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New surprises continue to be revealed about La$_2$CuO$_4$, the parent compound of the original cuprate superconductor. Here we present neutron scattering evidence that the structural symmetry is lower than commonly assumed. The static distortion results in anisotropic Cu-O bonds within the CuO$_2$ planes; such anisotropy is relevant to pinning charge stripes in hole-doped samples. Associated with the extra structural modulation is a soft phonon mode. If this phonon were to soften completely, the resulting change in CuO$_6$ octahedral tilts would lead to weak ferromagnetism. Hence, we suggest that this mode may be the "chiral" phonon inferred from recent studies of the thermal Hall effect. We also note the absence of interaction between the antiferromagnetic spin waves and low-energy optical phonons, in contrast to what is observed in hole-doped samples., Comment: 12 pages, 10 figures; accepted version

This article introduces software called Phonon Explorer that implements a data mining workflow for large datasets of the neutron scattering function, S(Q, {\omega}), measured on time-of-flight neutron spectrometers. This systematic approach takes advantage of all useful data contained in the dataset. It includes finding Brillouin zones where specific phonons have the highest scattering intensity, background subtraction, combining statistics in multiple Brillouin zones, and separating closely spaced phonon peaks. Using the software reduces the time needed to determine phonon dispersions, linewidths, and eigenvectors by more than an order of magnitude.

Time resolved measurements provide a new way to disentangle complex interactions in quantum materials due to their different timescales. We used pump-probe Raman scattering to investigate the apical oxygen vibration in YBa$_2$Cu$_3$O$_{6+x}$ under nonequilibrium conditions. Time-dependence of the phonon population demonstrated strong electron-phonon coupling. Most importantly, the phonon shifts to a higher energy due to transient smearing of the Fermi surface in a remarkable agreement with diagrammatic theory. We also discuss new insights into photoinduced superconductivity reported at lower doping that follow from these results., Comment: New expanded version including analysis and comparison of phonon softening to diagrammatic theory

We present a comprehensive investigation of lattice dynamics in the double-helix antiferromagnet FeP by means of high-resolution time-of-flight neutron spectroscopy and ab-initio calculations. Phonons can hybridize with the magnetic excitations in noncollinear magnets to significantly influence their properties. We observed a rich spectrum of phonon excitations, which extends up to $\sim$50 meV. We performed detailed analysis of the observed and calculated spectra for all high-symmetry points and high-symmetry directions of the Brillouin zone. We show that the DFT calculations quantitatively capture the essential features of the observed phonons, including both dispersions and scattering intensities. By making use of the detailed intensity comparison between the theory and the data, we were able to identify displacement vectors for the majority of the observed modes. The overall excellent agreement between the DFT predictions and the experimental results breaks down for the lowest mode at the $Y$-point, whose energy is lower than calculated by $\sim$13%. The present study provides vital information on the lattice dynamics in FeP and demonstrates applicability of the DFT to novel pressure-induced phenomena in related materials, such as MnP and CrAs., Comment: 12 pages, 10 figures

Doped antiferromagnets host a vast array of physical properties and learning how to control them is one of the biggest challenges of condensed matter physics. La$_{1.7}$Sr$_{0.3}$NiO$_4$ (LSNO) is a classic example of such a material. At low temperatures holes introduced via substitution of La by Sr segregate into lines to form boundaries between magnetically ordered domains in the form of stripes. The stripes become dynamic at high temperatures, but LSNO remains insulating presumably because an interplay between magnetic correlations and electron-phonon coupling localizes charge carriers. Magnetic degrees of freedom have been extensively investigated in this system, but phonons are almost completely unexplored. We searched for electron-phonon anomalies in LSNO by inelastic neutron scattering. Giant renormalization of plane Ni-O bond-stretching modes that modulate the volume around Ni appears on entering the dynamic charge stripe phase. Other phonons are a lot less sensitive to stripe melting. Dramatic overdamping of the breathing modes indicates that dynamic stripe phase may host small polarons. We argue that this feature sets electron-phonon coupling in nickelates apart from that in cuprates where breathing phonons are not overdamped and point out remarkable similarities with the colossal magnetoresistance (CMR) manganites.

