We measured phonon dispersion in single crystal EuTiO$_3$ using inelastic x-ray scattering. A structural transition to an antiferrodistortive phase was found at a critical temperature $T_0$=287$\pm$1 K using powder and single-crystal x-ray diffraction. Clear softening of the zone boundary \emph{R}-point \textbf{q}=(0.5 0.5 0.5) acoustic phonon shows this to be a displacive transition. The mode energy plotted against reduced temperature could be seen to nearly overlap that of $\rm SrTiO_3$, suggesting a universal scaling relation. Phonon dispersion was measured along $Γ$-$X$ (0 0 0)$\rightarrow$(0.5 0 0). Mode eigenvectors were obtained from a shell model consistent with the \textbf{q}-dependence of intensity and energy, which also showed that the dispersion is nominally the same as in $\rm SrTiO_3$ at room temperature, but corrected for mass. The lowest energy optical mode, determined to be of Slater character, softens approximately linearly with temperature until the 70-100 K range where the softening stops, and at low temperature, the mode disperses linearly near the zone center.
We study the fundamental question of the lattice dynamics of a metallic ferromagnet in the regime where the static long range magnetic order is replaced by the fluctuating local moments embedded in a metallic host. We use the \textit{ab initio} Density Functional Theory(DFT)+embedded Dynamical Mean-Field Theory(eDMFT) functional approach to address the dynamic stability of iron polymorphs and the phonon softening with increased temperature. We show that the non-harmonic and inhomogeneous phonon softening measured in iron is a result of the melting of the long range ferromagnetic order, and is …
We predict a possible phonon softening instability in strongly correlated coupled semiconductor bilayer systems. By studying the plasmon-phonon coupling in coupled bilayer structures, we find that the renormalized acoustic phonon frequency may be softened at a finite wave vector due to many-body local field corrections, particularly in low density systems where correlation effects are strong. We discuss experimental possibilities to search for this predicted phonon softening phenomenon.
We study the half-breathing phonon in the three-band model of a high temperature superconductor, allowing for vibrations of atoms and resulting changes of hopping parameters. Two different approaches are compared. From the three-band model a t-J model with phonons can be derived, and phonon properties can be calculated. To make contact to density functional calculations, we also study the three-band model in the Hartree-Fock (HF) approximation. The paramagnetic HF solution, appropriate for the doped cuprates, has similarities to the local-density approximation (LDA). However, in contrast to th…
We study spin dynamics of a spin-Peierls chain with nearest-neighbor and next-nearest-neighbor Heisenberg spin exchange interactions together with a gapped and dispersionless phonon. The dynamical spin correlation function and phonon excitation spectrum are calculated at zero temperature by using dynamical density-matrix renormalization-group method. We find a new spin excitation assisted by non-softening phonon. The excitation is located above phonon in energy and shows a dispersive feature with strong intensity near the momentum $π$. The phonon excitation spectrum is also influenced by the s…
We investigate the periodic Anderson-Holstein model by using the dynamical mean-field theory combined with the exact diagonalization method. For the strong electron-phonon coupling $g\simg g_c$, the system shows an anomalous heavy-fermion behaviour which is accompanied by a large lattice fluctuation and an extreme phonon softening. We also calculate an effective potential for the ions and find that a simple harmonic potential for $g\siml g_c$ changes into a double-well potential for $g\simg g_c$. The effective pairing interaction between the conduction electrons shows a maximum at $g \approx g…
Inelastic neutron scattering is used to measure the temperature dependent phonon dispersion in Ca$_{2-x}$Sr$_{x}$RuO$_{4}$ ($x=0.4$, 0.6). The in-plane $Σ_{4}$ octahedral tilt mode softens significantly at the zone boundary of the high temperature tetragonal (HTT) \textit{I4}$_{\mathit{1}}$\textit{/acd} structure as the temperature approaches the transition to a low temperature orthorhombic (LTO) \textit{Pbca} phase. This behavior is similar to that in La$_2$CuO$_4$, but a new inelastic feature that is not found in the cuprate is present. An anomalous phonon mode is observed at energy transfer…
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 elect…
We investigate the influence of the electron-phonon coupling in the one-dimensional spinless Holstein model at half-filling using both a recently developed projector-based renormalization method (PRM) and an refined exact diagonalization technique in combination with the kernel polynomial method. At finite phonon frequencies the system shows a metal-insulator transition accompanied by the appearance of a Peierls distorted state at a finite critical electron-phonon coupling. We analyze the opening of a gap in terms of the (inverse) photoemission spectral functions which are evaluated in both ap…
