Nematic Correlation Length in Iron-Based Superconductors Probed by Inelastic X-Ray Scattering.

Nematicity is ubiquitous in electronic phases of high-T_{c} superconductors, particularly in the Fe-based systems. We used inelastic x-ray scattering to extract the temperature-dependent nematic correlation length ξ from the anomalous softening of acoustic phonon modes in FeSe, underdoped Ba(Fe_{0.97}Co_{0.03})_{2}As_{2}, and optimally doped Ba(Fe_{0.94}Co_{0.06})_{2}As_{2}. In all cases, we find that ξ is well described by a power law (T-T_{0})^{-1/2} extending over a wide temperature range. Combined with the previously reported Curie-Weiss behavior of the nematic susceptibility, these results point to the mean-field character of the nematic transition, which we attribute to a sizable nematoelastic coupling that is likely detrimental to superconductivity.

Magnetic and Structural Quantum Phase Transitions in CeCu_{6-x}Au_{x} are Independent.

The heavy-fermion compound CeCu_{6-x}Au_{x} has become a model system for unconventional magnetic quantum criticality. For small Au concentrations 0≤x<0.16, the compound undergoes a structural transition from orthorhombic to monoclinic crystal symmetry at a temperature T_{s} with T_{s}→0 for x≈0.15. Antiferromagnetic order sets in close to x≈0.1. To shed light on the interplay between quantum-critical magnetic and structural fluctuations we performed neutron-scattering and thermodynamic measurements on samples with 0≤x≤0.3. The resulting phase diagram shows that the antiferromagnetic and monoclinic phase coexist in a tiny Au concentration range between x≈0.1 and 0.15. The application of hydrostatic and chemical pressure allows us to clearly separate the transitions from each other and to explore a possible effect of the structural transition on the magnetic quantum-critical behavior. Our measurements demonstrate that at low temperatures the unconventional quantum criticality exclusively arises from magnetic fluctuations and is not affected by the monoclinic distortion.

Emergence of coherence in the charge-density wave state of 2H-NbSe2.

A charge-density wave (CDW) state has a broken symmetry described by a complex order parameter with an amplitude and a phase. The conventional view, based on clean, weak-coupling systems, is that a finite amplitude and long-range phase coherence set in simultaneously at the CDW transition temperature T(cdw). Here we investigate, using photoemission, X-ray scattering and scanning tunnelling microscopy, the canonical CDW compound 2H-NbSe2 intercalated with Mn and Co, and show that the conventional view is untenable. We find that, either at high temperature or at large intercalation, CDW order becomes short-ranged with a well-defined amplitude, which has impacts on the electronic dispersion, giving rise to an energy gap. The phase transition at T(cdw) marks the onset of long-range order with global phase coherence, leading to sharp electronic excitations. Our observations emphasize the importance of phase fluctuations in strongly coupled CDW systems and provide insights into the significance of phase incoherence in 'pseudogap' states.

Hour-glass magnetic excitations induced by nanoscopic phase separation in cobalt oxides.

The magnetic excitations in the cuprate superconductors might be essential for an understanding of high-temperature superconductivity. In these cuprate superconductors the magnetic excitation spectrum resembles an hour-glass and certain resonant magnetic excitations within are believed to be connected to the pairing mechanism, which is corroborated by the observation of a universal linear scaling of superconducting gap and magnetic resonance energy. So far, charge stripes are widely believed to be involved in the physics of hour-glass spectra. Here we study an isostructural cobaltate that also exhibits an hour-glass magnetic spectrum. Instead of the expected charge stripe order we observe nano phase separation and unravel a microscopically split origin of hour-glass spectra on the nano scale pointing to a connection between the magnetic resonance peak and the spin gap originating in islands of the antiferromagnetic parent insulator. Our findings open new ways to theories of magnetic excitations and superconductivity in cuprate superconductors.

Magnetically driven suppression of nematic order in an iron-based superconductor.

A theory of superconductivity in the iron-based materials requires an understanding of the phase diagram of the normal state. In these compounds, superconductivity emerges when stripe spin density wave (SDW) order is suppressed by doping, pressure or atomic disorder. This magnetic order is often pre-empted by nematic order, whose origin is yet to be resolved. One scenario is that nematic order is driven by orbital ordering of the iron 3d electrons that triggers stripe SDW order. Another is that magnetic interactions produce a spin-nematic phase, which then induces orbital order. Here we report the observation by neutron powder diffraction of an additional fourfold-symmetric phase in Ba1-xNaxFe2As2 close to the suppression of SDW order, which is consistent with the predictions of magnetically driven models of nematic order.

Electron-phonon coupling in the conventional superconductor YNi2B2C at high phonon energies studied by time-of-flight neutron spectroscopy.

We report an inelastic neutron scattering investigation of phonons with energies up to 159 meV in the conventional superconductor YNi(2)B(2)C. Using the sweep mode, a newly developed time-of-flight technique involving the continuous rotation of a single crystal specimen, allowed us to measure a four-dimensional volume in (Q, E) space and, thus, determine the dispersion surface and linewidths of the A(1g) (≈102 meV) and A(u) (≈159 meV) type phonon modes over the whole Brillouin zone. Despite of having linewidths of Γ=10 meV, A(1g) modes do not strongly contribute to the total electron-phonon coupling constant λ. However, experimental linewidths show a remarkable agreement with ab initio calculations over the complete phonon energy range, demonstrating the accuracy of such calculations in a rare comparison to a comprehensive experimental data set.

