α-RuCl_{3}, a prime candidate for realizing such physics: beyond a magnetic field of B_{c}≈7.5  T, κ increases by about one order of magnitude, both for in-plane as well as out-of-plane transport. This clarifies the unusual magnetic field dependence unambiguously to be the result of severe scattering of phonons off putative Kitaev-Heisenberg excitations in combination with a drastic field-induced change of the magnetic excitation spectrum. In particular, an unexpected, large energy gap arises, which increases linearly with the magnetic field, reaching remarkable ℏω_{0}/k_{B}≈50  K at 18 T.

An external magnetic field can induce a transition in α-RuCl3 from an ordered zigzag state to a disordered state that is possibly related to the Kitaev quantum spin liquid. Here we present new field dependent inelastic neutron scattering and magnetocaloric effect measurements implying the existence of an additional transition out of the quantum spin liquid phase at an upper field limit Bu. The neutron scattering shows three distinct regimes of magnetic response. In the low field ordered state the response shows magnon peaks; the intermediate field regime shows only continuum scattering, and above Bu the response shows sharp magnon peaks at the lower bound of a strong continuum. Measurable dispersion of magnon modes along the (0, 0, L) direction implies non-negligible inter-plane interactions. Combining the magnetocaloric effect measurements with other data a T − B phase diagram is constructed. The results constrain the range where one might expect to observe quantum spin liquid behavior in α-RuCl3. arXiv:1903.00056v3 [cond-mat.str-el]

We report measurements of optical absorption in the zigzag antiferromagnet α-RuCl_{3} as a function of temperature T, magnetic field B, and photon energy ℏω in the range ∼0.3-8.3 meV, using time-domain terahertz spectroscopy. Polarized measurements show that threefold rotational symmetry is broken in the honeycomb plane from 2 to 300 K. We find a sharp absorption peak at 2.56 meV upon cooling below the Néel temperature of 7 K at B=0 that we identify as the magnetic-dipole excitation of a zero-wave-vector magnon, or antiferromagnetic resonance (AFMR). With the application of B, the AFMR broadens and shifts to a lower frequency as long-range magnetic order is lost in a manner consistent with transitioning to a spin-disordered phase. From a direct, internally calibrated measurement of the AFMR spectral weight, we place an upper bound on the contribution to the dc susceptibility from a magnetic excitation continuum.

We present high-field electron spin resonance (ESR) studies of the honeycomb-lattice material α-RuCl3, a prime candidate to exhibit Kitaev physics. Two modes of antiferromagnetic resonance were detected in the zigzag ordered phase, with magnetic field applied in the ab plane. A very rich excitation spectrum was observed in the field-induced quantum paramagnetic phase. The obtained data are compared with results of recent numerical calculations, strongly suggesting a very unconventional multiparticle character of the spin dynamics in α-RuCl3. The frequency-field diagram of the lowest-energy ESR mode is found consistent with the behavior of the field-induced energy gap, revealed by thermodynamic measurements.