To explore the driving mechanisms of the metal-insulator transition (MIT) and the structural transition in VO2, we have investigated phonon dispersions of rutile VO2 (R-VO2) in the DFT and the DFT+U (U : Coulomb correlation) band calculations. We have found that the phonon softening instabilities occur in both cases, but the softened phonon mode only in the DFT+U describes properly both the MIT and the structural transition from R-VO2 to monoclinic VO2 (M1-VO2). This feature demonstrates that the Coulomb correlation effect plays an essential role of assisting the Peierls transition in R-VO2. W…
The highly distinctive phonon self-energy dependences on the wave vector, calculated respectively for the static and dynamic stripe phase models of the underdoped cuprates are presented. The negative values of the real part of the on-stripe holes polarization loop lead to appearance of localized vibration states in the presence of well-separated stripes, relevant for underdoped cuprates. The localized modes split below the bare optical phonon frequencies exhibiting strong ``softening effect''. The calculated gap between localized and propagating phonon frequencies is practically doping indepen…
We derive a t-J model with electron-phonon coupling from the three-band model, considering modulation of both hopping and Coulomb integrals by phonons. While the modulation of the hopping integrals dominates, the modulation of the Coulomb integrals cannot be neglected. The model explains the experimentally observed anomalous softening of the half-breathing mode upon doping and a weaker softening of the breathing mode. It is shown that other phonons are not strongly influenced, and, in particular, the coupling to a buckling mode is not strong in this model.
We investigate the effect of electron-phonon interaction on the phononic properties in the one-dimensional half-filled Holstein model of spinless fermions. By means of determinantal Quantum Monte Carlo simulation we show that the behavior of the phonon dynamics gives a clear signal of the transition to a charge-ordered phase, and the phase diagram obtained in this way is in excellent agreement with previous DMRG results. By analyzing the phonon propagator we extract the renormalized phonon frequency, and study how it first softens as the transition is approached and then subsequently hardens i…
Polarized Raman scattering measurements have been performed on Na0.5CoO2 single crystal from 8 to 305 K. Both the A1g and E1g phonon modes show a softening below Tc1 ~ 83 K. Additionally, the A1g phonon mode, which is forbidden in the scattering geometry of cross polarization for the triangular CoO2 layers, appears below Tc1. In contrast, the metal-insulator transition at Tc2 ~ 46 K has only secondary effect on the Raman spectra. The phonon softening and the ``forbidden'' Raman intensity follow closely magnetic order parameter and the gap function at the Fermi surface, indicating that the dist…
In this work we present the results of an inelastic x-ray scattering experiment detailing the behavior of the transverse acoustic [110] phonon in BaFe2As2 as a function of temperature. When cooling through the structural transition temperature, the transverse acoustic phonon energy is reduced from the value at room temperature, reaching a maximum shift near inelastic momentum transfer q=0.1. This softening of the lattice results in a change of the symmetry from tetragonal to orthorhombic at the same temperature as the transition to long-range antiferromagnetic order. While the lattice distorti…
We present an inelastic light scattering study of single crystalline (La$_{1-y}$Pr$_y$)$_{1-x}$Sr$_{x}$MnO$_3$ ($0\leq x\leq0.14$,$y=0$ and $x=1/8$,$0\leq y\leq0.5$). A giant softening up to 20 - 30 cm$^{-1}$ of the Mn-O breathing mode has been observed only for the ferromagnetic insulating (FMI) samples ($0.11\leq x \leq 0.14$) upon cooling below the Curie temperature. With increasing Pr-doping the giant softening is gradually suppressed. This is attributed to a coupling of the breathing mode to orbital polarons which are present in the FMI phase.
We employ inelastic helium atom-surface scattering to measure the low energy phonon dispersion along high-symmetry directions on the surface of the topological insulator Bi$_2$Te$_3$. Results indicate that one particular low-frequency branch experiences noticeable mode softening attributable to the interaction between Dirac fermion quasiparticles and phonons on the surface. This mode softening constitutes a renormalization of the real part of the phonon self-energy. We obtain the imaginary part, and hence lifetime information, via a Hilbert transform. In doing so we are able to calculate an av…
Phonons in nearly optimally doped HgBa$_2$CuO$_{4+δ}$ were studied by inelastic X-ray scattering. The dispersion of the low energy modes is well described by a shell model, while the Cu-O bond stretching mode at high energy shows strong softening towards the zone boundary, which deviates strongly from the model. This seems to be common in the hole-doped high-$T_\mathrm{c}$ superconducting cuprates, and, based on this work, not related to a lattice distortion specific to each material.
