Topological magnon band structure of emergent Landau levels in a skyrmion lattice.

The motion of a spin excitation across topologically nontrivial magnetic order exhibits a deflection that is analogous to the effect of the Lorentz force on an electrically charged particle in an orbital magnetic field. We used polarized inelastic neutron scattering to investigate the propagation of magnons (i.e., bosonic collective spin excitations) in a lattice of skyrmion tubes in manganese silicide. For wave vectors perpendicular to the skyrmion tubes, the magnon spectra are consistent with the formation of finely spaced emergent Landau levels that are characteristic of the fictitious magnetic field used to account for the nontrivial topological winding of the skyrmion lattice. This provides evidence of a topological magnon band structure in reciprocal space, which is borne out of the nontrivial real-space topology of a magnetic order.

Coexistence of Ferromagnetic and Stripe-Type Antiferromagnetic Spin Fluctuations in YFe_{2}Ge_{2}.

We report neutron scattering measurements of single-crystalline YFe_{2}Ge_{2} in the normal state, which has the same crystal structure as the 122 family of iron pnictide superconductors. YFe_{2}Ge_{2} does not exhibit long-range magnetic order but exhibits strong spin fluctuations. Like the iron pnictides, YFe_{2}Ge_{2} displays anisotropic stripe-type antiferromagnetic spin fluctuations at (π, 0, π). More interesting, however, is the observation of strong spin fluctuations at the in-plane ferromagnetic wave vector (0, 0, π). These ferromagnetic spin fluctuations are isotropic in the (H, K) plane, whose intensity exceeds that of stripe spin fluctuations. Both the ferromagnetic and stripe spin fluctuations remain gapless down to the lowest measured energies. Our results naturally explain the absence of magnetic order in YFe_{2}Ge_{2} and also imply that the ferromagnetic correlations may be a key ingredient for iron-based materials.

Spin Fluctuations in Sr_{2}RuO_{4} from Polarized Neutron Scattering: Implications for Superconductivity.

Triplet pairing in Sr_{2}RuO_{4} was initially suggested based on the hypothesis of strong ferromagnetic spin fluctuations. Using polarized inelastic neutron scattering, we accurately determine the full spectrum of spin fluctuations in Sr_{2}RuO_{4}. Besides the well-studied incommensurate magnetic fluctuations, we do find a sizable quasiferromagnetic signal, quantitatively consistent with all macroscopic and microscopic probes. We use this result to address the possibility of magnetically driven triplet superconductivity in Sr_{2}RuO_{4}. We conclude that, even though the quasiferromagnetic signal is stronger and sharper than previously anticipated, spin fluctuations alone are not enough to generate a triplet state strengthening the need for additional interactions or an alternative pairing scenario.

Fractionalized excitations in the partially magnetized spin liquid candidate YbMgGaO4.

Quantum spin liquids (QSLs) are exotic states of matter characterized by emergent gauge structures and fractionalized elementary excitations. The recently discovered triangular lattice antiferromagnet YbMgGaO4 is a promising QSL candidate, and the nature of its ground state is still under debate. Here we use neutron scattering to study the spin excitations in YbMgGaO4 under various magnetic fields. Our data reveal a dispersive spin excitation continuum with clear upper and lower excitation edges under a weak magnetic field (H = 2.5 T). Moreover, a spectral crossing emerges at the Γ point at the Zeeman-split energy. The corresponding redistribution of the spectral weight and its field-dependent evolution are consistent with the theoretical prediction based on the inter-band and intra-band spinon particle-hole excitations associated with the Zeeman-split spinon bands, implying the presence of fractionalized excitations and spinon Fermi surfaces in the partially magnetized QSL state in YbMgGaO4.

Spin Fluctuations Drive the Inverse Magnetocaloric Effect in Mn_{5}Si_{3}.

Inelastic neutron scattering measurements are performed on single crystals of the antiferromagnetic compound Mn_{5}Si_{3} in order to investigate the relation between the spin dynamics and the magnetothermodynamics properties. It is shown that, among the two stable antiferromagnetic phases of this compound, the high temperature one has an unusual magnetic excitation spectrum where propagative spin waves and diffuse spin fluctuations coexist. Moreover, it is evidenced that the inverse magnetocaloric effect of Mn_{5}Si_{3}, the cooling by adiabatic magnetization, is associated with field induced spin fluctuations.

Control of Chiral Magnetism Through Electric Fields in Multiferroic Compounds above the Long-Range Multiferroic Transition.

Polarized neutron scattering experiments reveal that type-II multiferroics allow for controlling the spin chirality by external electric fields even in the absence of long-range multiferroic order. In the two prototype compounds TbMnO_{3} and MnWO_{4}, chiral magnetism associated with soft overdamped electromagnons can be observed above the long-range multiferroic transition temperature T_{MF}, and it is possible to control it through an electric field. While MnWO_{4} exhibits chiral correlations only in a tiny temperature interval above T_{MF}, in TbMnO_{3} chiral magnetism can be observed over several kelvin up to the lock-in transition, which is well separated from T_{MF}.

Spin Resonance and Magnetic Order in an Unconventional Superconductor.

