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...

Muon spin relaxation (μSR) experiments on single crystals of the structurally perfect triangular antiferromagnet YbMgGaO_{4} indicate the absence of both static long-range magnetic order and spin freezing down to 0.048 K in a zero field. Below 0.4 K, the μ^{+} spin relaxation rates, which are proportional to the dynamic correlation function of the Yb^{3+} spins, exhibit temperature-independent plateaus. All these μSR results unequivocally support the formation of a gapless U(1) quantum spin liquid ground state in the triangular antiferromagnet YbMgGaO_{4}.

The low temperature state of CeRu2Al10 has been studied by neutron powder diffraction and muon spin relaxation (µ + SR). By combining both techniques, we prove that the transition occurring below T * ∼27K, which has been the subject of considerable debate, is unambiguously magnetic due to the ordering of the Ce sublattice. The magnetic structure with propagation vector k=(1,0,0) involves collinear antiferromagnetic alignment of the Ce moments along the c-axis of the Cmcm space group with a reduced moment of 0.34(2)µB . No structural changes within the resolution limit have been detected below the transition temperature. However, the temperature dependence of the magnetic Bragg peaks and the muon precession frequency show an anomaly around T2 ∼12K indicating a possible second transition.

We report the synthesis, structure, and magnetic and transport properties of a new ternary intermetallic compound PrRhSn3 which crystallizes in LaRuSn3-type cubic structure (space group P m3n). At low applied fields the dc magnetic susceptibility exhibits a sharp anomaly below 6 K with an irreversible behavior in zero field cooled (ZFC) and field cooled (FC) susceptibility below 5.5 K. The ac susceptibility exhibits a frequency dependent anomaly revealing a spin-glass behavior with a freezing temperature, T f = 4.3 K. The observation of spin-glass behavior is further supported by a very slow decay of thermo-remnant magnetization (mean relaxation time τ = 2149 s). However, a small jump at very low field in the isothermal magnetization at 2 K and a weak anomaly in the specific heat near 5.5 K reveal the presence of ferromagnetic clusters. The frequency dependence of the transition temperature T f in the ac susceptibility obeys the Vogel-Fulcher law, ν = ν0exp[−Ea/kB(T f − T0)] with activation energy Ea/kB = 19.1 K. This together with an intermediate value of the parameter δT f = ∆T f /T f ∆(log 10 ν) = 0.086 provide an evidence for the formation of a cluster-glass state in PrRhSn3. Further, we have analyzed the frequency dependence of transition temperature within the framework of critical slowing down, τ = τ0[(T f −TSG)/TSG) −zν ′ ] and found the characteristic time constant τ0 = 2.04 × 10 −10 s and critical exponent zν ′ = 10.9, which also support a cluster spin-glass behavior in this compound. The magnetic contribution of the specific heat reveals a broad Schottky-type anomaly centered around 10 K and the analysis based on the crystal electric field model indicates a singlet ground state. Further, below T f the magnetic part of the specific heat exhibits a T 3/2 temperature dependence. The strong influence of the crystal electric field and a T 3/2 temperature dependence are also seen in the electrical resistivity which reveals a metallic character and a high magnetoresistance. We also obtain a surprisingly large value of Sommerfeld-Wilson ratio RW ≈ 247.

We present the structural characterization and low-temperature magnetism of the triangular-lattice delafossite NaYbO 2 . Synchrotron x-ray diffraction and neutron scattering exclude both structural disorder and crystalelectric-field randomness, whereas heat-capacity measurements and muon spectroscopy reveal the absence of magnetic order and persistent spin dynamics down to at least 70 mK. Continuous magnetic excitations with the low-energy spectral weight accumulating at the K-point of the Brillouin zone indicate the formation of a novel spin-liquid phase in a triangular antiferromagnet. This phase is gapless and shows a non-trivial evolution of the low-temperature specific heat. Our work demonstrates that NaYbO 2 practically gives the most direct experimental access to the spin-liquid physics of triangular antiferromagnets.