Phonon softening is a ubiquitous phenomenon in condensed matter systems which is often associated with charge density wave (CDW) instabilities and anharmonicity. The interplay between phonon softening, CDW and superconductivity is a topic of intense debate. In this work, the effects of anomalous soft phonon instabilities on superconductivity are studied based on a recently developed theoretical framework that accounts for phonon damping and softening within the Migdal-Eliashberg theory. Model calculations show that the phonon softening in the form of a sharp dip in the phonon dispersion relati…
Monoclinic crystal structure of the undoped BaBiO3 can be described as a cubic perovskite distorted by a frozen breathing and tilting phonon modes of BiO6 octahedra. The phonon mode softening is experimentally observed [M. Braden et al., Europhysics Letters (EPL) 34, 531 (1996)] in Ba1-xKxBiO3 through potassium doping followed by a transition into an ideal cubic perovskite structure at x = 0.37 close to the appearance of superconductivity. In our previous paper [D. Korotin et al., Journal of Physics: Condensed Matter 24, 415603 (2012)] we demonstrated that it is necessary to take into account …
The layered compound $\mathrm{Ta_2NiSe_5}$ is a quasi-one-dimensional and narrow-gap semiconductor, which is proposed to undergo a transition to an excitonic insulator at $T_\mathrm{c}=326$ K. We found a clear anomaly at $T_\mathrm{c}$ in the in-plane thermal conductivities both parallel ($\parallel$ $a$) and perpendicular ($\parallel$ $c$) to the one-dimensional chains, $κ_\mathrm{a}$ and $κ_\mathrm{c}$. While $κ_\mathrm{a}$ shows a rapid decrease below $T_\mathrm{c}$, $κ_\mathrm{c}$ shows a pronounced V-shaped suppression centered at $T_\mathrm{c}$. We argue that the decrease of $κ_\mathrm{a…
We report the first measurement of the optical phonon dispersion in optimally doped single layer Bi2Sr1.6La0.4Cu2O6+delta using inelastic x-ray scattering. We found a strong softening of the Cu-O bond stretching phonon at about q=(0.25,0,0) from 76 to 60 meV, similar to the one reported in other cuprates. A direct comparison with angle-resolved photoemission spectroscopy measurements taken on the same sample, revealed an excellent agreement in terms of energy and momentum between the ARPES nodal kink and the soft part of the bond stretching phonon. Indeed, we find that the momentum space where…
Quasiparticle dynamics of FeSe single crystals revealed by dual-color transient reflectivity measurements (ΔR/R) provides unprecedented information on Fe-based superconductors. The amplitude of fast component in ΔR/R clearly tells a competing scenario between spin fluctuations and superconductivity. Together with the transport measurements, the relaxation time analysis further exhibits anomalous changes at 90 K and 230 K. The former manifests a structure phase transition as well as the associated phonon softening. The latter suggests a previously overlooked phase transition or crossover in FeS…
Energy- and time-resolved spectroscopy reveals a photoinduced softening of the charge-transfer gap in the insulating copper oxide Sr2CuO2Cl2 that indicates rapid and efficient photoproduction of optical phonons. By relating the pump-probe signal amplitude to the thermal difference spectrum, we estimate that eleven to twenty optical phonons are created for every one 3 eV photon. Assuming relaxation to the optical absorption edge at 1.5 eV, this corresponds to 70-130 meV per boson. While the lower limit is consistent with relaxation exclusively through optical phonons, the upper limit suggests a…
We report a direct observation of a sharp Kohn-like anomaly in the doubly degenerate copper-oxygen bond-stretching phonon mode occurring at $\mathbf{q}\mathrm{=(0.3, 0,0)}$ in La$_{2-x}$Ba$_x$CuO$_{4+δ}$ with $\mathrm{x=0.14\pm0.01}$, thanks to the high $\mathbf{Q}$ resolution of inelastic x-ray scattering. This anomaly is clearly seen when the inelastic signal is analysed using a single mode but is also consistent with a two mode hypothesis possibly due to a splitting of the degenerate modes due to symmetry breaking stripes. Our observation shows that the effect persists at the stripe propaga…
