Spin-ice materials are magnetic substances in which the spin directions map onto hydrogen positions in water ice. Their low-temperature magnetic state has been predicted to be a phase that obeys a Gauss' law and supports magnetic monopole excitations: in short, a Coulomb phase. We used polarized neutron scattering to show that the spin-ice material Ho2Ti2O7 exhibits an almost perfect Coulomb phase. Our result proves the existence of such phases in magnetic materials and strongly supports the magnetic monopole theory of spin ice.

PACS numbers: * Electronic address: stockert@cpfs.mpg.de 1The origin of unconventional superconductivity, including high-temperature and heavy-fermion superconductivity, is still a matter of controversy. Spin excitations instead of phonons are thought to be responsible for the formation of Cooper pairs. Using inelastic neutron scattering, we present the first in-depth study of the magnetic excitation spectrum in momentum and energy space in the superconducting and the normal states of CeCu 2 Si 2 . A clear spin excitation gap is observed in the superconducting state. We determine a lowering of the magnetic exchange energy in the superconducting state, in an amount considerably larger than the superconducting condensation energy. Our findings identify the antiferromagnetic excitations as the major driving force for superconducting pairing in this prototypical heavy-fermion compound located near an antiferromagnetic quantum critical point.While conventional superconductivity (SC) is generally incompatible with magnetism, magnetic excitations seem to play an important role in the Cooper pair formation of unconventional superconductors such as the high-T c cuprates or the low-T c organic and heavyfermion (HF) superconductors. Since the discovery of SC in CeCu 2 Si 2 1 , antiferromagnetic (AF) spin excitations have been proposed as a viable mechanism for SC 2-4 . The discovery of SC at the boundary of AF order in CePd 2 Si 2 5 has pushed this notion into the framework of AF quantum criticality 6 . Unfortunately, such quantum critical points (QCPs) proximate to HF superconductors typically arise under pressure, which makes it difficult to probe their magnetic excitation spectrum.Here, we report a detailed study of the magnetic excitations in CeCu 2 Si 2 , which exhibits SC below T c ≈ 0.6 K. This prototypical HF compound is ideally suited for our purpose, since SC here is in proximity to an AF QCP already at ambient pressure (cf. Fig. 1(a)).As displayed in Fig. 1(b) CeCu 2 Si 2 crystallises in a structure with body-centred tetragonal symmetry and is one of the best studied HF superconductors and well characterised by low-temperature transport and thermodynamic measurements 7 . Moreover, those measurements in the field-induced normal state have already provided evidence that the QCP in this compound is of the three-dimensional (3D) spin-density-wave (SDW) type 8 . The spatial anisotropy of the spin fluctuations in superconducting CeCu 2 Si 2 was measured at T = 0.06 K and at an energy transfer ω = 0.2 meV and is shown in Fig. 1(c). These magnetic correlations display only a small anisotropy (a factor of 1.5) in the correlation lengths 2 between the [110] and the [001] direction. Therefore, these quite isotropic spin fluctuations are in line with thermodynamic and transport measurements exhibiting C/T = γ 0 − a √ T or ρ − ρ 0 = AT α , α = 1 − 1.5 8,9 , and strongly support a three-dimensional quantum critical SDW scenario 10 . We are able to identify the magnetic excitations in the normal state of paramagnetic, ...

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...

Magnetic properties D 9000Magnetic Coulomb Phase in the Spin Ice Ho2Ti2O7. -The existence of an almost perfect Coulomb phase, a phase that obeys Gauss law and supports magnetic monopole excitations in the spin-ice material Ho2Ti2O7 is demonstrated by polarized neutron scattering. Bound monopole pairs dominate at finite temperature, but unbound pairs become more important at low temperatures. The length of the longest Dirac strings is estimated to rise to macroscopic scales at temperatures below 1 K. The results strongly support the magnetic monopole theory of spin ice. -(FENNELL*, T.; DEEN, P. P.; WILDES, A. R.; SCHMALZL, K.; PRABHAKARAN, D.; BOOTHROYD, A. T.; ALDUS, R. J.; MCMORROW, D. F.; BRAMWELL, S. T.; Sci. (Washington, D. C., USA) 326 (2009) 5951, 415-417; Inst. Laue-Langevin, CNRS, Univ. Joseph Fourier, F-38042 Grenoble, Fr.; Eng.) -W. Pewestorf 51-015

We present a detailed study of magnetism in LuFe2O4, combining magnetization measurements with neutron and soft x-ray diffraction. The magnetic phase diagram in the vicinity of TN involves a metamagnetic transition separating an antiferro-and a ferrimagnetic phase. For both phases the spin structure is refined by neutron diffraction. Observed diffuse magnetic scattering far above TN is explained in terms of near degeneracy of the magnetic phases.