High-energy spin and charge excitations in electron-doped copper oxide superconductors

Collective Nature of Orbital Excitations in Layered Cuprates in the Absence of Apical Oxygens

We have investigated the 3d orbital excitations in CaCuO_{2} (CCO), Nd_{2}CuO_{4} (NCO), and La_{2}CuO_{4} (LCO) using high-resolution resonant inelastic x-ray scattering. In LCO they behave as well-localized excitations, similarly to several other cuprates. On the contrary, in CCO and NCO the d_{xy} orbital clearly disperses, pointing to a collective character of this excitation (orbiton) in compounds without apical oxygen. We ascribe the origin of the dispersion as stemming from a substantial next-nearest-neighbor (NNN) orbital superexchange. Such an exchange leads to the liberation of the orbiton from its coupling to magnons, which is associated with the orbiton hopping between nearest neighbor copper sites. Finally, we show that the exceptionally large NNN orbital superexchange can be traced back to the absence of apical oxygens suppressing the charge transfer energy.

Evolution of the Magnetic Excitations in Electron-Doped La_{2-x}Ce_{x}CuO_{4}

We investigated the high energy spin excitations in electron-doped La_{2-x}Ce_{x}CuO_{4}, a cuprate superconductor, by resonant inelastic x-ray scattering (RIXS) measurements. Efforts were paid to disentangle the paramagnon signal from non-spin-flip spectral weight mixing in the RIXS spectrum at Q_{∥}=(0.6π,0) and (0.9π,0) along the (1 0) direction. Our results show that, for doping level x from 0.07 to 0.185, the variation of the paramagnon excitation energy is marginal. We discuss the implication of our results in connection with the evolution of the electron correlation strength in this system.

Unusual Low-Energy Collective Charge Excitations in High-Tc Cuprate Superconductors

Despite decades of intensive experimental and theoretical efforts, the physics of cuprate high-temperature superconductors in general, and, in particular, their normal state, is still under debate. Here, we report our investigation of low-energy charge excitations in the normal state. We find that the peculiarities of the electronic band structure at low energies have a profound impact on the nature of the intraband collective modes. It gives rise to a new kind of mode with huge intensity and non-Lorentzian spectral function in addition to well-known collective excitations like conventional plasmons and spin fluctuation. We predict two such modes with maximal spectral weight in the nodal and antinodal directions. Additionally, we found a long-living quasi-one-dimensional plasmon becoming an intense soft mode over an extended momentum range along the antinodal direction. These modes might explain some of the resonant inelastic X-ray scattering spectroscopy data.

Long-lived spin waves in a metallic antiferromagnet

Collective spin excitations in magnetically ordered crystals, called magnons or spin waves, can serve as carriers in novel spintronic devices with ultralow energy consumption. The generation of well-detectable spin flows requires long lifetimes of high-frequency magnons. In general, the lifetime of spin waves in a metal is substantially reduced due to a strong coupling of magnons to the Stoner continuum. This makes metals unattractive for use as components for magnonic devices. Here, we present the metallic antiferromagnet CeCo2P2, which exhibits long-living magnons even in the terahertz (THz) regime. For CeCo2P2, our first-principle calculations predict a suppression of low-energy spin-flip Stoner excitations, which is verified by resonant inelastic X-ray scattering measurements. By comparison to the isostructural compound LaCo2P2, we show how small structural changes can dramatically alter the electronic structure around the Fermi level leading to the classical picture of the strongly damped magnons intrinsic to metallic systems. Our results not only demonstrate that long-lived magnons in the THz regime can exist in bulk metallic systems, but they also open a path for an efficient search for metallic magnetic systems in which undamped THz magnons can be excited.

Robust charge-density-wave correlations in the electron-doped single-band Hubbard model

There is growing evidence that the hole-doped single-band Hubbard and t - J models do not have a superconducting ground state reflective of the high-temperature cuprate superconductors but instead have striped spin- and charge-ordered ground states. Nevertheless, it is proposed that these models may still provide an effective low-energy model for electron-doped materials. Here we study the finite temperature spin and charge correlations in the electron-doped Hubbard model using quantum Monte Carlo dynamical cluster approximation calculations and contrast their behavior with those found on the hole-doped side of the phase diagram. We find evidence for a charge modulation with both checkerboard and unidirectional components decoupled from any spin-density modulations. These correlations are inconsistent with a weak-coupling description based on Fermi surface nesting, and their doping dependence agrees qualitatively with resonant inelastic x-ray scattering measurements. Our results provide evidence that the single-band Hubbard model describes the electron-doped cuprates.