The cuprates exhibit a prominent charge-density-wave (CDW) instability with wavevector along [100], i.e., the Cu-O bond direction. Whereas CDW order is most prominent at moderate doping and low temperature, there exists increasing evidence for dynamic charge correlations throughout a large portion of the temperature-doping phase diagram. In particular, signatures of incipient charge order have been observed as phonon softening and/or broadening near the CDW wavevector approximately half-way through the Brillouin zone. Most of this work has focused on moderately-doped cuprates, for which the CDW order is robust, or on optimally-doped samples, for which the superconducting transition temperature ($T_c$) attains its maximum. Here we present a time-of-flight neutron scattering study of phonons in simple-tetragonal $\text{HgBa}_2\text{CuO}_{4+\delta}$ ($T_c = 55$ K) at a low doping level where prior work showed the CDW order to be weak. We employ and showcase a new software-based technique that mines the large number of measured Brillouin zones for useful data in order to improve accuracy and counting statistics. Density-functional theory has not provided an accurate description of phonons in $\text{HgBa}_2\text{CuO}_{4+\delta}$, yet we find the right set of parameters to qualitatively reproduce the data. The notable exception is a dispersion minimum in the longitudinal Cu-O bond-stretching branch along [100]. This discrepancy suggests that, while CDW order is weak, there exist significant dynamic charge correlations in the optic phonon range at low doping, near the edge of the superconducting dome.

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 $\xi$ 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 $\xi$ is well described by a power law $(T-T_0)^{-1/2}$ extending over a wide temperature range. We attributed this mean-field behavior and the extended fluctuation regime to a sizable nemato-elastic coupling, which may be detrimental to superconductivity.

Significant developments in the field of additive manufacturing (AM) allowed the fabrication of complex microarchitectured components with varying porosity across different scales. However, due to the high complexity of this process, the final parts can exhibit significant variations in the nominal geometry. Computer tomographic images of 3D printed components provide extensive information about these microstructural variations, such as process-induced porosity, surface roughness, and other undesired morphological discrepancies. Yet, techniques to incorporate these imperfect AM geometries into the numerical material characterization analysis are computationally demanding. In this contribution, an efficient image-to-material-characterization framework using the high-order parallel Finite Cell Method is proposed. In this way, a flexible non-geometry-conforming discretization facilitates mesh generation for very complex microstructures at hand and allows a direct analysis of the images stemming from CT-scans. Numerical examples including a comparison to the experiments illustrate the potential of the proposed framework in the field of additive manufacturing product simulation.

La$_{1.67}$Sr$_{0.33}$NiO$_4$ develops charge and spin stripe orders at temperatures of roughly 200 K, with modulation wave vectors that are temperature independent. Various probes of spin and charge response have provided independent evidence for some sort of change below $\sim50$ K. In combination with a new set of neutron scattering measurements, we propose a unified interpretation of all of these observations in terms of a freezing of Ni-centered charges stripes, together with a glassy ordering of the spin stripes that shows up in neutron scattering as a slight rotation of the average spin direction., Comment: 9 pages, 6 figs; version accepted for publication

Nematicity is ubiquitous in electronic phases of high-$T_c$ superconductors, particularly in the Fe-based systems. While several experiments have probed nematic fluctuations, they have been restricted to uniform or momentum averaged fluctuations. Here, we investigate the behavior of finite-momentum nematic fluctuations by utilizing the anomalous softening of acoustic phonon modes in optimally doped Ba(Fe$_{0.94}$Co$_{0.06}$)$_2$As$_2$. We determine the nematic correlation length and find that it sharply changes its $T$-dependence at $T_c$, revealing a strong connection between nematicity and superconductivity.

According to standard theory the magnetoresistance magnitude in ferromagnetic manganites crucially depends on the electron-phonon coupling strength. We showed that in La0.7Sr0.3MnO3 the phonon renormalization is strong, despite its relatively small magnetoresistance. Here, we report results of a similar inelastic neutron scattering investigation of a closely related compound, La0.8Sr0.2MnO3, where the magnetoresistance is enhanced. We find similar phonon renormalization and dynamic CE-type polaron correlations as in La0.7Sr0.3MnO3. However, quantitative comparison of the results for the two samples shows that only polaron lifetime is well correlated with the strength of the CMR., Comment: 5 figures

Electron-phonon interaction in copper oxide superconductors is still enigmatic. Strong coupling for certain optic phonons is now well established experimentally, but theoretical understanding is challenging. Scattering of electrons near the Fermi surface by the longitudinal acoustic (LA) phonons is expected from basic theory because these phonons modulate electron density. We used inelastic neutron scattering on a large single crystal sample of optimally-doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ to show that low-energy LA phonons could couple to electronic density fluctuations only at small phonon wavevectors, which naturally limits any interaction to forward scattering. Such scattering should not be pairbreaking in the case of the d-wave gap. We also found that previously the reported low energy phonon spectral weight half-way to the zone boundary is consistent with conventional lattice dynamics and does not reflect an incipient charge density wave., Comment: Updated Oct. 2019 to include new measurements and additional discussion. 7 pages, 4 figures, Supplementary included: 6 pages, 5 figures

