We present a detailed analysis of the incident-photon-energy and polarization dependences of the resonant inelastic x-ray scattering (RIXS) spectra at the Cu $K$ edge in La$_{2}$CuO$_{4}$. Our analysis is based on the formula developed by Nomura and Igarashi, which describes the spectra by a product of an incident-photon-dependent factor and a density-density correlation function for 3d states. We calculate the former factor using the $4p$ density of states from an ab initio band structure calculation and the latter using a multiorbital tight-binding model within the Hartree-Fock approximation and the random phase approximation. We obtain spectra with rich structures in the energy-loss range 2-5 eV, which vary with varying momentum and incident-photon energy, in semi-quantitative agreement with recent experiments. We clarify the origin of such changes as a combined effect of the incident-photon-dependent factor and the density-density correlation function.
We report a Cu K-edge resonant inelastic x-ray scattering (RIXS) study of momentum-dependent charge excitations in Nd$_{2-x}$Ce$_x$CuO$_4$ ($x$ = 0.075 and 0.18). The peak position and width of the excitations coincide excellently with those observed in Cu L$_3$-edge RIXS. It demonstrates that the same charge excitations are observed at the two edges.
We use resonant inelastic x-ray scattering (RIXS) at the Cu L$_3$ edge to measure the charge and spin excitations in the "half-stuffed" Cu--O planes of the cuprate antiferromagnet Ba$_2$Cu$_3$O$_4$Cl$_2$. The RIXS line shape reveals distinct contributions to the $dd$ excitations from the two structurally inequivalent Cu sites, which have different out-of-plane coordinations. The low-energy response exhibits magnetic excitations. We find a spin-wave branch whose dispersion follows the symmetry of a CuO$_2$ sublattice, similar to the case of the "fully-stuffed" planes of tetragonal CuO (T-CuO). …
Observation of spin-conserving two-spinon continuum in the $S$=1/2 antiferromagnetic chain system Sr$_2$CuO$_3$ using Cu $K$-edge resonant inelastic x-ray scattering
By means of resonant inelastic x-ray scattering at the Cu L$_3$ edge, we measured the spin wave dispersion along $\langle$100$\rangle$ and $\langle$110$\rangle$ in the undoped cuprate Ca$_2$CuO$_2$Cl$_2$. The data yields a reliable estimate of the superexchange parameter $J$ = 135 $\pm$ 4 meV using a classical spin-1/2 2D Heisenberg model with nearest-neighbor interactions and including quantum fluctuations. Including further exchange interactions increases the estimate to $J$ = 141 meV. The 40 meV dispersion between the magnetic Brillouin zone boundary points (1/2,\,0) and (1/4,\,1/4) indicat…
We study theoretically resonant inelastic x-ray scattering (RIXS) at the Cu $L_3$-edge in a typical parent compound of high-$T_c$ cuprate superconductors La$_2$CuO$_4$ on the basis of a detailed electronic band structure. We construct a realistic and precise tight-binding model by employing the maximally-localized Wannier functions derived from a first-principles electronic structure calculation, and then take account of the Coulomb repulsion between d electrons at each Cu site. The antiferromagnetic ground state is described within the Hartree-Fock approximation, and take account of electron …
We find excitations lower in energy than known phonon modes in underdoped La$\_{2-x}$Sr$\_x$CuO$\_{4+δ}$ (x=0.08), with both inelastic X-Ray scattering (IXS) and inelastic neutron scattering (INS). A non dispersive excitation at 9 meV is identified and is also seen by INS in (La,Nd)$\_{2-x}$Sr$\_x$CuO$\_{4+δ}$, with 40$\%$ Nd substitution. INS also identifies a still lower energy dispersive mode at low q in the Nd free sample. These modes are clearly distinct from the longitudinal acoustic phonon and correspond in energy to the Zone Centre modes measured by optical spectroscopy and associated …
Resonant inelastic x-ray scattering in electronically quasi-zero-dimensional CuB2O4
我们探讨了一般现象的共振非弹性散射（RIXS），使用CuB 2 O 4，一个网络的CuO 4斑块电子隔离的B+3离子。光谱显示了少量的分离良好的功能，我们利用简单的电子结构，探索RIXS现象，通过开发一个计算，允许在标准方法中忽略的中间态效应。这些影响被认为是不可忽略的，我们的模型和实验之间的良好对应关系导致这样的现象的简单图片的起源在K边缘的d-d激发和中间态干涉效应。
Lattice coupling and Franck-Condon effects in K-edge resonant inelastic X-ray scattering
我们讨论了最近的铜K-边共振非弹性散射（RIXS）的结果CuB 2 O 4，模型系统组成的电子隔离的CuO 4斑块，表现出异常的入射光子能量的依赖性，不被捕获的电子只有模型。我们表明，这些异常的功能，可以定性地描述扩展的电子只考虑到包括晶格自由度。我们的研究结果具有重要的一般意义的K-边缘RIXS结果的解释电子高维过渡金属氧化物。
