Antiferromagnetism is relevant to high temperature (high-T c ) superconductivity because copper oxide and iron arsenide high-T c superconductors arise from electron-or hole-doping of their antiferromagnetic (AF) ordered parent compounds 1-6 . There are two broad classes of explanation for the phenomenon of antiferromagnetism: in the "local moment" picture, appropriate for the insulating copper oxides 1 , AF interactions are well described by a Heisenberg Hamiltonian 7,8 ; while in the "itinerant model", suitable for metallic chromium, AF order arises from quasiparticle excitations of a nested Fermi surface 9,10 . There has been contradictory evidence regarding the microscopic origin of the AF order in iron arsenide materials 5,6 , with some favoring a localized picture 11-15 while others supporting an

Elucidating the nature of the magnetism of a high-temperature superconductor is crucial for establishing its pairing mechanism. The parent compounds of the cuprate and iron-pnictide superconductors exhibit Néel and stripe magnetic order, respectively. However, FeSe, the structurally simplest iron-based superconductor, shows nematic order (Ts=90 K), but not magnetic order in the parent phase, and its magnetic ground state is intensely debated. Here we report inelastic neutron-scattering experiments that reveal both stripe and Néel spin fluctuations over a wide energy range at 110 K. On entering the nematic phase, a substantial amount of spectral weight is transferred from the Néel to the stripe spin fluctuations. Moreover, the total fluctuating magnetic moment of FeSe is ∼60% larger than that in the iron pnictide BaFe2As2. Our results suggest that FeSe is a novel S=1 nematic quantum-disordered paramagnet interpolating between the Néel and stripe magnetic instabilities.

Geometrical constraints to the electronic degrees of freedom within condensed-matter systems often give rise to topological quantum states of matter such as fractional quantum Hall states, topological insulators, and Weyl semimetals 1-3 . In magnetism, theoretical studies predict an entangled magnetic quantum state with topological ordering and fractionalized spin excitations, the quantum spin liquid 4 . In particular, the so-called Kitaev spin model 5 , consisting of a network of spins on a honeycomb lattice, is predicted to host Majorana fermions as its excitations. By means of a combination of specific heat measurements and inelastic neutron scattering experiments, we demonstrate the emergence of Majorana fermions in single crystals of α-RuCl 3 , an experimental realization of the Kitaev spin lattice. The specific heat data unveils a two-stage release of magnetic entropy that is characteristic of localized and itinerant Majorana fermions. The neutron scattering results corroborate this picture by revealing quasielastic excitations at low energies around the Brillouin zone centre and an hour-glass-like magnetic continuum at high energies. Our results confirm the presence of Majorana fermions in the Kitaev quantum spin liquid and provide an opportunity to build a unified conceptual framework for investigating fractionalized excitations in condensed matter 1,6-8 .Quantum spin liquids (QSLs) are an unconventional electronic phase of matter characterized by an absence of magnetic longrange order down to zero temperature. They are typically predicted to occur in geometrically frustrated magnets such as triangular, kagome, and pyrochlore lattices 4 , and typically display a macroscopic degeneracy that stabilizes a topologically ordered ground state. The Kitaev QSL state arises as an exact solution of the ideal two-dimensional (2D) honeycomb lattice with bond-directional Ising-type interactions (H = J γ K S γ i S γ j ; γ = x, y, z) on the three dis-

We apply moderate-high-energy inelastic neutron scattering (INS) measurements to investigate Yb 3+ crystalline electric field (CEF) levels in the triangular spin-liquid candidate YbMgGaO4. Three CEF excitations from the ground-state Kramers doublet are centered at the energies~! = 39, 61, and 97 meV in agreement with the e↵ective spin-1/2 g-factors and experimental heat capacity, but reveal sizable broadening. We argue that this broadening originates from the site mixing between Mg 2+ and Ga 3+ giving rise to a distribution of Yb-O distances and orientations and, thus, of CEF parameters that account for the peculiar energy profile of the CEF excitations. The CEF randomness gives rise to a distribution of the e↵ective spin-1/2 g-factors and explains the unprecedented broadening of low-energy magnetic excitations in the fully polarized ferromagnetic phase of YbMgGaO4, although a distribution of magnetic couplings due to the Mg/Ga disorder may be important as well.PACS numbers: 75.10. Dg, 75.10.Kt, 78.70.Nx Introduction.-Quantum spin liquid (QSL) is a novel state of matter with zero entropy and without conventional symmetry breaking even at zero temperature. Such states were proposed to host 'spinons', exotic spin excitations with fractional quantum numbers [1][2][3]. Although many candidate QSL materials with two-dimensional or three-dimensional interaction topologies on the triangular, kagome, and pyrochlore lattices were reported [4][5][6][7][8][9][10][11][12][13][14][15][16][17], they typically suffer from magnetic or non-magnetic defects [18][19][20][21][22], spatial anisotropy [4,7,15], antisymmetric DzyaloshinskyMoriya anisotropy [23][24][25], and (or) interlayer magnetic couplings [25][26][27] that reduce or even completely release magnetic frustration [25,[27][28][29][30].Many of the aforementioned shortcomings can be remedied in a new triangular antiferromagnet YbMgGaO 4 that was recently reported by our group [31][32][33]. No spin freezing was detected down to at least 0.048 K, which is about 3% of the nearest-neighbor interaction J 0 ⇠ 1.5 K [33]. Residual spin entropy is nearly zero at 0.06 K, excluding any magnetic transitions at lower temperatures [31]. Below 0.4 K, thermodynamic properties evidence the putative QSL regime with temperature-independent magnetic susceptibility = const [33] and power-law behavior of the magnetic heat capacity, C m ⇠ T 2/3 [31], the observations that are consistent with theoretical predictions for the U(1) QSL ground state (GS) on the triangular lattice [34][35][36].Very recently, two inelastic neutron scattering (INS) studies of YbMgGaO 4 [37, 38] reported continuous excitations at transfer energies of 0.1 2.5 meV extending well above the energy scale of the magnetic coupling J 0 ⇠ 0.13 meV. These spectral features were identified as fractionalized excitations ('spinons') from the QSL GS [37]. Surprisingly, though, magnetic excitations remain very broad in both energy and wave-vector (Q) even in the almost fully polarized state at 7.8 T, where only narrow spin-wave e...