We investigated the crystal structure and lattice excitations of the ternary intermetallic stannide Ca3Ir4Sn13 using neutron and x-ray scattering techniques. For T > T* ~ 38 K the x-ray diffraction data can be satisfactorily refined using the space group Pm-3n. Below T* the crystal structure is modulated with a propagation vector of q = (1/2, 1/2, 0). This may arise from a merohedral twinning in which three tetragonal domains overlap to mimic a higher symmetry, or from a doubling of the cubic unit cell. Neutron diffraction and neutron spectroscopy results show that the structural transition at…
Neutron spectroscopy is used to probe transverse acoustic phonons near the (2, 2, 0) Bragg position in colossal magnetoresistive La0.7Ca0.3MnO3 and La0.7Sr0.3MnO3. Upon warming to temperatures near Tc = 257 K the phonon peaks in La0.7Ca0.3MnO3 soften and damp significantly with the phonon half width at half maximum approaching 2.5 meV for phonons at a reduced wave vector of q = (0.2, 0.2, 0). Concurrently a quasielastic component develops that dominates the spectrum near the polaron position at high temperatures. This quasielastic scattering is ~5 times more intense near Tc than in La0.7Sr0.3M…
We have investigated the phonon and the magnetic excitations in LaCoO3 by inelastic neutron scattering measurements. The acoustic phonon dispersions show some characteristic features of the folded Brillouin zone (BZ) for the rhombohedrally distorted perovskite structure containing two chemical formula units of LaCoO3 in the unit cell. We observed two transverse optical (TO) phonon branches along (delta, delta, delta), consistent with previously reported Raman active Eg modes which show remarkable softening associated with the spin-state transition [Ishikawa et al., (Phys. Rev. Lett. 93 (2004) …
Spin dynamics is calculated in the ferromagnetic (FM) state of the generalized Kondo lattice model taking into account strong on-site correlations between e_g electrons and antiferromagnetic (AFM) exchange among t_{2g} spins. Our study suggests that competing FM double-exchange and AFM super-exchange interaction lead to a rather nontrivial spin-wave spectrum. While spin excitations have a conventional Dq^2 spectrum in the long-wavelength limit, there is a strong deviation from the spin-wave spectrum of the isotropic Heisenberg model close to the zone boundary. The relevance of our results to t…
Unique Charge-density-wave Order and Fluctuation-induced Phonon Softening in the Optimally-doped Trilayer Cuprate Bi$_2$Sr$_2$Ca$_2$Cu$_3$O$_{10+δ}$
University of Hyogo（兵库大学）；National Institutes for Quantum Science and Technology (QST)（量子科学技术研究开发机构）；National Synchrotron Radiation Research Center（国家同步辐射研究中心）；Institute of Multidisciplinary Research for Advanced Materials (IMRAM), Tohoku University（东北大学先进物质多学科研究所）；University of Tokyo（东京大学）；National Institute of Advanced Industrial Science and Technology（产业技术综合研究所）
We study the ultrafast phonon response of mixed-valence perovskite Cs$_2$Au$_2$I$_6$ using pump-probe spectroscopy under high-pressure in a diamond anvil cell. We observed a remarkable softening and broadening of the Au - I stretching phonon mode with both applied pressure and photoexcitation. Using a double-pump scheme we measured a lifetime of the charge transfer excitation into single valence Au$^{2+}$ of less than 4 ps, which is an indication of the local character of the Au$^{2+}$ excitation. Furthermore, the strong similarity between the pressure and fluence dependence of the phonon soft…
We observe a giant increase of the infrared intensity and a softening of the in-plane antisymmetric phonon mode Eu (~0.2 eV) in bilayer graphene as a function of the gate-induced doping. The phonon peak has a pronounced Fano-like asymmetry. We suggest that the intensity growth and the softening originate from the coupling of the phonon mode to the narrow electronic transition between parallel bands of the same character, while the asymmetry is due to the interaction with the continuum of transitions between the lowest hole and electron bands. The growth of the peak is a manifestation of the "c…
The phonon dispersion curve of SmS under pressure was studied by inelastic x-ray scattering around the pressure-induced valence transition. A significant softening of the longitudinal acoustic modes propagating along the [111] direction was observed spanning a wide $q$ region from ($\frac{2π}{3a},\frac{2π}{3a},\frac{2π}{3a}$) up to the zone boundary as SmS becomes metallic. The largest softening occurs at the zone boundary and stays stable up to the highest measured pressure of 80 kbar while a gradual hardening of the low $q$ modes simultaneously appears. This phonon spectrum indicates favorab…