Nematic order is ubiquitous in liquid crystals and is characterized by a rotational symmetry breaking in an otherwise uniform liquid. Recently a similar phenomenon has been observed in some electronic phases of quantum materials related to high temperature superconductivity, particularly in the Fe-based superconductors. While several experiments have probed nematic fluctuations, they have been primarily restricted to the uniform nematic susceptibility, i.e. q = 0 fluctuations. Here, we investigate the behavior of finite-momentum nematic fluctuations by measuring transverse acoustic phonon modes with wavelengths of up to 25 unit cells in the prototypical Fe-based compound Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$. While the slope of the phonon dispersion gives information about the uniform nematic susceptibility, deviations from this linear behavior at finite but small wave-vectors are attributed to finite-momentum nematic fluctuations. Surprisingly, these non-zero q fluctuations lead to a softening of the phonon mode below the superconducting transition temperature, in contrast to the behavior of the phonon velocity at q = 0, which increases below $T_c$. Our work not only establishes a sound method to probe long wavelength nematic fluctuations, but also sheds light on the unique interplay between nematicity and superconductivity in Fe-based compounds.

Among colossal magnetoresistive manganites the prototypical ferromagnetic manganite La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ has a relatively small magnetoresistance, and has been long assumed to have only weak electron-lattice coupling. Here we report that La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ has strong electron-phonon coupling: Our neutron and x-ray scattering experiments show strong softening and broadening of transverse acoustic phonons on heating through the Curie temperature T$_C$ = 350 K. Simultaneously, we observe two phases where metallic resistivity and polarons coexist. The ferromagnetic polaronic metal phase between 200 K and T$_C$ is characterized by quasielastic scattering from dynamic CE-type polarons with the relatively short lifetime of $\mathbf{\tau}\approx 1\,\rm{ps}$. This scattering is greatly enhanced above T$_C$ in the paramagnetic polaronic metal phase. Our results suggest that the strength of magnetoresistance in manganites scales with the inverse of polaron lifetime, not the strength of electron-phonon coupling.

We report neutron scattering measurements of the structural correlations associated with the apparent relaxor transition in K$_{1-x}$Li$_x$TaO$_3$ for $x=0.02$ (KLT(0.02)). This compound displays a broad and frequency-dependent peak in the dielectric permittivity, which is the accepted hallmark of all relaxors. However, no evidence of elastic diffuse scattering or any soft mode anomaly is observed in KLT(0.02) [J. Wen et al., Phys. Rev. B 78, 144202 (2008)], a situation that diverges from that in other relaxors such as PbMg$_{1/3}$Nb$_{2/3}$O$_3$. We resolve this dichotomy by showing that the structural correlations associated with the transition in KLT(0.02) are purely dynamic at all temperatures, having a timescale on the order of $\sim$THz. These fluctuations are overdamped, non-propagating, and spatially uncorrelated. Identical measurements made on pure KTaO$_3$ show that they are absent (within experimental error) in the undoped parent material. They exhibit a temperature dependence that correlates well with the dielectric response, which suggests that they are associated with local ferroelectric regions induced by the Li$^+$ doping. The ferroelectric transition that is induced by the introduction of Li$^+$ cations is therefore characterized by quasistatic fluctuations, which represents a stark contrast to the soft harmonic-mode-driven transition observed in conventional perovskite ferroelectrics like PbTiO$_3$. The dynamic, glass-like, structural correlations in KLT(0.02) are much faster than those measured in random-field-based lead-based relaxors, which exhibit a frequency scale of order of $\sim$GHz and are comparatively better correlated spatially. Our results support the view that random fields give rise to the relaxor phenomena, and that the glass-like dynamics observed here characterize a nascent response., Comment: (13 pages, 11 figures)

Parent compounds of Fe-based superconductors undergo a structural phase transition from a tetragonal to an orthorhombic structure. We investigated the temperature dependence of the frequencies of transverse acoustic (TA) phonons that extrapolate to the shear vibrational mode at the zone center, which corresponds to the orthorhombic deformation of the crystal structure at low temperatures in BaFe 2 As 2 and SrFe 2 As 2 . We found that acoustic phonons at small wavevectors soften gradually towards the transition from high temperatures, tracking the increase of the size of slowly fluctuating magnetic domains. On cooling below the transition to base temperature the phonons harden, following the square of the magnetic moment. Our results provide evidence for close correlation between magnetic and phonon properties in Fe-based superconductors., Comment: 5 pages, 4 figures

We present a combined density-functional-perturbation-theory and inelastic neutron scattering study of the lattice dynamical properties of YNi2B2C. In general, very good agreement was found between theory and experiment for both phonon energies and line widths. Our analysis reveals that the strong coupling of certain low energy modes is linked to the presence of large displacements of the light atoms, i.e. B and C, which is unusual in view of the rather low phonon energies. Specific modes exhibiting a strong coupling to the electronic quasiparticles were investigated as a function of temperature. Their energies and line widths showed marked changes on cooling from room temperature to just above the superconducting transition at Tc = 15.2 K. Calculations simulating the effects of temperature allow to model the observed temperature dependence qualitatively.

