We report high-resolution resonant inelastic x-ray scattering (RIXS) measurements of the collective spin fluctuations in three compositions of the superconducting cuprate system La2-xSrxCuO4. We have mapped out the excitations throughout much of the 2-D (h,k) Brillouin zone. The spin fluctuations in La2-xSrxCuO4 are found to be fairly well-described by a damped harmonic oscillator model, thus our data allows us to determine the full wavevector dependence of the damping parameter. This parameter increases with doping and is largest along the (h, h) line, where it is peaked near (0.2,0.2). We have used a new procedure to determine the absolute wavevector-dependent susceptibility for the doped compositions La2-xSrxCuO4 (x=0.12,0.16) by normalising our data to La2CuO4 measurements made with inelastic neutron scattering (INS). We find that the evolution with doping of the intensity of high-energy excitations measured by RIXS and INS is consistent. For the doped compositions, the wavevector-dependent susceptibility is much larger at (1/4,1/4) than at (1/2,0). It increases rapidly along the (h,h) line towards the antiferromagnetic wavevector of the parent compound (1/2,1/2). Thus, the strongest magnetic excitations, and those predicted to favour superconductive pairing, occur towards the (1/2,1/2) position as observed by INS.
Inelastic Neutron Scattering (INS) data in LSCO, YBCO and Bi2212 are discussed. In the literature, the INS spectra remain far from being comprehensively understood. We show that local (Q-integrated) susceptibility data and the energy dependence of the spin susceptibility at antiferromagnetic vector, Q = (p,p), can be interpreted by using the phase diagram for hole-doped cuprates. We analyze also the origin of the resonant peak which relates to the order parameter for long-range phase coherence in hole-doped cuprates. Thus, we present an interpretation of neutron data in LSCO, YBCO and Bi2212 p…
Resonant inelastic x-ray scattering (RIXS) tuned for the Cu L edge is a possible tool to detect charge excitations in cuprate superconductors. We theoretically investigate the possibility for observing a collective charge excitation by the RIXS. The RIXS process via the intermediate state inevitably makes the spectral weight of charge excitation stronger in electron doping than in hole doping. Electron-hole asymmetry also appears in the dynamical charge structure factor, showing a new enhanced small-momentum low-energy mode in electron doping. These facts indicate a possibility of detecting th…
High Tc superconductors show a rich variety of phases associated with their charge degrees of freedom. Valence charges can give rise to charge ordering or acoustic plasmons in these layered cuprate superconductors. While charge ordering has been observed for both hole- and electron-doped cuprates, acoustic plasmons have only been found in electron-doped materials. Here, we use resonant inelastic X-ray scattering (RIXS) to observe the presence of acoustic plasmons in two families of hole-doped cuprate superconductors [La2-xSrxCuO4 (LSCO) and Bi2Sr1.6La0.4CuO6+d (Bi2201)], crucially completing t…
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 collective magnetic excitations in the spin-orbit Mott insulator (Sr$_{1-x}$La$_x$)$_2$IrO$_4$ ($x=0,\,0.01,\,0.04,\, 0.1$) were investigated by means of resonant inelastic x-ray scattering. We report significant magnon energy gaps at both the crystallographic and antiferromagnetic zone centers at all doping levels, along with a remarkably pronounced momentum-dependent lifetime broadening. The spin-wave gap is accounted for by a significant anisotropy in the interactions between $J_\text{eff}=1/2$ isospins, thus marking the departure of Sr$_2$IrO$_4$ from the essentially isotropic Heisenbe…
How coherent quasiparticles emerge by doping quantum antiferromagnets is a key question in correlated electron systems, whose resolution is needed to elucidate the phase diagram of copper oxides. Recent resonant inelastic X-ray scattering (RIXS) experiments in hole-doped cuprates have purported to measure high-energy collective spin excitations that persist well into the overdoped regime and bear a striking resemblance to those found in the parent compound, challenging the perception that spin excitations should weaken with doping and have a diminishing effect on superconductivity. Here we sho…
