A quantum spin liquid is an exotic quantum state of matter in which spins are highly entangled and remain disordered down to zero temperature. Such a state of matter is potentially relevant to high-temperature superconductivity and quantum-information applications, and experimental identification of a quantum spin liquid state is of fundamental importance for our understanding of quantum matter. Theoretical studies have proposed various quantum-spin-liquid ground states [1][2][3][4] , most of which are characterized by exotic spin excitations with fractional quantum numbers (termed 'spinon'). Here, we report neutron scattering measurements that reveal broad spin excitations covering a wide region of the Brillouin zone in a triangular antiferromagnet YbMgGaO 4 . The observed diffusive spin excitation persists at the lowest measured energy and shows a clear upper excitation edge, which is consistent with the particle-hole excitation of a spinon Fermi surface. Our results therefore point to a QSL state with a spinon Fermi surface in YbMgGaO 4 that has a perfect spin-1/2 triangular lattice as in the original proposal 4 of quantum spin liquids.In 1973, Anderson proposed the pioneering idea of the quantum spin liquid (QSL) in the study of the triangular lattice Heisenberg antiferromagnet 4 . This idea was revived after the discovery in 1986 of high-temperature superconductivity 5 . A QSL, as currently understood, does not fit into Landau's conventional paradigm of symmetry breaking phases 1,2,6,7 , and is arXiv:1607.02615v2 [cond-mat.str-el] 31 Jul 2017 2 instead an exotic state of matter characterized by spinon excitations and emergent gauge structures [1][2][3]6 . The search for QSLs in models and materials [8][9][10][11][12] has been partly facilitated by the Oshikawa-Hastings-Lieb-Schultz-Mattis (OHLSM) theorem that may hint at the possibility of QSLs in Mott insulators with odd electron fillings and a global U(1) spin rotational symmetry [13][14][15] .Indeed, a continuum of spin excitations has been observed in a kagome-lattice material ZnCu 3 (OD) 6 Cl 2 (refs 12,16). However, the requirement of the U(1) spin rotational symmetry, prevents the application of OHLSM theorem in strong spin-orbit-coupled (SOC) Mott insulators in which the spin rotational symmetry is completely absent. A recent theory addressed this limitation of the OHLSM theorem, arguing that, as long as time-reversal symmetry is preserved, the ground state of an SOC Mott insulator with odd electron fillings must be exotic 17 .The newly discovered triangular antiferromagnet YbMgGaO 4 (refs 18,19) displays no indication of magnetic ordering or symmetry breaking at temperatures as low as 30 mK despite approximately 4 K for the spin interaction energy scale. Because of the strong SOC of the Yb electrons, YbMgGaO 4 was the first QSL to be proposed beyond the OHLSM theorem 19 . The thirteen 4 f electrons of the Yb 3+ ion form the spin-orbit-entangled Kramers doublets that are split by the D 3d crystal electric fields [20][21][22] . At temperatures co...

Elucidating the microscopic origin of nematic order in iron-based superconducting materials is important because the interactions that drive nematic order may also mediate the Cooper pairing 1 .Nematic order breaks fourfold rotational symmetry in the iron plane, which is believed to be driven by either orbital or spin degrees of freedom [1][2][3][4][5] . However, as the nematic phase often develops at a temperature just above or coincides with a stripe magnetic phase transition, experimentally determining the dominant driving force of nematic order is difficult 1,6 . Here, we use neutron scat- tering to study structurally the simplest iron-based superconductor FeSe (ref. 7), which displays a nematic (orthorhombic) phase transition at T s = 90 K, but does not order antiferromagnetically.Our data reveal substantial stripe spin fluctuations, which are coupled with orthorhombicity and are enhanced abruptly on cooling to below T s . Moreover, a sharp spin resonance develops in the superconducting state, whose energy (∼ 4 meV) is consistent with an electron boson coupling mode revealed by scanning tunneling spectroscopy 8 , thereby suggesting a spin fluctuation-mediated signchanging pairing symmetry. By normalizing the dynamic susceptibility into absolute units, we show that the magnetic spectral weight in FeSe is comparable to that of the iron arsenides 9,10 . Our findings support recent theoretical proposals that both nematicity and superconductivity are driven by spin fluctuations 1,2,11-14 .Most parent compounds of iron-based superconductors exhibit a stripe-type long-range antiferromagnetic (AFM) order which is pre-empted by a nematic order: a correlation of electronic states which breaks rotational, but not translational, symmetry. Superconductivity emerges when the magnetic and nematic order are partially or completely suppressed by chemical doping or by the application of pressure 1,6 . The stripe AFM order consists of columns of parallel spins along the orthorhombic b direction, together with antiparallel spins along the a direction. Similar to the stripe AFM order, the nematic order also breaks the fourfold rotational symmetry, which is signaled by the tetragonal to orthorhombic structure phase transition and pronounced in-plane anisotropy of electronic and magnetic properties 1,6,[15][16][17][18] . It has been proposed that nematicity could be driven either by orbital or spin fluctuations, and that orbital fluctuations tend to lead to a sign-preserving s ++ -wave pairing, while spin fluctuations favor a sign-changing s ± -wave or d-wave pairing [1][2][3][4][5][6]14,19,20 . However, as orbital and spin degrees of freedom are coupled and could be easily affected by the nearby stripe magnetic order, it remains elusive which of them is the primary driving force of nematicity [1][2][3][4][5]14,19 .FeSe (T c ≈ 8 K) has attracted great attention not only because of the simple crystal structure (Fig. 1a), 3 but also because it displays a variety of exotic properties unprecedented for other iron based superconduc...