The ferropnictide superconductors exhibit a sensitive interplay between the lattice and magnetic degrees of freedom, including a number of phonon modes that are much softer than predicted by nonmagnetic calculations using density functional theory (DFT). However, it is not known what effect, if any, the long-range magnetic order has on phonon frequencies above 23 meV, where several phonon branches are very closely spaced in energy and it is challenging to isolate them from each other. We measured these phonons using inelastic time-of-flight neutron scattering in ~40 Brillouin zones, and developed a technique to determine their frequencies. We find this method capable of determining phonon energies to ~0.1 meV accuracy, and that the DFT calculations using the experimental structure yield qualitatively correct energies and eigenvectors. We do not find any effect of the magnetic transition on these phonons., Comment: To be published in Physical Review B

In superconducting copper oxides some Cu-O bond-stretching phonons around 70meV show anomalous giant softening and broadening of electronic origin and electronic dispersions have large renormalization kinks near the same energy. These observations suggest that phonon broadening originates from quasiparticle excitations across the Fermi surface and the electronic dispersion kinks originate from coupling to anomalous phonons. We measured the phonon anomaly in underdoped (x=0.05) and overdoped (x=0.20,0.25) La$_{2-x}$Sr$_x$CuO$_4$ by inelastic neutron and x-ray scattering with high resolution. Combining these and previously published data, we found that doping-dependence of the magnitude of the giant phonon anomaly is very different from that of the ARPES kink, i.e. the two phenomena are not connected. We show that these results provide indirect evidence that the phonon anomaly originates from novel collective charge excitations as opposed to interactions with electron-hole pairs. Their amplitude follows the superconducting dome so these charge modes may be important for superconductivity., Comment: 5 pages, 3 figures. Accepted for publication in PRB Rapid Communications

Colossal magnetoresistance (CMR) is associated with the phase transition from a metallic ferromagnetic to insulating paramagnetic phase, which can be controlled by an applied magnetic field. The insulating phase occurs due to trapping of the charge carriers by polaronic lattice distortions, which raise the resistivity. Theories based on local physics predict that the magnitude of the resistivity jump at Tc is determined by how much, on average, the amplitude of these distortions increases at the phase transition. Using neutron scattering, we measured the average distortion amplitude in La0.7Sr0.3MnO3. Surprisingly, its increase from below to above Tc is just as large as in other manganites, which have a much larger resistivity jump. This result suggests that the strength of CMR is determined not by the size of distortions, but by their cooperative nature specific to each compound. Existing theories need to be extended to include correlations between different unit cells to explain and predict the strength of CMR.

The insulator-to-metal transition continues to be a challenging subject, especially when electronic correlations are strong. In layered compounds, such as La2-xSrxNiO4 and La2-xBaxCuO4, the doped charge carriers can segregate into periodically-spaced charge stripes separating narrow domains of antiferromagnetic order. Although there have been theoretical proposals of dynamically fluctuating stripes, direct spectroscopic evidence of charge-stripe fluctuations has been lacking. Here we report the detection of critical lattice fluctuations, driven by charge-stripe correlations, in La2-xSrxNiO4 using inelastic neutron scattering. This scattering is detected at large momentum transfers where the magnetic form factor suppresses the spin fluctuation signal. The lattice fluctuations associated with the dynamic charge stripes are narrow in q and broad in energy. They are strongest near the charge stripe melting temperature. Our results open the way towards the quantitative theory of dynamic stripes and for directly detecting dynamical charge stripes in other strongly-correlated systems, including high-temperature superconductors such as La2-xSrxCuO4., Comment: Nature Communications, in press, 9 pages 10 figures, completely new version

Electronic band dispersions in copper oxide superconductors have kinks around 70 meV that are typically attributed to coupling of electrons to a bosonic mode. We performed angle resolved photoemission spectroscopy (ARPES) experiments on overdoped cuprate high temperature superconductors to test the relationship between the superconducting transition temperature and electron-bosonic mode coupling. Remarkably, the kinks remain strong in the heavily overdoped region of the doping phase diagram of LSCO, even when the superconductivity completely disappears. This unexpected observation is incompatible with the conventional picture of superconductivity mediated by the sharp bosonic modes that are responsible for the kink. Therefore, the pairing likely originates from something else, such as from interactions with a very broad electronic spectrum or from an unconventional mechanism without pairing glue., Comment: 5 pages, 3 figures. For the Supp. Mat., please contact the authors