We present a three-band Hubbard Hamiltonian and the associated Cu K-edge RIXS spectra for electron and hole doped cuprates over a wide range of energy and momentum transfers. By comparing computed spectra for the unfilled case with the corresponding results for 15% electron or hole doping at two different values of the effective Hubbard parameter U, generic signatures of the collapse of the magnetic gap and the characteristic momentum dependencies and evolution of the spectra with doping are identified. Available RIXS data support the gap collapse scenario for electron doped cuprates, but the …
Magnetic excitations in Ba(Fe0.94Co0.06)2As2 are studied by polarized inelastic neutron scattering (INS) above and below the superconducting transition. In the superconducting state we find clear evidence for two resonance-like excitations. At a higher energy of about 8 meV there is an isotropic resonance mode with weak dispersion along the c-direction. In addition we find a lower excitation at 4 meV that appears only in the c-polarized channel and whose intensity strongly varies with the L-component of the scattering vector. These resonance excitations behave remarkably similar to the gap mod…
Measurements of spin excitations are essential for an understanding of spin-mediated pairing for superconductivity; and resonant inelastic X-ray scattering (RIXS) provides a considerable opportunity to probe high-energy spin excitations. However, whether RIXS correctly measures the collective spin excitations of doped superconducting cuprates remains under debate. Here we demonstrate distinct Raman- and fluorescence-like RIXS excitations of Bi$_{1.5}$Pb$_{0.6}$Sr$_{1.54}$CaCu$_{2}$O$_{8+δ}$ in the mid-infrared energy region. Combining photon-energy and momentum dependent RIXS measurements with…
An optimally doped iron-based superconductor LaFeAsO$_{0.92}$F$_{0.08}$ with $T_c = 29$ K has been studied by inelastic powder neutron scattering. The magnetic excitation at $Q=1.15$ Å$^{-1}$ is enhanced below $T_c$, leading to a peak at $E_{res}\sim13$ meV as the resonance mode, in addition to the formation of a gap at low energy below the crossover energy $Δ_{c}\sim10 meV$. The peak energy at $Q=1.15$ Å$^{-1}$ corresponds to $5.2 k_B T_c$ in good agreement with the other values of resonance mode observed in the various iron-based superconductors, even in the high-$T_c$ cuprates. Although the…
We present a microscopic study of the nuclear magnetic relaxation rate 1/T1 based on the five-orbital model for iron-based superconductors. We mainly discuss the effect of the "inelastic" quasi-particle damping rate γ due to many-body interaction on the size of the coherence peak, for both s++ and s+- wave superconducting states. We focus on Ba(Fe1-xCox)2As2, and systematically evaluate γ in the normal state from the experimental resistivity, from optimally to over-doped compounds. Next, γ in the superconducting state is calculated microscopically based on the second order perturbation theory.…
The in-plane oxygen vibrations in La2NiO4 are investigated for several hole-doping concentrations both theoretically and experimentally via inelastic neutron scattering. Using an inhomogeneous Hartree-Fock plus RPA numerical method in a two-dimensional Peierls-Hubbard model, it is found that the doping induces stripe ordering of localized charges, and that the strong electron-lattice coupling causes the in-plane oxygen modes to split into two subbands. This result agrees with the phonon band splitting observed by inelastic neutron scattering in La2-xSrxNiO4. Predictions of strong electron-latt…
The evolution of electronic (spin and charge) excitations upon carrier doping is an extremely important issue in superconducting layered cuprates and the knowledge of its asymmetry between electron- and hole-dopings is still fragmentary. Here we combine x-ray and neutron inelastic scattering measurements to track the doping dependence of both spin and charge excitations in electron-doped materials. Copper L3 resonant inelastic x-ray scattering spectra show that magnetic excitations shift to higher energy upon doping. Their dispersion becomes steeper near the magnetic zone center and deeply mix…
