Anharmonicity due to Electron-Phonon Coupling in Magnetite

We present the results of inelastic x-ray scattering for magnetite and analyze the energies and spectral widths of the phonon modes with different symmetries in a broad range of temperature 125<T<293 K. The phonon modes with X_4 and Delta_5 symmetries broaden in a nonlinear way with decreasing temperature when the Verwey transition is approached. It is found that the maxima of phonon widths occur away from high-symmetry points which indicates the incommensurate character of critical fluctuations. Strong phonon anharmonicity induced by electron-phonon coupling is discovered within ab initio calculations which take into account local Coulomb interactions at Fe ions. It (i) explains observed anomalous phonon broadening, and (ii) demonstrates that the Verwey transition is a cooperative phenomenon which involves a wide spectrum of phonons coupled to charge fluctuations condensing in the low-symmetry phase.Comment: 5 pages, 5 figures, accepted in Physical Review Letter

Inelastic X-ray scattering studies of phonon dispersions in superconductors at high pressures

Electron-phonon interaction is of central importance for the electrical and heat transport properties of metals, and is directly responsible for charge-density-waves or (conventional) superconducting instabilities. The direct observation of phonon dispersion anomalies across electronic phase transitions can provide insightful information regarding the mechanisms underlying their formation. Here, we review the current status of phonon dispersion studies in superconductors under hydrostatic and uniaxial pressure. Advances in the instrumentation of high resolution inelastic X-ray scattering beamlines and pressure generating devices allow these measurements to be performed routinely at synchrotron beamlines worldwide.Comment: 8 pages, 6 figures. Invited review submitted to Superconductor Science and Technology, Focus issue on Hydride & High-Pressure Superconductors. References in figure caption fixed. Hyperlinks adde

Short-Range Correlations in Magnetite above the Verwey Temperature

Magnetite, Fe$_3$O$_4$, is the first magnetic material discovered and utilized by mankind in Ancient Greece, yet it still attracts attention due to its puzzling properties. This is largely due to the quest for a full and coherent understanding of the Verwey transition that occurs at $T_V=124$ K and is associated with a drop of electric conductivity and a complex structural phase transition. A recent detailed analysis of the structure, based on single crystal diffraction, suggests that the electron localization pattern contains linear three-Fe-site units, the so-called trimerons. Here we show that whatever the electron localization pattern is, it partially survives up to room temperature as short-range correlations in the high-temperature cubic phase, easily discernible by diffuse scattering. Additionally, {\it ab initio} electronic structure calculations reveal that characteristic features in these diffuse scattering patterns can be correlated with the Fermi surface topology.Comment: 7 pages, 6 figure

Phonon surface mapping of graphite: disentangling quasi--degenerate phonon dispersions

The two-dimensional mapping of the phonon dispersions around the $K$ point of graphite by inelastic x-ray scattering is provided. The present work resolves the longstanding issue related to the correct assignment of transverse and longitudinal phonon branches at $K$. We observe an almost degeneracy of the three TO, LA and LO derived phonon branches and a strong phonon trigonal warping. Correlation effects renormalize the Kohn anomaly of the TO mode, which exhibits a trigonal warping effect opposite to that of the electronic band structure. We determined the electron--phonon coupling constant to be 166$\rm(eV/\AA)^2$ in excellent agreement to $GW$ calculations. These results are fundamental for understanding angle-resolved photoemission, double--resonance Raman and transport measurements of graphene based systems

Changing energy accelerated turbulent fluid flow in the pipeline according to spectral analysis

За результатами теоретичних і експериментальних досліджень пришвидшеної течії рідини в циліндричному напірному трубопроводі проведено якісну оцінку спектрального складу енергії турбулентного потоку. Отримані густини спектрів нарізних відстанях від стінки труби. Згідно оцінок, передача енергії між низькими і високими частотами в нестаціонарному потоці суттєво відрізняються від передачі енергії в стаціонарному потоці.According to the results of theoretical and experimental studies of accelerated fluid flow in a cylindrical pressure pipe made a qualitative assessment of the spectral composition of the energy of turbulent flow. Density spectra obtained at different distances from the pipe wall. According to estimates, the transfer of energy between the low and high frequencies in unsteady flow significantly different from the energy transfer in a steady stream. In the transition to the low-frequency components of turbulent currents of the spectra in the near-wall local rate of flow with a relatively large part of the total energy than in the core flow. In steady flow relative share of low-energy component decreases with the increase of average flow velocity (number Re). Transient currents reverse process occurs after the turbulence of flow turbulence is a small-scale and large-scale development of the current portion of the increase.По результатам теоретических и экспериментальных исследований ускоренного течения жидкости в цилиндрическом напорном трубопроводе проведена качественная оценка спектрального состава энергии турбулентного потока. Полученные плотности спектров на разных расстояниях от стенки трубы. По оценкам, передача энергии между низкими и высокими частотами в нестационарном потоке существенно отличаются от передачи энергии в стационарном потоке

The phonon dispersion of graphite by inelastic x-ray scattering

We present the full in-plane phonon dispersion of graphite obtained from inelastic x-ray scattering, including the optical and acoustic branches, as well as the mid-frequency range between the $K$ and $M$ points in the Brillouin zone, where experimental data have been unavailable so far. The existence of a Kohn anomaly at the $K$ point is further supported. We fit a fifth-nearest neighbour force-constants model to the experimental data, making improved force-constants calculations of the phonon dispersion in both graphite and carbon nanotubes available.Comment: 7 pages; submitted to Phys. Rev.