We present an investigation of the lattice dynamics of the charge-density-wave compound 2H-NbSe2. We analyze the precise nature of the wave vector dependent electron-phonon coupling (EPC) and derive the bare dispersion of the charge-density-wave (CDW) soft phonon mode using inelastic x-ray scattering combined with ab-initio calculations. Experimentally, phonon modes along the {\Gamma} - M line, i.e. q = (h, 0, 0) with 0 <= h <= 0.5, with the same longitudinal symmetry ({\Sigma}1) as the CDW soft mode were investigated up to 32 meV. In agreement with our calculations we observe significant EPC in the optic modes at h <= 0.2. We analyze the EPC in the optic as well as acoustic modes and show that the q dependences stem from scattering processes between two bands at the Fermi surface both having Nb 4d character. Finally, we demonstrate that the soft mode dispersion at T = 33 K (= {T_{CDW}}) can be well described on the basis of a strongly q dependent EPC matrix element and an acoustic-like bare phonon dispersion in agreement with observations near room temperature., Comment: accepted as regular article in Physical Review B

Stripe order where electrons self-organize into alternating periodic charge-rich and magnetically-ordered charge-poor parallel lines was proposed as a way of optimizing the kinetic energy of holes in a doped Mott insulator. Static stripes detected as extra peaks in diffraction patterns, appear in a number of oxide perovskites as well as some other systems. The more controversial dynamic stripes, which are not detectable by diffraction, may be universally present in copper oxide superconductors. Thus it is important to learn how to detect dynamic stripes as well as to understand their influence on electronic properties. This review article focuses on lattice vibrations (phonons) that might show signatures of the charge component of dynamic stripes. The first part of the article describes recent progress in learning about how the phonon signatures of different types of electronic charge fluctuations including stripes can be distinguished from purely structural instabilities and from each other. Then I will focus on the evidence for dynamic stripes in the phonon spectra of copper oxide superconductors., Comment: Review article to be published in a special issues of Physica C on stripes. 35 pages, 30 figures, new version including corrections and additions throughout the text

The Fe1+y Te1-x Sex compounds belong to the family of iron-based high temperature superconductors, in which superconductivity often appears upon doping antiferromagnetic parent compounds. Unlike other Fe-based superconductors (in which the antiferromagnetic order is at the Fermi surface nesting wavevector [1/2,1/2,1]), the Fe1+y Te1-x Sex parent compound Fe1+y Te orders at a different wavevector, [1/2, 0, 1/2]. Furthermore, the ordering wavevector depends on y, the occupation of interstitial sites with excess iron; the origin of this behavior is controversial. Using inelastic neutron scattering on Fe1.08 Te, we find incommensurate magnetic fluctuations above the Neel temperature, even though the ordered state is bicollinear and commensurate with gapped spin waves. This behavior can be understood in terms of a competition between commensurate and incommensurate order, which we explain as a lock-in transition caused by the magnetic anisotropy.

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 $15\,\rm{meV}$, we observe an abrupt increase (decrease) of the phonon energies (linewidths) of a transverse acoustic phonon branch at $\mathbf{q} = (h, h, 0)$, $h\le0.3$, upon entering the low temperature charge and orbital ordered state ($T_{COO} = 225\,\rm{K}$). 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., Comment: accepted in Physical Review Letters

Purely local experimental probes of many copper oxide superconductors show that their electronic states are inhomogeneous in real space. For example, scanning tunneling spectroscopic (STS) imaging shows strong variations in real space, and according to nuclear quadrupole resonance (NQR) studies the charge distribution in the bulk varies on the nanoscale. However, the analysis of the experimental results utilizing spatially-averaged probes often ignores this fact. We have performed a detailed investigation of the doping-dependence of the energy and line width and position of the zone-boundary Cu-O bond-stretching vibration in La_{2-x}Sr_xCuO_4 by inelastic neutron scattering. Both our new results as well as previously reported angle-dependent momentum widths of the electronic spectral function detected by angle-resolved photoemission can be reproduced by including the same distribution of local environments extracted from the NQR analysis., Comment: 6 pages, 4 figures. Accepted for publication in PRB

Motivated by predictions of a substantial contribution of the "buckling" vibration of the CuO2 layers to d-wave superconductivity in the cuprates, we have performed an inelastic neutron scattering study of this phonon in an array of untwinned crystals of YBa2Cu3O7. The data reveal a pronounced softening of the phonon at the in-plane wave vector q = (0, 0.3) upon cooling below ~ 105 K, but no corresponding anomaly at q = (0.3, 0). Based on the observed in-plane anisotropy, we argue that the electron-phonon interaction responsible for this anomaly supports an electronic instability associated with a uniaxial charge-density modulation and does not mediate d-wave superconductivity., Comment: to appear in PRL

Chiral nematic liquid crystals sometimes form blue phases characterized by spirals twisting in different directions. By combining model calculations with neutron-scattering experiments, we show that the magnetic analogue of blue phases does form in the chiral itinerant magnet MnSi in a large part of the phase diagram. The properties of this blue phase explain a number of previously reported puzzling features of MnSi such as partial magnetic order and a two-component specific-heat and thermal-expansion anomaly at the magnetic transition.