We use variable-temperature x-ray thermal diffuse scattering and inelastic scattering to investigate the lattice dynamics in single crystals of multiferroic CaMn7O12 which undergo a series of orbital and magnetic transitions at low temperatures. Upon approaching the charge and orbital ordering temperature To=250 K from above, we observe intense diffuse scattering features and a pronounced optical phonon softening centered around the superstructure reflections of the incommensurately modulated structure. The phonon anomaly appears well above To and continuously increases upon cooling, following…
We have used a combination of ultrafast coherent phonon spectroscopy, ultrafast thermometry, and time-dependent Landau theory to study the inversion symmetry breaking phase transition at $T_c = 200$ K in the strongly spin-orbit coupled correlated metal Cd$_2$Re$_2$O$_7$. We establish that the structural distortion at $T_c$ is a secondary effect through the absence of any softening of its associated phonon mode, which supports a purely electronically driven mechanism. However, the phonon lifetime exhibits an anomalously strong temperature dependence that decreases linearly to zero near $T_c$. W…
We investigate the effect of electron-phonon coupling on low temperature phases in metallic single-wall carbon nanotubes. We obtain low-temperature phase diagrams of armchair and zigzag type nanotubes with screened interactions with a weak-coupling renormalization group approach. In the absence of electron-phonon coupling, two types of nanotubes have similar phase diagrams. A $D$-Mott phase or $d$-wave superconductivity appears when the on-site interaction is dominant, while a charge-density wave or an excitonic insulator phase emerges when the nearest neighbor interaction becomes comparable t…
A strong electron-phonon interaction arises from the modulation of the superexchange interaction by lattice vibrations. It is responsible for the softening of the half-breathing modes around (pm pi/a,0) and (0, pm pi/a) in the two-dimensional Brillouin zone, with a being the lattice constant of CuO_2 planes, as is studied in Phys. Rev. B70, 184514 (2004). Provided that antiferromagnetic spin fluctuations are developed around Q=(pm 3 pi/4a, pm pi/a) and (pm pi/a, pm 3 pi/4a), the electron-phonon interaction can also cause the softening of Cu-O bond stretching modes around 2Q, or around (pm pi/2…
We present results on the dynamical correlation functions of the particle-hole symmetric Holstein-Hubbard model at zero temperature, calculated using the dynamical mean field theory which is solved by the numerical renormalization group method. We clarify the competing influences of the electron-electron and electron-phonon interactions particularity at the different metal to insulator transitions. The Coulomb repulsion is found to dominate the behaviour in large parts of the metallic regime. By suppressing charge fluctuations, it effectively decouples electrons from phonons. The phonon propag…
We study the one-dimensional Holstein model of spinless fermions interacting with dispersion-less phonons by using a recently developed projector-based renormalization method (PRM). At half-filling the system shows a metal-insulator transition to a Peierls distorted state at a critical electron-phonon coupling where both phases are described within the same theoretical framework. The transition is accompanied by a phonon softening at the Brillouin zone boundary and a gap in the electronic spectrum. For different filling, the phonon softening appears away from the Brillouin zone boundary and th…
The magnetic excitations in electron doped (Sr$_{1-x}$La$_x$)$_2$IrO$_4$ with $x = 0.03$ were measured using resonant inelastic X-ray scattering at the Ir $L_3$-edge. Although much broadened, well defined dispersive magnetic excitations were observed. Comparing with the magnetic dispersion from the parent compound, the evolution of the magnetic excitations upon doping is highly anisotropic. Along the anti-nodal direction, the dispersion is almost intact. On the other hand, the magnetic excitations along the nodal direction show significant softening. These results establish the presence of str…
Diffuse X-ray data for mixed stack organic charge-transfer crystals approaching the neutral-ionic phase transition can be quantitatively explained as due to the softening of the optical phonon branch. The interpretation is fully consistent with vibrational spectra, and underlines the importance of electron-phonon coupling in low-dimensional systems with delocalized electrons.