We have performed resonant inelastic x-ray scattering (RIXS) near the Cu-K edge on cuprate superconductors La(2-x)Sr(x)CuO(4), La(2-x)Ba(x)CuO(4), La(2-x)Sr(x)Cu(1-y)Fe(y)O(4) and Bi(1.76)Pb(0.35)Sr(1.89)CuO(6+d), covering underdoped to heavily overdoped regime and focusing on charge excitations inside the charge-transfer gap. RIXS measurements of the 214 systems with Ei = 8.993 keV have revealed that the RIXS intensity at 1 eV energy transfer has a minimum at (0,0) and maxima at (0.4pi, 0) and $(0, 0.4pi) for all doping points regardless of the stripe ordered state, suggesting that the corres…
We use polarized inelastic neutron scattering (INS) to study spin excitations of optimally hole-doped superconductor Ba$_{0.67}$K$_{0.33}$Fe$_2$As$_{2}$ ($T_c=38$ K). In the normal state, the imaginary part of the dynamic susceptibility, $χ^{\prime\prime}(Q,ω)$, shows magnetic anisotropy for energies below $\sim$7 meV with c-axis polarized spin excitations larger than that of the in-plane component. Upon entering into the superconducting state, previous unpolarized INS experiments have shown that spin gaps at $\sim$5 and 0.75 meV open at wave vectors $Q=(0.5,0.5,0)$ and $(0.5,0.5,1)$, respecti…
Charge order in underdoped and optimally doped high-$T_\mathrm{c}$ superconductors Bi$_{2}$Sr$_{2-x}$La$_x$CuO$_{6+δ}$ (Bi2201) is investigated by Cu $L_3$ edge resonant inelastic x-ray scattering (RIXS). We have directly observed charge density modulation in the optimally doped Bi2201 at momentum transfer $Q_{\|} \simeq 0.23$ rlu, with smaller intensity and correlation length with respect to the underdoped sample. This demonstrates that short-range charge order in Bi2201 persists up to optimal doping, as in other hole-doped cuprates. We explored the nodal (diagonal) direction and found no cha…
Tunneling and inelastic neutron scattering (INS) measurements in cuprates are discussed. There is a clear discrepancy among energy-gap values for different 90 K cuprates, inferred from tunneling measurements. By using the phase diagram of hole-doped cuprates we interpret tunneling measurements in 90 K cuprates and INS data in YBCO.
Magnetic excitations in the optimally doped high-$T_\mathrm{c}$ superconductor Bi$_{1.5}$Pb$_{0.55}$Sr$_{1.6}$La$_{0.4}$CuO$_{6+δ}$ (OP-Bi2201, $T_\mathrm{c}\simeq 34$ K) are investigated by Cu $L_3$ edge resonant inelastic x-ray scattering (RIXS), below and above the pseudogap opening temperature. At both temperatures the broad spectral distribution disperses along the (1,0) direction up to $\sim$350~meV at zone boundary, similarly to other hole-doped cuprates. However, above $\sim$0.22 reciprocal lattice units, we observe a concurrent intensity decrease for magnetic excitations and quasi-ela…
The memory function approach to spin dynamics in doped antiferromagnetic insulator combined with the assumption of temperature independent static spin correlations and constant collective mode damping leads to omega/T scaling in a broad range. The theory involving a non universal scaling parameter is used to analyze recent inelastic neutron scattering results for underdoped cuprates. Adopting modified damping function also the emerging central peak in low-doped cuprates at low temperatures can be explained within the same framework.
A theory of the anomalous $ω/T$ scaling of the dynamic magnetic response in cuprates at low doping is presented. It is based on the memory function representation of the dynamical spin suceptibility in a doped antiferromagnet where the damping of the collective mode is constant and large, whereas the equal-time spin correlations saturate at low $T$. Exact diagonalization results within the t-J model are shown to support assumptions. Consequences, both for the scaling function and the normalization amplitude, are well in agreement with neutron scattering results.
The resonant inelastic x-ray scattering spectrum in insulating cuprates is examined by using the exact diagonalization technique on small clusters in the two-dimensional Hubbard model with second and third neighbor hopping terms. When the incident photon energy is tuned near the Cu K absorption edges, we find that the features of the unoccupied upper Hubbard band can be extracted from the spectrum through an anisotropic momentum dependence. They provide an opportunity for the understanding of the different behavior of hole- and electron-doped superconductors.