We report temperature dependence of low-energy phonons in magnetic nonsuperconducting TbNi2B2C single crystals measured by inelastic neutron scattering. We observed a low-temperature softening and broadening of two phonon branches, qualitatively similar to that previously reported for superconducting RNi2B2C (R= rare earth, Y) compounds. This result suggests that the superconductivity in TbNi2B2C compounds is absent not because of a weak electron-phonon coupling but as a result of pairbreaking due to magnetism.

We report inelastic x-ray scattering measurements of the temperature dependence of phonon dispersion in the prototypical charge-density-wave (CDW) compound NbSe2. Surprisingly, acoustic phonons soften to zero frequency and become overdamped over an extended region around the CDW wavevector. 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 wavevector dependence of the electron-phonon coupling that drives the CDW formation in NbSe$_2$ and determines its periodicity. This mechanism explains the so far enigmatic behavior of CDW in NbSe$_2$ and may provide a new approach to other strongly correlated systems where electron-phonon coupling is important.

Charge carriers in low-doped semiconductors may distort the atomic lattice and trap themselves forming so-called small polarons. High carrier concentrations can lead to short range ordered polarons (large polarons) and even to long range charge and orbital order. Both systems should be insulating with a large electrical resistivity, which decreases with increasing temperature. However, photoemission measurements recently found a polaronic pseudogap, in a metallic phase of La2-2xSr1+2xMn2O7. This layered manganite is famous for colossal magnetoresistance (CMR) associated with a phase transition from this low-temperature metallic phase to a high temperature insulating phase. Broad charge order peaks due to large polarons observed by neutron and x-ray scattering in the insulating phase disappear when La2-2xSr1+2xMn2O7 becomes metallic. We report results of inelastic neutron scattering measurements showing that polarons remain inside the metallic phase as fluctuations that strongly broaden and soften certain phonons near the wave vectors where the charge order peaks appeared in the insulating phase. Our findings imply that polaronic signatures in metals may generally come from a competing insulating charge-ordered phase. It is highly relevant to cuprate superconductors with both a pseudogap, and a similar phonon effect associated with a competing stripe order.

The pressure dependence of a large number of phonon modes in CaFe2As2 with energies covering the full range of the phonon spectrum has been studied using inelastic x-ray and neutron scattering. The observed phonon frequency changes are in general rather small despite the sizable changes of the lattice parameters at the phase transition. This indicates that the bonding properties are not profoundly altered by the phase transition. The transverse acoustic phonons propagating along the c-direction are an exception because they stiffen very significantly in response to the large contraction of the c-axis. The lattice parameters are found to change significantly as a function of pressure before, during and after the first-order phase transition. However, the frequencies change nearly uniformly with the change in the lattice parameters due to pressure, with no regard specifically to the first-order phase transition. Density functional theory describes the frequencies in both the zero pressure and in the collapsed phase in a satisfactory way if based on the respective crystal structures.

Interactions with electronic excitations can soften and/or broaden phonons. They are greatly amplified at wavevectors Q+- that connect parallel (nested) sheets of the Fermi surface. In such a case, called a Kohn anomaly, the phonon dispersion sharply dips and its linewidth has a maximum at Q+-. Here we present results of inelastic x-ray scattering measurements that uncovered soft phonons in chromium far from Q+-. They appear in addition to the previously reported soft phonons at Q+-. Calculations in the local density approximation (LDA) show that the new anomalies originate from enhanced electron-phonon coupling. A similar mechanism may explain phonon anomalies away from nesting wavevectors in copper oxide superconductors and other compounds.

Since conventional superconductivity is mediated by phonons, their role in the mechanism of high temperature superconductivity has been considered very early after the discovery of the cuprates. The initial consensus was that phonons could not produce transition temperatures near 100K, and the main direction of research focused on nonphononic mechanisms. Subsequent work last reviewed by L. Pintschovius in 2005 showed that electron-phonon coupling in the cuprates is surprisingly strong for some phonons and its role is controversial. Experiments performed since then identified anomalous behavior of certain Cu-O bond-stretching phonons in cuprates as an important phenomenon that is somehow related to the mechanism of superconductivity. A particularly big advance was made in the study of doped La2CuO4. This work is reviewed here., Comment: Review article. To appear in Advances in Condensed Matter Physics, Special Issue: Phonons and Electron Correlations in High-Temperature and Other Novel Superconductors (HTS)