We theoretically investigate the incident-photon energy omega_i dependence of resonant inelastic x-ray scattering (RIXS) tuned for the Cu L edge in cuprate superconductors by using the exact diagonalization technique for a single-band Hubbard model. Depending on the value of core-hole Coulomb interaction in the intermediate state, RIXS for non-spin-flip channel shows either a omega_i-dependent fluorescencelike or omega_i-independent Raman-like behavior for hole doping. An analysis of x-ray absorption suggests that the core-hole Coulomb interaction is larger than on-site Coulomb interaction in …
We use resonant inelastic x-ray scattering to investigate charge-stripe correlations in La$_{1.675}$Eu$_{0.2}$Sr$_{0.125}$CuO$_4$. By differentiating elastic from inelastic scattering, it is demonstrated that charge-stripe correlations precede both the structural low-temperature tetragonal phase and the transport-defined pseudogap onset. The scattering peak amplitude from charge stripes decays approximately as $T^{-2}$ towards our detection limit. The in-plane integrated intensity, however, remains roughly temperature independent. Therefore, although the incommensurability shows a remarkably l…
Core hole resonance is used in X-ray spectroscopy to incisively probe the local electronic states of many-body systems. Here, resonant inelastic X-ray scattering (RIXS) is studied as a function of incident photon energy on Mott insulators SrCuO2 and NiO to examine how resonance states decay into different excitation symmetries at the transition metal M-, L- and K-edges. Quantum interference patterns characteristic of the two major RIXS mechanisms are identified within the data, and used to distinguish the attosecond scale scattering dynamics by which fundamental excitations of a many-body syst…
We performed a resonant inelastic X-ray scattering (RIXS) study of La$_{2-x}$Sr$_{x}$NiO$_{4+δ}$ (LSNO) at the oxygen $K$ edge to investigate the nature of the doped holes with regard to charge excitations. Charge excitations of the hole-doped nickelates are found to be almost independent of momentum transfer, indicating that the doped holes are strongly localized in character. Additionally, conspicuous changes in energy position are in temperature dependence. These characters are observed in stark contrast to those of the high-$T_{c}$ cuprate La$_{2-x}$Sr$_{x}$CuO$_{4}$ (LSCO), where delocali…
In this short note, we report on the first inelastic neutron scattering (INS) study on high-energy magnetic excitations in Sr$_3$Ir$_2$O$_7$. We observed excitations between $\sim$80 meV and $\sim$180 meV. The peak position of the excitations is consistent with the dispersion of a single magnon determined by resonant inelastic X-ray scattering (RIXS) measurement. Thus, our results demonstrate that INS and RIXS observe identical excitations in iridate oxides, as in La$_2$CuO$_4$.
Dispersive spin excitations in highly overdoped cuprates revealed by resonant inelastic x-ray scattering
利用共振非弹性X射线散射（RIXS）在铜$L$吸收边，我们已经观察到强烈的，分散的自旋激发在高度过掺杂的Tl $_2$ Ba $_2$ CuO $_{6+δ}$（超导$T_c =6$ K），一种化合物，其正常状态的电荷传输和热力学性质已被广泛研究，并显示出典型的费米液体行为。补充RIXS实验上稍过掺杂的Tl $_2$ Ba $_2$ CuO $_{6+δ}$（$T_c =89$ K）和Y $_{1-x}$ Ca $_{x}$ Ba $_2$ Cu $_3$ O $_{6+δ}$化合物跨越广泛的掺杂水平表明，这些激发表现出的能量和能量积分光谱权重密切类似的反铁磁振子在未掺杂的铜酸盐。令人惊讶的共存费米液体的电荷激发和高能量的自旋激发，让人想起反铁磁绝缘体在高度过掺杂的化合物提出了挑战，目前的理论模型的铜酸盐。
The magnetic properties of CuO encompass several contemporary themes in condensed matter physics, including quantum magnetism, magnetic frustration, magnetically-induced ferroelectricity and orbital currents. Here we report polarized and unpolarized neutron inelastic scattering measurements which provide a comprehensive map of the cooperative spin dynamics in the low temperature antiferromagnetic (AFM) phase of CuO throughout much of the Brillouin zone. At high energies ($E \gtrsim 100$\,meV) the spectrum displays continuum features consistent with the des Cloizeax--Pearson dispersion for an i…
Motivated by the recent synthesis of Ba$_2$CuO$_{3+δ}$ (BCO), a high temperature superconducting cuprate with putative $d_{3z^2-r^2}$ ground state symmetry, we investigated its electronic structure by means of Cu $L_3$ x-ray absorption (XAS) and resonant inelastic x-ray scattering (RIXS) at the Cu $L_3$ edge on a polycrystalline sample. We show that the XAS profile of BCO is characterised by two peaks associated to inequivalent Cu sites, and that its RIXS response features a single, sharp peak associated to crystal-field excitations. We argue that these observations are only partially compatib…
Observation of an unconventional metal-insulator transition in overdoped CuO_2 compounds
用非弹性光散射方法研究了$_2$ $_2$ $_2$ O $_{8+δ}$在较宽掺杂范围内正常态的电子动力学.电子弛豫的各向异性很强，不能单独用单粒子性质来解释。结果强烈表明存在一个非常规的量子临界金属-绝缘体过渡的“热”（波节）准粒子成为绝缘，而“冷”（节）准粒子保持金属。一种现象学的发展，它允许一个定量的拉曼结果的理解，并提供了一个场景，链接单和多粒子的属性。