Unconventional superconductivity in many materials is believed to be mediated by magnetic fluctuations. It is an open question how magnetic order can emerge from a superconducting condensate and how it competes with the magnetic spin resonance in unconventional superconductors. Here we study a model d-wave superconductor that develops spin-density wave order, and find that the spin resonance is unaffected by the onset of static magnetic order. This result suggests a scenario, in which the resonance in Nd_{0.05}Ce_{0.95}CoIn_{5} is a longitudinal mode with fluctuating moments along the ordered magnetic moments.

Anisotropic resonance modes emerging in an antiferromagnetic superconducting state.

Two strong arguments in favor of magnetically driven unconventional superconductivity arise from the coexistence and closeness of superconducting and magnetically ordered phases on the one hand, and from the emergence of magnetic spin-resonance modes at the superconducting transition on the other hand. Combining these two arguments one may ask about the nature of superconducting spin-resonance modes occurring in an antiferromagnetic state. This problem can be studied in underdoped BaFe2 As2, for which the local coexistence of large moment antiferromagnetism and superconductivity is well established by local probes. However, polarized neutron scattering experiments are required to identify the nature of the resonance modes. In the normal state of Co underdoped BaFe2 As2 the antiferromagnetic order results in broad magnetic gaps opening in all three spin directions that are reminiscent of the magnetic response in the parent compound. In the superconducting state two distinct anisotropic resonance excitations emerge, but in contrast to numerous studies on optimum and over-doped BaFe2 As2 there is no isotropic resonance excitation. The two anisotropic resonance modes appearing within the antiferromagnetic phase are attributed to a band selective superconducting state, in which longitudinal magnetic excitations are gapped by antiferromagnetic order with sizable moment.

Absence of a Large Superconductivity-Induced Gap in Magnetic Fluctuations of Sr_{2}RuO_{4}.

Inelastic neutron scattering experiments on Sr_{2}RuO_{4} determine the spectral weight of the nesting induced magnetic fluctuations across the superconducting transition. There is no observable change at the superconducting transition down to an energy of ∼0.35 meV, which is well below the 2Δ values reported in several tunneling experiments. At this and higher energies magnetic fluctuations clearly persist in the superconducting state. Only at energies below ∼0.3 meV can evidence for partial suppression of spectral weight in the superconducting state be observed. This strongly suggests that the one-dimensional bands with the associated nesting fluctuations do not form the active, highly gapped bands in the superconducting pairing in Sr_{2}RuO_{4}.

Evidence for a spinon Fermi surface in a triangular-lattice quantum-spin-liquid candidate.

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, most of which are characterized by exotic spin excitations with fractional quantum numbers (termed 'spinons'). Here we report neutron scattering measurements of the triangular-lattice antiferromagnet YbMgGaO4 that reveal broad spin excitations covering a wide region of the Brillouin zone. The observed diffusive spin excitation persists at the lowest measured energy and shows a clear upper excitation edge, consistent with the particle-hole excitation of a spinon Fermi surface. Our results therefore point to the existence of a quantum spin liquid state with a spinon Fermi surface in YbMgGaO4, which has a perfect spin-1/2 triangular lattice as in the original proposal of quantum spin liquids.

Commensurate antiferromagnetic excitations as a signature of the pseudogap in the tetragonal high-Tc cuprate HgBa2CuO(4+δ).

Antiferromagnetic correlations have been argued to be the cause of the d-wave superconductivity and the pseudogap phenomena exhibited by the cuprates. Although the antiferromagnetic response in the pseudogap state has been reported for a number of compounds, there exists no information for structurally simple HgBa2CuO(4+δ). Here we report neutron-scattering results for HgBa2CuO(4+δ) (superconducting transition temperature Tc≈71 K, pseudogap temperature T*≈305 K) that demonstrate the absence of the two most prominent features of the magnetic excitation spectrum of the cuprates: the X-shaped 'hourglass' response and the resonance mode in the superconducting state. Instead, the response is Y-shaped, gapped and significantly enhanced below T*, and hence a prominent signature of the pseudogap state.

Strong interplay between stripe spin fluctuations, nematicity and superconductivity in FeSe.

In iron-based superconductors the interactions driving the nematic order (that breaks four-fold rotational symmetry in the iron plane) may also mediate the Cooper pairing. The experimental determination of these interactions, which are believed to depend on the orbital or the spin degrees of freedom, is challenging because nematic order occurs at, or slightly above, the ordering temperature of a stripe magnetic phase. Here, we study FeSe (ref. )-which exhibits a nematic (orthorhombic) phase transition at Ts = 90 K without antiferromagnetic ordering-by neutron scattering, finding substantial stripe spin fluctuations coupled with the nematicity that are enhanced abruptly on cooling through Ts. A sharp spin resonance develops in the superconducting state, whose energy (∼4 meV) is consistent with an electron-boson coupling mode revealed by scanning tunnelling spectroscopy. The magnetic spectral weight in FeSe is found to be comparable to that of the iron arsenides. Our results support recent theoretical proposals that both nematicity and superconductivity are driven by spin fluctuations.