Paramagnons and high-temperature superconductivity in a model family of cuprates

Cuprate superconductors have the highest critical temperatures (T_c) at ambient pressure, yet a consensus on the superconducting mechanism remains to be established. Finding an empirical parameter that limits the highest reachable T_c can provide crucial insight into this outstanding problem. Here, in the first two Ruddlesden-Popper members of the model Hg-family of cuprates, which are chemically nearly identical and have the highest T_c among all cuprate families, we use inelastic photon scattering to reveal that the energy of magnetic fluctuations may play such a role. In particular, we observe the single-paramagnon spectra to be nearly identical between the two compounds, apart from an energy scale difference of ~30% which matches their difference in T_c. The empirical correlation between paramagnon energy and maximal T_c is further found to extend to other cuprate families with relatively high T_c’s, hinting at a fundamental connection between them.

Finding a parameter that limits the critical temperature of cuprate superconductors can provide crucial insight on the superconducting mechanism. Here, the authors use inelastic photon scattering on two Ruddlesden-Popper members of the model Hg-family of cuprates to reveal that the energy of magnetic fluctuations may play such a role, and suggest that the Cooper pairing is mediated by paramagnons.

Normal-State Transport Properties of Infinite-Layer Sr1-xLaxCuO2 Electron-Doped Cuprates in Optimal- and Over-Doped Regimes

Transport properties of electron-doped cuprate Sr1−xLaxCuO2 thin films have been investigated as a function of doping. In particular, optimal- and over-doped samples were obtained by tuning the Sr:La stoichiometric ratio. Optimal-doped samples show a non-Fermi liquid behavior characterized by linear dependence of the resistivity from room temperature down to intermediate temperature (about 150–170 K). However, by approaching temperatures in the superconducting transition, a Fermi-liquid behavior-characterized by a T2-scaling law-was observed. Once established, the transition from a linear-T to a quadratic-T2 behavior was successfully traced back in over-doped samples, even occurring at lower temperatures. In addition, the over-doped samples show a crossover to a linear-T to a logarithmic dependence at high temperatures compatible with anti-ferromagnetic spin fluctuations dominating the normal state properties of electron-doped cuprates.

Overdamped Antiferromagnetic Strange Metal State in Sr_{3}IrRuO_{7}

The unconventional electronic ground state of Sr_{3}IrRuO_{7} is explored via resonant x-ray scattering techniques and angle-resolved photoemission measurements. As the Ru content approaches x=0.5 in Sr_{3}(Ir_{1-x}Ru_{x})_{2}O_{7}, intermediate to the J_{eff}=1/2 Mott state in Sr_{3}Ir_{2}O_{7} and the quantum critical metal in Sr_{3}Ru_{2}O_{7}, a thermodynamically distinct metallic state emerges. The electronic structure of this intermediate phase lacks coherent quasiparticles, and charge transport exhibits a linear temperature dependence over a wide range of temperatures. Spin dynamics associated with the long-range antiferromagnetism of this phase show nearly local, overdamped magnetic excitations and an anomalously large energy scale of 200 meV-an energy far in excess of exchange energies present within either the Sr_{3}Ir_{2}O_{7} or Sr_{3}Ru_{2}O_{7} solid-solution end points. Overdamped quasiparticle dynamics driven by strong spin-charge coupling are proposed to explain the incoherent spectral features of the strange metal state in Sr_{3}IrRuO_{7}.