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 recent development of x-ray scattering techniques revealed the charge-excitation spectrum in high-$T_c$ cuprate superconductors. While the presence of a dispersive signal in the high-energy charge-excitation spectrum is well accepted in the electron-doped cuprates, its interpretation and universality are controversial. Since charge fluctuations are observed ubiquitously in cuprate superconductors, the understanding of its origin is a pivotal issue. Here, we employ the layered $t$-$J$ model with the long-range Coulomb interaction and show that an acoustic-like plasmon mode with a gap at in-…
We analyze high-resolution scanning tunneling spectra of the electron-doped cuprate Pr0.88LaCe0.12CuO4 (T_c = 24 K). We find that the spectral fine structure below 35 meV is consistent with strong coupling to a bosonic mode at 16 meV, in quantitative agreement with early tunneling spectra of Nd1.85Ce0.15CuO4. Since the energy of the bosonic mode is significantly higher than that (9.5-11 meV) of the magnetic resonance-like mode observed by inelastic neutron scattering, the coupling feature at 16 meV cannot arise from strong coupling to the magnetic mode. The present work thus demonstrates that …
The phonon dispersions of $\mathrm{Nd_{1.86}Ce_{0.14}CuO_{4+δ}}$ along the $[ξ,0,0]$ direction have been determined by inelastic x-ray scattering. Compared to the undoped parent compound, the two highest longitudinal phonon branches, associated with the Cu-O bond-stretching and out-of-plane oxygen vibration, are shifted to lower energies. Moreover, an anomalous softening of the bond-stretching band is observed around $\mathbf{q}=(0.2,0,0)$. These signatures provide evidence for strong electron-phonon coupling in this electron-doped high-temperature superconductor.
Inelastic neutron scattering is used to probe the collective spin excitations of the near optimally-doped superconductor Ba(Fe1-xCox)2As2 ($x$=0.065). Previous measurements on the antiferromagnetically ordered parents of this material show a strongly anisotropic spin-wave velocity. Here we measure the magnetic excitations up to 80 meV and show that a similar anisotropy persists for superconducting compositions. The dispersive mode measured here connects directly with the spin resonance previously observed in this compound. When placed on an absolute scale, our measurements show that the local-…
Extending our previous studies we present results for the doping-, momentum-, frequency-, and temperature- dependence of the kink-like change of the quasiparticle velocity resulting from the coupling to spin fluctuations. In the nodal direction a kink is found in both the normal and superconducting state while in the antinodal direction a kink occurs only below $T_c$ due to the opening of the superconducting gap. A pronounced kink is obtained only for hole-doped, but not for electron-doped cuprates and is characteristically different from what is expected due to electron-phonon interaction. We…
We probe the collective magnetic modes of La$_2$CuO$_4$ (LCO) and underdoped La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) by momentum resolved Resonant Inelastic X-ray Scattering (RIXS) at the Cu $L_3$ edge. In LCO the single magnon dispersion measured by RIXS coincides with the one determined by inelastic neutron scattering. For LSCO the spin dynamics shows a branch dispersing up to $\sim$400 meV coexisting with a branch at lower energy. Only the latter has been observed with neutrons so far and is considered a key signature of doped cuprates. The presence of the high-energy branch indicates that LSCO is i…
Inelastic neutron scattering measurements on Ba(Fe$_{0.963}$Ni$_{0.037}$)$_2$As$_2$ manifest a neutron spin resonance in the superconducting state with anisotropic dispersion within the Fe layer. Whereas the resonance is sharply peaked at Q$_{AFM}$ along the orthorhombic a axis, the resonance disperses upwards away from Q$_{AFM}$ along the b axis. In contrast to the downward dispersing resonance and hour-glass shape of the spin excitations in superconducting cuprates, the resonance in electron-doped BaFe$_2$As$_2$ compounds possesses a magnon-like upwards dispersion.
The phase diagram of order parameters for pairing and phase coherence in hole-doped cuprates is discussed. By examining carefully some recent inelastic neutron scattering data obtained on hole-doped cuprates and heavy fermion compound UPd2Al3 in which the superconductivity is mediated by spin fluctuations, we conclude that the coherent gap in hole-doped cuprates has most likely the magnetic origin and scales with Tc, on average, as 2Dc/kBTc = 5.4. We discuss a model of the superconductivity in hole-doped cuprates and the symmetries of two order parameters.
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. We attributed this mean-field behavior and the extended fluctuation regime to a sizable nem…
Calculations are presented for electronic Raman scattering and infrared conductivity in a $d_{x^{2}-y^{2}}$ superconductor including the effects of elastic scattering via anisotropic impurities and inelastic spin-fluctuation scattering. A consistent description of experiments on optimally doped Bi-2212 is made possible by considering the effects of correlations on both inelastic and elastic scattering.