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The anisotropy of the magnetic excitations in BaFe2As2 was studied by polarized inelastic neutron scattering which allows one to separate the components of the magnetic response. Despite the inplane orientation of the static ordered moment we find the in-plane polarized magnons to exhibit a larger gap than the out-of-plane polarized ones indicating very strong single-ion anisotropy within the layers. It costs more energy to rotate a spin within the orthorhombic a-b plane than rotating it perpendicular to the FeAs layers.

The elucidation of the pseudogap phenomenon of the cuprates, a set of anomalous physical properties below the characteristic temperature T * and above the superconducting transition temperature T c , has been a major challenge in condensed matter physics for the past two decades [1]. Following initial indications of broken time-reversal symmetry in photoemission experiments [2], recent polarized neutron diffraction work demonstrated the universal existence of an unusual magnetic order below T * [3,4]. These findings have the profound implication that the pseudogap regime constitutes a genuine new phase of matter rather than a mere crossover phenomenon. They are furthermore consistent with a particular type of order involving circulating orbital currents, and with the notion that the phase diagram is controlled by a quantum critical point [5]. Here we report inelastic neutron scattering results for HgBa 2 CuO 4+δ (Hg1201) that reveal a fundamental collective magnetic mode associated with the unusual order, and that further support this picture. The mode's intensity rises below the same temperature T * and its dispersion is weak, as expected for an Ising-like order parameter [6]. Its energy of 52-56 meV and its enormous integrated spectral weight render it a new candidate for the hitherto unexplained ubiquitous electron-boson coupling features observed in spectroscopic studies [7][8][9][10].Inelastic neutron scattering (INS) is the most direct probe of magnetic excitations in solids. In the present work, we employed both spin-polarized and unpolarized INS measurements. The use of spin-polarized neutrons was crucial to unambiguously identify the magnetic response reported here, because such neutrons are separately collected according to whether their spins have or have not been flipped in the scattering process, which renders magnetic and nuclear scattering clearly distinguishable (Supplementary Information Section 1). Our measurements were carried out on three samples made of co-aligned crystals, which were grown by a self-flux method [11] and free from substantial macroscopic impurity phases and inhomogeneity (SI Section 2). Hg1201 exhibits the highest value of T c of all cuprates with one copper-oxygen plane per unit cell, has a simple tetragonal structure, and is furthermore thought to be relatively free of disorder effects [12,13]. The scattering wave vector is quoted as Q = Ha* + Kb* + Lc* ≡ (H,K,L) in reciprocal lattice units (r.l.u.). Neutron intensities are presented in normalized units in most figures to facilitate a direct comparison of the intensity among the measurements (SI Section 3).Spin-polarized INS data ( Fig. 1) demonstrate the existence of a magnetic excitation throughout the two-dimensional (2D) Brillouin zone in a nearly-optimally-doped sample (T c = 94.5 ± 2 K, denoted as OP95). Energy scans in the spin-flip channel reveal a resolution-limited feature at low temperatures, with a weak dispersion and a maximum of 56 meV at the 2D zone-corner q AF (H = K = 0.5). The feature cannot be due to a p...