We measured phonon frequencies and linewidths in doped and undoped BaFe2As2 single crystals by inelastic x-ray scattering and compared our results with density functional theory (DFT) calculations. In agreement with previous work, the calculated frequencies of some phonons depended on whether the ground state was magnetic or not and, in the former case, whether phonon wavevector was parallel or perpendicular to the magnetic ordering wavevector. The experimental results agreed better with the magnetic calculation than with zero Fe moment calculations, except the peak splitting expected due to magnetic domain twinning was not observed. Furthermore, phonon frequencies were unaffected by the breakdown of the magnetic ground state due to either doping or increased temperature. Based on these results we propose that phonons strongly couple not to the static order, but to high frequency magnetic fluctuations., Comment: Minor revision of the text

Extensive inelastic neutron scattering measurements of phonons on a single crystal of CaFe2As2 allowed us to establish a fairly complete picture of phonon dispersions in the main symmetry directions. The phonon spectra were also calculated by density functional theory (DFT) in the local density approximation (LDA). There are serious discrepancies between calculations done for the optimized structure and experiment, because the optimised structure is not the ambient pressure structure but is very close to the collapsed structure reached at p = 3.5 kbar. However, if the experimental crystal structure is used the calculation gives correct frequencies of most phonons. The most important new result is that linewidths/frequencies of certain modes are larger/softer than predicted by DFT-LDA. We also observed strong temperature dependence of some phonons near the structural phase transition near 173K. This behavior may indicate anomalously strong electron phonon coupling and/or anharmonicity, which may be important to the mechanism of superconductivity., Comment: 12 pages, 3 figues Revised version, Final version, Accepted for publication in Physical Review Letters

We show that the superconducting energy gap $\Delta$ can be directly observed in phonon spectra, as predicted by recent theories. In addition, since each phonon probes the gap on only a small part of the Fermi surface, the gap anisotropy can be studied in detail. Our neutron scattering investigation of the anisotropic conventional superconductor YNi$_2$B$_2$C demonstrates this new application of phonon spectroscopy., Comment: 4 pages, 5 figures

In Fe-As based superconductors magnetism and superconductivity show strong sensitivity to the lattice, suggesting a possibility of unconventional electron-phonon coupling. We investigated c-axis polarized phonons in doped and undoped BaFe2As2 by inelastic X-ray scattering. Phonon peak positions and linewidths did not vary significantly as a function of doping either by Co or by K. The linewidth of the Fe vibration shows unusual wavevector-dependence, which may be due to hybridization with in-plane modes. Comparison with the density functional theory shows significant difference for the energy of the As-As vibrations (Raman active at the zone center) but not for the Fe-As vibrations (infrared-active at the zone center). This behavior cannot be explained by a 10% softening of Fe-As interaction strength as proposed previously for in-plane polarized vibrations.

One of the possible mechanisms of high Tc superconductivity is Cooper pairing with the help of bosons, which change the slope of the electronic dispersion as observed by photoemission. Giustino et al. calculated that in the high temperature superconductor La1.85Sr0.15CuO4 crystal lattice vibrations (phonons) should have a negligible effect on photoemission spectra and concluded that phonons do not play an important role. We show that the calculations employed by Giustino et al. fail to reproduce huge influence of electron-phonon coupling on important phonons observed in experiments. Thus one would expect these calculations to similarly fail in explaining the role of electron-phonon coupling for the electronic dispersion., Comment: To appear in Nature as a Brief Communiction Arising

The recent discovery and subsequent developments of FeAs-based superconductors have presented novel challenges and opportunities in the quest for superconducting mechanisms in correlated-electron systems. Central issues of ongoing studies include interplay between superconductivity and magnetism as well as the nature of the pairing symmetry reflected in the superconducting energy gap. In the cuprate and RE(O,F)FeAs (RE = rare earth) systems, the superconducting phase appears without being accompanied by static magnetic order, except for narrow phase-separated regions at the border of phase boundaries. By muon spin relaxation measurements on single crystal specimens, here we show that superconductivity in the AFe$_{2}$As$_{2}$ (A = Ca,Ba,Sr) systems, in both the cases of composition and pressure tunings, coexists with a strong static magnetic order in a partial volume fraction. The superfluid response from the remaining paramagnetic volume fraction of (Ba$_{0.5}$K$_{0.5}$)Fe$_{2}$As$_{2}$ exhibits a nearly linear variation in T at low temperatures, suggesting an anisotropic energy gap with line nodes and/or multi-gap effects., Comment: 14 pages 7 figures (4 for main text and 3 for on-line supplementary documents)