The spin dynamics in single crystal, electron-doped Ba(Fe1-xCox)2As2 has been investigated by inelastic neutron scattering over the full range from undoped to the overdoped regime. We observe damped magnetic fluctuations in the normal state of the optimally doped compound (x=0.06) that share a remarkable similarity with those in the paramagnetic state of the parent compound (x=0). In the overdoped superconducting compound (x=0.14), magnetic excitations show a gap-like behavior, possibly related to a topological change in the hole Fermi surface (Lifshitz transition), while the imaginary part of…
We study the interplay between superconductivity and antiferromagnetic spin fluctuations in electron-doped cobaltate Na$_{x}$CoO$_{2}\cdot y$H$_{2}$O based on the kinetic energy driven superconductivity mechanism. We show that the superconducting state is governed by both charge carrier pairing and quasiparticle coherent, and displays a common dome-shaped phase diagram in agreement with experimental results. By calculating the dynamical spin structure factor, we theoretically find that the magnetic excitation shows a commensurate resonance peak, which locates at antiferromagnetic wave vector $…
We investigated the doping dependence of magnetic excitations in the lightly doped cuprate La2-xSrxCuO4 via combined studies of resonant inelastic x-ray scattering (RIXS) at the Cu L3-edge and theoretical calculations. With increasing doping, the magnon dispersion is found to be essentially unchanged, but the spectral width broadens and the spectral weight varies differently at different momenta. Near the Brillouin zone center, we directly observe bimagnon excitations which possess the same energy scale and doping dependence as previously observed by Raman spectroscopy. They disperse weakly in…
We report a Cu K-edge resonant inelastic x-ray scattering (RIXS) study of high-Tc cuprates. Momentum-resolved charge excitations in the CuO2 plane are examined from parent Mott insulators to carrier-doped superconductors. The Mott gap excitation in undoped insulators is found to commonly show a larger dispersion along the [pi,pi] direction than the [pi,0] direction. On the other hand, the resonance condition displays material dependence. Upon hole doping, the dispersion of the Mott gap excitation becomes weaker and an intraband excitation appears as a continuum intensity below the gap at the s…
The spin dynamics of high temperature superconductors measured by inelastic neutron scattering is reviewed. The spin susceptibility evolves a lot with increasing doping from the undoped insulating state to the overdoped metallic state. In the superconducting state, a strong magnetic resonance peak occurs in the spin excitation spectrum whose energy is proportional to the superconducting temperature. In underdoped and optimally doped regimes, normal state antiferromagnetic fluctuations are observed, proving the existence of strong electronic correlations in cuprates. They are characterized by a…
We used resonant inelastic x-ray scattering (RIXS) with and without analysis of the scattered photon polarization, to study dispersive spin excitations in the high temperature superconductor YBa2Cu3O6+x over a wide range of doping levels (0.1 < x < 1). The excitation profiles were carefully monitored as the incident photon energy was detuned from the resonant condition, and the spin excitation energy was found to be independent of detuning for all x. These findings demonstrate that the largest fraction of the spin-flip RIXS profiles in doped cuprates arises from magnetic collective modes, rath…
We use inelastic neutron scattering to explore the evolution of the low energy spin dynamics in the electron-doped cuprate Pr0.88LaCe0.12CuO4-d (PLCCO) as the system is tuned from its nonsuperconducting, as-grown antiferromagnetic (AF) state into an optimally-doped superconductor (Tc~24 K) without static AF order. The low temperature, low energy response of the spin excitations in under-doped samples is coupled to the presence of the AF phase, whereas the low-energy magnetic response for samples near optimal Tc exhibits spin fluctuations surprisingly insensitive to the sample temperature. This…
Momentum resolved inelastic resonant x-ray scattering is used to map the evolution of charge excitations over a large range of energies, momenta and doping levels in the electron doped Mott insulator class Nd$_{2-x}$Ce$_x$CuO$_4$. As the doping induced AFM-SC (antiferromagnetic-superconducting) transition is approached, we observe an anisotropic softening of collective charge modes over a large energy scale along the Gamma to (π,π)-direction, whereas the modes exhibit broadening ($\sim$ 1 eV) with relatively little softening along Gamma to (π,0) with respect to the parent Mott insulator (x=0).…