Response of acoustic phonons to charge and orbital order in the 50% doped bilayer manganite LaSr2Mn2O7.

We report an inelastic neutron scattering study of acoustic phonons in the charge and orbitally ordered bilayer manganite LaSr(2)Mn(2)O(7). For excitation energies less than 15 meV, we observe an abrupt increase (decrease) of the phonon energies (linewidths) of a transverse acoustic phonon branch at q = (h, h, 0), h ≤ 0.3, upon entering the low temperature charge and orbital ordered state (T(COO) = 225 K). This indicates a reduced electron-phonon coupling due to a decrease of electronic states at the Fermi level leading to a partial removal of the Fermi surface below T(COO) and provides direct experimental evidence for a link between electron-phonon coupling and charge order in manganites.

Effect of Fermi surface nesting on resonant spin excitations in Ba(1-x)K(x)Fe2As2.

We report inelastic neutron scattering measurements of the resonant spin excitations in Ba(1-x)K(x)Fe(2)As(2) over a broad range of electron band filling. The fall in the superconducting transition temperature with hole doping coincides with the magnetic excitations splitting into two incommensurate peaks because of the growing mismatch in the hole and electron Fermi surface volumes, as confirmed by a tight-binding model with s(±)-symmetry pairing. The reduction in Fermi surface nesting is accompanied by a collapse of the resonance binding energy and its spectral weight, caused by the weakening of electron-electron correlations.

Extended phonon collapse and the origin of the charge-density wave in 2H-NbSe2.

We report inelastic x-ray scattering measurements of the temperature dependence of phonon dispersion in the prototypical charge-density-wave (CDW) compound 2H-NbSe2. Surprisingly, acoustic phonons soften to zero frequency and become overdamped over an extended region around the CDW wave vector. This extended phonon collapse is dramatically different from the sharp cusp in the phonon dispersion expected from Fermi surface nesting. Instead, our experiments, combined with ab initio calculations, show that it is the wave vector dependence of the electron-phonon coupling that drives the CDW formation in 2H-NbSe2 and determines its periodicity. This mechanism explains the so far enigmatic behavior of CDW in 2H-NbSe2 and may provide a new approach to other strongly correlated systems where electron-phonon coupling is important.

Electron-phonon coupling and the soft phonon mode in TiSe2.

We report high-resolution inelastic x-ray measurements of the soft phonon mode in the charge-density-wave compound TiSe(2). We observe a complete softening of a transverse optic phonon at the L point, i.e., q=(0.5, 0, 0.5), at T≈T(CDW). Detailed ab initio calculations for the electronic and lattice dynamical properties of TiSe(2) are in quantitative agreement with experimental frequencies for the soft phonon mode. The observed broad range of renormalized phonon frequencies, (0.3, 0, 0.5)≤q≤(0.5, 0, 0.5), is directly related to a broad peak in the electronic susceptibility stabilizing the charge-density-wave ordered state. Our analysis demonstrates that a conventional electron-phonon coupling mechanism can explain a structural instability and the charge-density-wave order in TiSe(2) although other mechanisms might further boost the transition temperature.

Structural Fluctuations in the spin-liquid state of Tb2Ti2O7.

High-resolution x-ray scattering measurements on single crystal Tb2Ti2O7 reveal finite structural correlations at low temperatures. This geometrically frustrated pyrochlore is known to exhibit a spin-liquid or cooperative paramagnetic state at temperatures below approximately 20 K. Parametric studies of structural Bragg peaks appropriate to the Fd3[over ]m space group of Tb2Ti2O7 reveal substantial broadening and peak intensity reduction in the temperature regime 20 K to 300 mK. We also observe a small, anomalous lattice expansion on cooling below a density maximum at approximately 18 K. These measurements are consistent with the development of fluctuations above a cooperative Jahn-Teller, cubic-tetragonal phase transition at very low temperatures.

Random fields and the partially paramagnetic state of CsCo0.83Mg0.17Br3: critical scattering study.

We have performed measurements of the critical neutron scattering on CsCo0.83Mg0.17Br3, a dilute stacked triangular lattice (STL) Ising antiferromagnet (AF). A two component line shape associated with the critical fluctuations appears at a temperature coincident with T(N1) observed in pure CsCoBr3. Such scattering is indicative of fluctuations in prototypical random field Ising model (RFIM) systems. The random field domain state arises in this case due to geometrical frustration within the STL Ising AF, which gives rise to a three sublattice Néel state, in which one sublattice is disordered. Magnetic vacancies nucleate AF domains in which the vacancies reside on the disordered sublattice thereby generating a RFIM state in the absence of an applied magnetic field.

High-resolution study of spin excitations in the singlet ground state of SrCu2(BO3)2.

High-resolution, inelastic neutron scattering measurements on SrCu2(BO3)2, a realization of the Shastry-Sutherland model for two-dimensional Heisenberg antiferromagnets, reveal the dispersion of the three single triplet excitations continuously across the (H,0) direction within its tetragonal basal plane. These measurements also show distinct Q dependencies for the single and multiple triplet excitations, and that these excitations are largely dispersionless perpendicular to this plane. The temperature dependence of the intensities of these excitations is well described as the complement of the dc susceptibility of SrCu2(BO3)2.