Highly Anisotropic Magnon Dispersion in Ca_{2}RuO_{4}: Evidence for Strong Spin Orbit Coupling.

The magnon dispersion in Ca_{2}RuO_{4} has been determined by inelastic neutron scattering on single crytals containing 1% of Ti. The dispersion is well described by a conventional Heisenberg model suggesting a local moment model with nearest neighbor interaction of J=8 meV. Nearest and next-nearest neighbor interaction as well as interlayer coupling parameters are required to properly describe the entire dispersion. Spin-orbit coupling induces a very large anisotropy gap in the magnetic excitations in apparent contrast with a simple planar magnetic model. Orbital ordering breaking tetragonal symmetry, and strong spin-orbit coupling can thus be identified as important factors in this system.

Magnetic moments induce strong phonon renormalization in FeSi.

The interactions of electronic, spin and lattice degrees of freedom in solids result in complex phase diagrams, new emergent phenomena and technical applications. While electron-phonon coupling is well understood, and interactions between spin and electronic excitations are intensely investigated, only little is known about the dynamic interactions between spin and lattice excitations. Noncentrosymmetric FeSi is known to undergo with increasing temperature a crossover from insulating to metallic behaviour with concomitant magnetic fluctuations, and exhibits strongly temperature-dependent phonon energies. Here we show by detailed inelastic neutron-scattering measurements and ab initio calculations that the phonon renormalization in FeSi is linked to its unconventional magnetic properties. Electronic states mediating conventional electron-phonon coupling are only activated in the presence of strong magnetic fluctuations. Furthermore, phonons entailing strongly varying Fe-Fe distances are damped via dynamic coupling to the temperature-induced magnetic moments, highlighting FeSi as a material with direct spin-phonon coupling and multiple interaction paths.

Universality of the dispersive spin-resonance mode in superconducting BaFe2As2.

Spin fluctuations in superconducting BaFe2(As(1-x)P(x))2 (x=0.34, T(c)=29.5 K) are studied using inelastic neutron scattering. Well-defined commensurate magnetic signals are observed at (π, 0), which is consistent with the nesting vector of the Fermi surface. Antiferromagnetic (AFM) spin fluctuations in the normal state exhibit a three-dimensional character reminiscent of the AFM order in nondoped BaFe2As2. A clear spin gap is observed in the superconducting phase forming a peak whose energy is significantly dispersed along the c axis. The bandwidth of dispersion becomes larger with approaching the AFM ordered phase universally in all superconducting BaFe2As2, indicating that the dispersive feature is attributed to three-dimensional AFM correlations. The results suggest a strong relationship between the magnetism and superconductivity.

Splitting of resonance excitations in nearly optimally doped Ba(Fe0.94Co0.06)2As2: an inelastic neutron scattering study with polarization analysis.

Magnetic excitations in Ba(Fe0.94Co0.06)2As2: are studied by polarized inelastic neutron scattering above and below the superconducting transition. In the superconducting state, we find clear evidence for two resonancelike excitations. At a higher energy of about 8 meV, there is an isotropic resonance mode with weak dispersion along the c direction. In addition, we find a lower excitation at 4 meV that appears only in the c-polarized channel and whose intensity strongly varies with the l component of the scattering vector. These resonance excitations behave remarkably similar to the gap modes in the antiferromagnetic phase of the parent compound BaFe2As2.

Hourglass dispersion in overdoped single-layered manganites.

The incommensurate stripelike magnetic ordering in two single-layered manganites, Nd0.33Sr1.67MnO4 and Pr0.33Ca1.67MnO4, is found to exhibit an hourglasslike excitation spectrum very similar to that seen in various cuprates superconductors, but only for sufficiently short correlation lengths. Several characteristic features of an hourglass dispersion can be identified: enhancement of intensity at the merging of the incommensurate branches, rotation of the intensity maxima with higher energy transfer, and suppression of the outward-dispersing branches at low energy. The correlation length of the magnetic ordering and the large ratio of intra- to interstripe couplings are identified as the decisive parameters causing the hourglass shape of the spectrum.

Inelastic neutron-scattering measurements of incommensurate magnetic excitations on superconducting LiFeAs single crystals.

Magnetic correlations in superconducting LiFeAs were studied by elastic and by inelastic neutron-scattering experiments. There is no indication for static magnetic ordering, but inelastic correlations appear at the incommensurate wave vector (0.5±Î´,0.5-/+δ,0) with δ~0.07 slightly shifted from the commensurate ordering observed in other FeAs-based compounds. The incommensurate magnetic excitations respond to the opening of the superconducting gap by a transfer of spectral weight.

Evidence for three fluctuation channels in the spin resonance of the unconventional superconductor CeCoIn5.

Polarized inelastic neutron scattering under a magnetic field is used to get a microscopic insight into the spin resonance of the heavy fermion superconductor CeCoIn(5). The resonance line shape is found to depend on the neutron polarization: Some of the spectral weight is common to the two polarization channels while the remaining part is distributed equally between them. This is evidence for the spin resonance being a degenerate mode with three fluctuation channels: A Zeeman split contribution and an additional longitudinal mode.