The detailed derivation of a theory for transport in quasi-two-dimensional metals, with small-angle elastic scattering and angle-independent inelastic scattering is presented. The transport equation is solved for a model Fermi surface representing a typical cuprate superconductor. Using the small-angle elastic and the inelastic scattering rates deduced from angle-resolved photoemission experiments, good quantitative agreement with the observed anomalous temperature dependence of the Hall angle in optimally doped cuprates is obtained, while the resistivity remains linear in temperature. The the…
The nature of the spin excitations in superconducting cuprates is a key question toward a unified understanding of the cuprate physics from long-range antiferromagnetism to superconductivity. The intense spin excitations up to the over-doped regime revealed by resonant inelastic X-ray scattering bring new insights as well as questions like how to understand their persistence or their relation to the collective excitations in ordered magnets (magnons). Here, we study the evolution of the spin excitations upon hole-doping the superconducting cuprate Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ by disentangling…
Using a Fermi-liquid-based theory we calculate the in-plane anisotropy of the spin susceptibility for hole-doped high-T_c cuprates. Employing the two-dimensional one-band Hubbard model and a generalized RPA-type theory we consider anisotropic hopping matrix elements ($t_x \neq t_y$) and a mixing of d- and s-wave symmetry of the superconducting order parameter in order to describe orthorhombic superconductors. We compare our calculations with available inelastic neutron scattering data on untwinned YBa{2}Cu{3}O{7-δ} and find good agreement. Furthermore, we predict a strongly anisotropic in-plan…
We study a two-dimensional single band Hubbard Hamiltonian with antisymmetric spin-orbit coupling. We argue that this is the minimal model to understand the electronic properties of locally non-centrosymmetric transition-metal (TM) oxides such as Sr$_2$IrO$_4$. Based on exact diagonalizations of small clusters and the random phase approximation, we investigate the correlation effects on charge and magnetic order as a function of doping and of the TM-oxygen-TM bond angle $θ$. For small doping and $θ$ $\lesssim$ $15^\circ$ we find dominant commensurate in-plane antiferromagnetic fluctuations whi…
We use inelastic neutron scattering to probe magnetic excitations of an optimally electron-doped superconductor Nd$_{1.85}$Ce$_{0.15}$CuO$_{4-δ}$ above and below its superconducting transition temperature $T_c=25$ K. In addition to gradually opening a spin pseudo gap at the antiferromagnetic ordering wavevector ${\bf Q}=(1/2,1/2,0)$, the effect of superconductivity is to form a resonance centered also at ${\bf Q}=(1/2,1/2,0)$ but at energies above the spin pseudo gap. The intensity of the resonance develops like a superconducting order parameter, similar to those for hole-doped superconductors…
It is widely accepted that: (i) the angle-resolved photoemission spectroscopy (ARPES) data produce evidences for the opening of a d-wave pairing gap in cuprates compounds described at low energies and temperatures by a BCS theory, and (ii) the basic pairing mechanism arises from the antiferromagnetic exchange correlations, but the charge fluctuations associated with double occupancy of a site also play an essential role in doped systems. The simplest model that is consistent with the two statements is the $t$-$U$-$V$-$J$ model. We have shown that the inelastic neutron scattering data on $YBa_2…
Manipulating spin fluctuations with ultrafast laser pulses is a promising route to dynamically control collective phenomena in strongly correlated materials. However, understanding how photoexcited spin degrees of freedom evolve at a microscopic level requires a momentum- and energy-resolved characterization of their nonequilibrium dynamics. Here, we study the photoinduced dynamics of finite-momentum spin excitations in two-dimensional Mott insulators on a square lattice. By calculating the time-resolved resonant inelastic x-ray scattering cross-section, we show that an ultrafast pump above th…
Motivated by the recent resonant x-ray scattering (RXS) and resonant inelastic x-ray scattering (RIXS) experiments in electron-doped cuprates, we study the charge excitation spectrum in a layered t-J model with the long-range Coulomb interaction. We show that the spectrum is not dominated by a specific type of charge excitations, but by different kinds of charge fluctuations, and is characterized by a dual structure in the energy space. Low-energy charge excitations correspond to various types of bond-charge fluctuations driven by the exchange term (J-term) whereas high-energy charge excitatio…