We report a Raman study of the effect of temperature on the self-energies of optical phonons in a number of transition metals with hexagonal-close-packed structure. Anisotropic softening of phonon energies and narrowing of phonon linewidths with increasing temperature are observed. These effects are reproduced in the calculations of phonon spectral functions based on \textit{ab initio} electronic structures and with carrier scattering by phonons taken into account. The combined observations and results of simulations indicate a relation between observed anomalies and the renormalization of the…
Temperature- and x-dependent Raman scattering studies of the charge density wave (CDW) amplitude modes in CuxTiSe2 show that the amplitude mode frequency omega_o exhibits identical power-law scaling with the reduced temperature, T/T_CDW, and the reduced Cu content, x/x_c, i.e., omega_o ~ (1 - p)^0.15 for p = T/T_CDW or x/x_c, suggesting that mode softening is independent of the control parameter used to approach the CDW transition. We provide evidence that x-dependent mode softening in CuxTiSe2 is caused by the reduction of the electron-phonon coupling constant lambda due to expansion of the l…
The charge-density-wave (CDW) order with macroscopically occupied electrons distorts the underlying lattice and usually causes the softening of the associated phonon mode. However, previous studies demonstrated that the spin-Peierls transition does not always induce an associated phonon softening, but the central-peak scenario applied in the quasi-one-dimensional compound CuGeO$_3$. We generalize the lattice-dynamics studies on the two-dimensional CDW state at van-Hove-singularity (VHS) filling and find that the CDW ordering could develop a central peak at zero frequency while the associated p…
We report on first investigation of the lattice dynamics in the novel superconducting material Na$\_{0.35}$CoO$\_2$$\cdot$1.3H$\_2$O and the non-hydrated parent compound Na$\_{0.7}$CoO$\_2$ by inelastic x-ray scattering. The measured phonon dispersion along the $Γ-M$ direction show a marked softening with hole doping of two optical phonon branches close to the Brillouin zone boundary. The phonon spectra, dispersion, and softening are well reproduced by first-principle calculations. The calculations indicates that the soft branches are mainly composed of Co-vibration modes. The estimation of th…
The electronic state around a single vacancy in silicon crystal is investigated by using the Green's function approach. The triply degenerate charge states are found to be widely extended and account for extremely large elastic softening at low temperature as observed in recent ultrasonic experiments. When we include the LS coupling $λ_{\rm Si}$ on each Si atom, the 6-fold spin-orbital degeneracy for the $V^{+}$ state with the valence +1 and spin 1/2 splits into $Γ_{7}$ doublet groundstates and $Γ_{8}$ quartet excited states with a reduced excited energy of $O(λ_{\rm Si}/10)$. We also consider…
Several experimental and theoretical studies in cobaltates suggest the proximity of the system to charge ordering (CO). We show, qualitatively, in the frame of a $t-V$ model coupled to phonons that optical phonon modes at the $K$ and $M$ points of the Brillouin zone, which involves only $O$-ions displacement around a $Co$-ion, are good candidates to display anomalies due to the CO proximity. If by increasing of $H_2O$ content the system is pushed closer to CO, the mentioned phonon modes should show softening and broadening.
Inelastic x-ray scattering (IXS) with very high (meV) energy resolution has become a valuable spectroscopic tool, complementing the well established coherent inelastic neutron scattering (INS) technique for phonon dispersion investigations. In the study of crystalline systems IXS is a viable alternative to INS, especially in cases where only small samples are available. Using IXS, we have measured the phonon dispersion of Nd_{1.86}Ce_{0.14}CuO_{4+δ} along the [x,0,0] and [x,x,0] in-plane directions. Compared to the undoped parent compound, the two highest longitudinal optical (LO) phonon branc…
The dispersion of the high-energy phonon modes in the electron doped high-temperature superconductor Nd$_{1.85}$Ce$_{0.15}$CuO$_4$ has been studied by inelastic neutron scattering. The frequencies of phonon modes with Cu-O bond-stretching character drop abruptly when going from the Brillouin zone center along the [100]-direction; this dispersion is qualitatively similar to observations in the hole-doped cuprates. We also find a softening of the bond-stretching modes along the [110]-direction but which is weaker and exhibits a sinusoidal dispersion. The phonon anomalies are discussed in compari…
We propose a microscopic mechanism for the incommensurate phase in TiOX compounds. The model includes the antiferromagnetic chains of Ti ions immersed in the phonon bath of the bilayer structure. Making use of the Cross-Fisher theory, we show that the geometrically frustrated character of the lattice is responsible for the structural instability which leads the chains to an incommensurate phase without an applied magnetic field. In the case of TiOCl, we show that our model is consistent with the measured phonon frequencies at $T=300K$ and the value of the incommensuration vector at the transit…
