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...
Most unconventional superconductors, including cuprates and iron-based superconductors, are derived from chemical doping or application of pressure on their collinearly magnetic-ordered parent compounds [1][2][3][4][5] . The recently discovered pressure-induced superconductor CrAs, as a rare example of a non-collinear helimagnetic superconductor, has therefore generated great interest in understanding microscopic magnetic properties and their interplay with superconductivity 6-8 . Unlike cuprates and iron based superconductors where the magnetic moment direction barely changes upon doping, here we show that CrAs exhibits a spin reorientation from the ab plane to the ac plane, along with an abrupt drop of the magnetic propagation vector at a critical pressure (P c ≈ 0.6 GPa). This magnetic phase transition coincides with the emergence of bulk superconductivity, indicating a direct connection between magnetism and superconductivity. With further increasing pressure, the magnetic order completely disappears near the optimal T c regime (P ≈ 0.94 GPa). Moreover, the Cr magnetic moments between nearest neighbors tend to be aligned antiparallel with increasing pressure toward the optimal superconductivity regime. Our findings suggest that the non-collinear helimagnetic or-
Heavily electron-doped iron-selenide high-transition-temperature (high-T c ) superconductors, which have no hole Fermi pockets, but have a notably high T c , have challenged the prevailing s ± pairing scenario originally proposed for iron pnictides containing both electron and hole pockets. The microscopic mechanism underlying the enhanced superconductivity in heavily electron-doped iron-selenide remains unclear. Here, we used neutron scattering to study the spin excitations of the heavily electron-doped iron-selenide material Li 0.8 Fe 0.2 ODFeSe (T c = 41 K). Our data revealed nearly ring-shaped magnetic resonant excitations surrounding (π, π) at ∼21 meV. As the energy increased, the spin excitations assumed a diamond shape, and they dispersed outward until the energy reached ∼60 meV and then inward at higher energies. The observed energy-dependent momentum structure and twisted dispersion of spin excitations near (π, π) are analogous to those of hole-doped cuprates in several aspects, thus implying that such spin excitations are essential for the remarkably high T c in these materials.
Van der Waals magnet VI3 demonstrates intriguing magnetic properties that render it great for use in various applications. However, its microscopic magnetic structure has not been determined yet. Here, we report neutron diffraction and susceptibility measurements in VI3 that revealed a ferromagnetic order with the moment direction tilted from the 𝑐-axis by ∼36 ∘ at 4 K. A spin reorientation accompanied by a structure distortion within the honeycomb plane is observed, before the magnetic order completely disappears at 𝑇C = 50 K. The refined magnetic moment of ∼1.3𝜇B at 4 K is much lower than the fully ordered spin moment of 2𝜇B/V 3+ , suggesting the presence of a considerable orbital moment antiparallel to the spin moment and strong spin-orbit coupling in VI3. This results in strong magnetoelastic interactions that make the magnetic properties of VI3 easily tunable via strain and pressure.
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