Inelastic x-ray scattering (IXS) was used to study the Cu-O bond-stretching vibrations in the static stripe phase compound La1.48Nd0.4Sr0.12CuO4. It was found that the intrinsic width in Q-space of the previously reported huge anomalous phonon softening and broadening is approximately 0.08r.l.u HWHM. A detailed comparison was also made to inelastic neutron scattering (INS) studies, which indicate a two-peak lineshape (with superimposed broad and narrow peaks) in the vicinity of the anomaly. The high resolution IXS data show that the narrow peak is mostly an artifact of the poor transverse Q-resolution of INS. Otherwise the agreement between the INS and IXS was excellent., Comment: 8 pages 3 figures SNS2007 conference proceedings; version 2: minor changes throughout the text

Inelastic neutron scattering was used to study the Cu-O bond-stretching vibrations in optimally doped La1.85Sr0.15CuO4 (Tc = 35 K) and in two other cuprates showing static stripe order at low temperatures, i.e. La1.48Nd0.4Sr0.12CuO4 and La1.875Ba0.125CuO4. All three compounds exhibit a very similar phonon anomaly, which is not predicted by conventional band theory. It is argued that the phonon anomaly reflects a coupling to charge inhomogeneities in the form of stripes, which remain dynamic in superconducting La1.85Sr0.15CuO4 down to the lowest temperatures. These results show that the phonon effect indicating stripe formation is not restricted to a narrow region of the phase diagram around the so-called 1/8 anomaly but occurs in optimally doped samples as well., Comment: to appear in J. Low Temp. Phys

We present results of neutron scattering experiments on YBa2Cu3O6.95 (Tc=93K). Our results indicate that magnetic collective modes due to correlated local moments are present both above and below Tc in optimally doped YBCO. The magnon-like modes are robust and not overdamped by itinerant particle-hole excitations, which may point at a substantial static or slowly fluctuating charge inhomogeneity. We compare the experimental results to predictions of the Fermi liquid (FL) theory in the Random Phase Approximation (RPA)., Comment: This is a new version, which is substantially different from the previous one. Physical Review B, in print

The dispersion of the Cu-O bond-stretching vibrations in overdoped La$_{1.7}$Sr$_{0.3}$CuO$_4$ (not superconducting) has been studied by high resolution inelastic neutron scattering. It was found that the doping-induced renormalization of the so-called breathing and the half-breathing modes is larger than in optimally doped La$_{1.85}$Sr$_{0.15}$CuO$_4$. On the other hand, the phonon linewidths are generally smaller in the overdoped sample. Features observed in optimally doped La$_{1.85}$Sr$_{0.15}$CuO$_4$ which suggest a tendency towards charge stripe formation are absent in overdoped La$_{1.7}$Sr$_{0.3}$CuO$_4$., Comment: 6 pages, 8 figures

Spin gap in optimally-doped YBCO was investigated by inelastic neutron scattering. We found that q-integrated spectral weight in the vicinity of the spin gap has a shape of a step function at 10K with sharp resolution-limited onset at 33 meV, i.e. there is no observable spectral weight at 31 meV but full spectral weight at 35 meV. The spin gap does not soften or "fill in" as the temperature is increased to Tc. Above Tc we find no evidence for q-dependent magnetic signal at 35 meV.

The attempt to understand cuprate superconductors is complicated by the presence of multiple strong interactions. While many believe that antiferromagnetism is important for the superconductivity, there has been revived interest in the role of electron-lattice coupling. The recently studied conventional superconductor MgB2 has a very strong electron-lattice coupling, involving a particular vibrational mode (phonon), that was predicted by standard theory and confirmed quantitatively by experiment. Here we present inelastic scattering measurements that show a similarly strong anomaly in the Cu-O bond-stretching phonon in the cuprate superconductors La2-xSrxCuO4 (with x=0.07, 0.15). This is in contrast to conventional theory, which does not predict such behavior. The anomaly is strongest in La1.875Ba0.125CuO4 and La1.48Nd0.4Sr0.12CuO4, compounds that exhibit spatially modulated charge and magnetic order, often called stripe order. It occurs at a wave vector corresponding to the charge order. These results suggest that this giant electron-phonon anomaly, which is absent in undoped and over-doped non-superconductors, is associated with charge inhomogeneity. It follows that electron-phonon coupling may be important to our understanding of superconductivity, although its contribution to the mechanism is likely to be indirect., Comment: to appear in Nature, 16 pages, 4 figures, very minor changes in text and figures from previous version

Using Angle-Resolved Photoemission (ARPES), we present the first observation of sharp quasiparticle-like peaks in a CMR manganite. We focus on the ($\pi$,0) regions of k-space and study their electronic scattering rates and dispersion kinks, uncovering the critical energy scales, momentum scales, and strengths of the interactions that renormalize the electrons. To identify these bosons we measured phonon dispersions in the energy range of the kink by inelastic neutron scattering (INS), finding a good match in both energy and momentum to the oxygen bond-stretching phonons.