Strongly correlated insulators are broadly divided into two classes: Mott-Hubbard insulators, where the insulating gap is driven by the Coulomb repulsion $U$ on the transition-metal cation, and charge-transfer insulators, where the gap is driven by the charge transfer energy $Δ$ between the cation and the ligand anions. The relative magnitudes of $U$ and $Δ$ determine which class a material belongs to, and subsequently the nature of its low-energy excitations. These energy scales are typically understood through the local chemistry of the active ions. Here we show that the situation is more co…
We report a Cu K- and L$_3$-edge resonant inelastic x-ray scattering study of charge and spin excitations of bulk Nd$_{2-x}$Ce$_x$CuO$_4$, with focus on post-growth annealing effects. For the parent compound Nd$_2$CuO$_4$ ($x = 0$), a clear charge-transfer gap is observed in the as-grown state, whereas the charge excitation spectra indicate that electrons are doped in the annealed state. This is consistent with the observation that annealed thin-film and polycrystalline samples of RE$_2$CuO$_4$ (RE = rare earth) can become metallic and superconducting at sufficiently high electron concentratio…
We present time-of-flight inelastic neutron scattering measurements of $La_{1.965}Ba_{0.035}CuO_{4}$ (LBCO), a lightly doped member of the high temperature superconducting La-based cuprate family. By using time-of-flight neutron instrumentation coupled with single crystal sample rotation we obtain a four-dimensional data set (three {\bf Q} and one energy) that is both comprehensive and spans a large region of reciprocal space. Our measurements identify rich structure in the energy dependence of the highly dispersive spin excitations, which are centered at equivalent ($\frac{1}{2},\frac{1}{2}, …
We report inelastic neutron scattering experiments in Ca2Y2Cu5O10 and map out the full one magnon dispersion which extends up to a record value of 53 meV for frustrated ferromagnetic (FM) edge-sharing CuO2 chain (FFESC) cuprates. A homogeneous spin-1/2 chain model with a FM nearest-neighbor (NN), an antiferromagnetic (AFM) next-nearest-neighbor (NNN) inchain, and two diagonal AFM interchain couplings (ICs) analyzed within linear spin-wave theory (LSWT) reproduces well the observed strong dispersion along the chains and a weak one perpendicularly. The ratio R=|J_{a2}/J_{a1}| of the FM NN and th…
Cuprate materials, like those hosting high temperature superconductivity, represent a famous class of materials where the correlations between the strongly entangled charges and spins produce complex phase diagrams. Several years ago the Zhang-Rice singlet was proposed as a natural quasiparticle in hole-doped cuprates. The occurance and binding energy of this quasiparticle, consisting of a pair of bound holes with antiparallel spins on the same CuO$_4$ plaquette, depends on the local electronic interactions, which are fundamental quantities for understanding the physics of the cuprates. Here, …
We investigate the Cu $L_3$ edge resonant inelastic x-ray scattering (RIXS) spectra of a quasi-1D antiferromagnet Ca$_2$CuO$_3$. In addition to the magnetic excitations, which are well-described by the two-spinon continuum, we observe two dispersive orbital excitations, the $3d_{xy}$ and the $3d_{yz}$ orbitons. We carry out a quantitative comparison of the RIXS spectra, obtained with two distinct incident polarizations, with a theoretical model. We show that any realistic spin-orbital model needs to include a finite, but realistic, Hund's exchange $J_H \approx 0.5$ eV. Its main effect is an in…
We present a study of resonant inelastic X-ray scattering (RIXS) spectra collected at the rare-earth $L$ edges of divalent hexaborides YbB$_6$ and EuB$_6$. In both systems, RIXS-active features are observed at two distinct resonances separated by $\sim10$ eV in incident energy, with angle-dependence suggestive of distinct photon scattering processes. RIXS spectra collected at the divalent absorption peak strongly resemble the unoccupied 5$d$ density of states calculated using density functional theory, an occurrence we ascribe to transitions between weakly-dispersing 4$f$ and strongly dispersi…
Energy-dependent crossover from anisotropic to isotropic magnetic dispersion in lightly-doped La1.96Sr0.04CuO4
对轻掺杂La $_{1.96}$ Sr $_{0.04}$ CuO $_{4}$进行了非弹性中子散射实验，发现低温下存在对角非公度自旋关联.我们以前报道过，这种晶体，与一个单一的斜方晶域，表现出“沙漏”分散在低能量[物理评论快报。101，197001（2008）]。在本文中，我们详细调查的能量演化的磁激发高达65毫电子伏。结果发现，在低能量的各向异性激发，仅沿自旋调制方向分散，交叉到各向同性，圆锥形的分散体，类似于在母体化合物La $_2$ CuO $_{4}$的自旋波。从两重到完全对称的变化跨越沙漏的腰部再现的行为首先在欠掺杂的YBa $_2$ Cu $_3$ O $_{6+x}$的研究中确定。我们讨论了这些结果的意义。