We use high-resolution inelastic neutron scattering to study the low-temperature magnetic excitations of electron-doped superconducting Pr$_{0.88}$LaCe$_{0.12}$CuO$_{4-δ}$ ($T_c=21\pm 1$ K) over a wide energy range (4 meV$\le\hbarω\le 330$ meV). The effect of electron-doping is to cause a wave vector ($Q$) broadening in the low-energy ($\hbarω\le 80$ meV) commensurate spin fluctuations at ($π$,$π$) and to suppress the intensity of spin-wave-like excitations at high energies ($\hbarω\ge 100$ meV). This leads to a substantial redistribution in the spectrum of the local dynamical spin susceptibil…
Motivated by the recent experiments reporting the doping dependence of the short-range charge order (CO) in electron-doped cuprates, we study the resonant x-ray scattering spectrum from d-wave bond-charge fluctuations obtained in the two-dimensional t-J model. We find that (i) the CO is short-range, (ii) the CO peak is pronounced at low temperature, (iii) the peak intensity increases with decreasing carrier doping $δ$ down to $δ\approx$ 0.10 and is substantially suppressed below $δ\approx$ 0.10 due to strong damping, and (iv) the momentum of the CO decreases monotonically down to $δ\approx$ 0.…
We use inelastic neutron scattering to study the effect of an in-plane magnetic field on the magnetic resonance in optimally doped superconductors FeSe$_{0.4}$Te$_{0.6}$ ($T_c=14$ K) and BaFe$_{1.9}$Ni$_{0.1}$As$_{2}$ ($T_c=20$ K). While the magnetic field up to 14.5 Tesla does not change the energy of the resonance, it particially suppresses $T_c$ and the corresponding superconductivity-induced intensity gain of the mode. However, we find no direct evidence for the field-induced spin-1 Zeeman splitting of the resonance. Therefore, it is still unclear if the resonance is the long-sought single…
We investigate whether the spin or charge degrees of freedom are responsible for the nodal gap in underdoped cuprates by performing inelastic neutron scattering and x-ray diffraction measurements on La$_{2-x}$Sr$_x$CuO$_4$, which is on the edge of the antiferromagnetic phase. We found that fluctuating incommensurate spin-density-wave (SDW) with a the bottom part of an hourglass dispersion exists even in this magnetic sample. The strongest component of these fluctuations diminishes at the same temperature where the nodal gap opens. X-ray scattering measurements on the same crystal show no signa…
We report inelastic neutron scattering experiments on single crystals of superconducting Ba0.67K0.33Fe2As2 (Tc = 38 K). In addition to confirming the resonance previously found in powder samples, we find that spin excitations in the normal state form longitudinally elongated ellipses along the QAFM direction in momentum space, consistent with density functional theory predictions. On cooling below Tc, while the resonance preserves its momentum anisotropy as expected, spin excitations at energies below the resonance become essentially isotropic in the in-plane momentum space and dramatically in…
Superconductivity appears to compete against the spin-density-wave in Fe pnictides. However, optimally cobalt doped samples show a quasi-two-dimensional spin excitation centered at the (0.5, 0.5, L) wavevector, "the spin resonance peak", that is strongly tied to the onset of superconductivity. By inelastic neutron scattering on single crystals we show the similarities and differences of the spin excitations in BaFe1.84Co0.16As2, with respect to the spin excitations in the high-temperature superconducting cuprates. As in the cuprates the resonance occurs as an enhancement to a part of the spin …
We investigate the doping dependence of the magnetic excitations in two-superconducting-dome-system LaFeAsO1-xDx. Using inelastic neutron scattering, spin fluctuations at different wavenumbers were observed under both superconducting domes around x = 0.1 and 0.4, but vanished at x = 0.2 corresponding to the Tc valley. Theoretical calculations indicate that the characteristic doping dependence of spin fluctuations is rationally explained as a consequence of the switching of the two intra-orbital nestings within Fe-3dYZ, ZX and 3dX2-Y2 by electron doping. The present results imply that the multi…
We present an inelastic neutron scattering study on single-crystalline LiFeAs devoted to the characterization of the incommensurate antiferromagnetic fluctuations at $\mathbf{Q}=(0.5\pmδ, 0.5\mpδ, q_l)$. Time-of-flight measurements show the presence of these magnetic fluctuations up to an energy transfer of 60 meV, while polarized neutrons in combination with longitudinal polarization analysis on a triple-axis spectrometer prove the pure magnetic origin of this signal. The normalization of the magnetic scattering to an absolute scale yields that magnetic fluctuations in LiFeAs are by a factor …