Three-dimensional collective charge excitations in electron-doped copper oxide superconductors

High-temperature copper oxide superconductors consist of stacked CuO₂ planes, with electronic band structures and magnetic excitations that are primarily two-dimensional^1,2, but with superconducting coherence that is three-dimensional. This dichotomy highlights the importance of out-of-plane charge dynamics, which has been found to be incoherent in the normal state^3,4 within the limited range of momenta accessible by optics. Here we use resonant inelastic X-ray scattering to explore the charge dynamics across all three dimensions of the Brillouin zone. Polarization analysis of recently discovered collective excitations (modes) in electron-doped copper oxides^5-7 reveals their charge origin, that is, without mixing with magnetic components^5-7. The excitations disperse along both the in-plane and out-of-plane directions, revealing its three-dimensional nature. The periodicity of the out-of-plane dispersion corresponds to the distance between neighbouring CuO₂ planes rather than to the crystallographic c-axis lattice constant, suggesting that the interplane Coulomb interaction is responsible for the coherent out-of-plane charge dynamics. The observed properties are hallmarks of the long-sought 'acoustic plasmon', which is a branch of distinct charge collective modes predicted for layered systems^8-12 and argued to play a substantial part in mediating high-temperature superconductivity^10-12.

Probing ultrafast spin-relaxation and precession dynamics in a cuprate Mott insulator with seven-femtosecond optical pulses

A charge excitation in a two-dimensional Mott insulator is strongly coupled with the surrounding spins, which is observed as magnetic-polaron formations of doped carriers and a magnon sideband in the Mott-gap transition spectrum. However, the dynamics related to the spin sector are difficult to measure. Here, we show that pump-probe reflection spectroscopy with seven-femtosecond laser pulses can detect the optically induced spin dynamics in Nd2CuO4, a typical cuprate Mott insulator. The bleaching signal at the Mott-gap transition is enhanced at ~18 fs. This time constant is attributable to the spin-relaxation time during magnetic-polaron formation, which is characterized by the exchange interaction. More importantly, ultrafast coherent oscillations appear in the time evolution of the reflectivity changes, and their frequencies (1400-2700 cm-1) are equal to the probe energy measured from the Mott-gap transition peak. These oscillations can be interpreted as the interference between charge excitations with two magnons originating from charge-spin coupling.

Magnon Splitting Induced by Charge Transfer in the Three-Orbital Hubbard Model

Understanding spin excitations and their connection to unconventional superconductivity have remained central issues since the discovery of cuprates. Direct measurement of the dynamical spin structure factor in the parent compounds can provide key information on important interactions relevant in the doped regime, and variations in the magnon dispersion have been linked closely to differences in crystal structure between families of cuprate compounds. Here, we elucidate the relationship between spin excitations and various controlling factors thought to be significant in high-T_{c} materials by systematically evaluating the dynamical spin structure factor for the three-orbital Hubbard model, revealing differences in the spin dispersion along the Brillouin zone axis and the diagonal. Generally, we find that the absolute energy scale and momentum dependence of the excitations primarily are sensitive to the effective charge-transfer energy, while changes in the on-site Coulomb interactions have little effect on the details of the dispersion. In particular, our result highlights the splitting between spin excitations along the axial and diagonal directions in the Brillouin zone. This splitting decreases with increasing charge-transfer energy and correlates with changes in the apical oxygen position, and general structural variations, for different cuprate families.

A high-energy-resolution resonant inelastic X-ray scattering spectrometer at ID20 of the European Synchrotron Radiation Facility

An end-station for resonant inelastic X-ray scattering and (resonant) X-ray emission spectroscopy at beamline ID20 of ESRF - The European Synchrotron is presented. The spectrometer hosts five crystal analysers in Rowland geometry for large solid angle collection and is mounted on a rotatable arm for scattering in both the horizontal and vertical planes. The spectrometer is optimized for high-energy-resolution applications, including partial fluorescence yield or high-energy-resolution fluorescence detected X-ray absorption spectroscopy and the study of elementary electronic excitations in solids. In addition, it can be used for non-resonant inelastic X-ray scattering measurements of valence electron excitations.

Nonperturbative Series Expansion of Green's Functions: The Anatomy of Resonant Inelastic X-Ray Scattering in the Doped Hubbard Model

We present a nonperturbative, divergence-free series expansion of Green's functions using effective operators. The method is especially suited for computing correlators of complex operators as a series of correlation functions of simpler forms. We apply the method to study low-energy excitations in resonant inelastic x-ray scattering (RIXS) in doped one- and two-dimensional single-band Hubbard models. The RIXS operator is expanded into polynomials of spin, density, and current operators weighted by fundamental x-ray spectral functions. These operators couple to different polarization channels resulting in simple selection rules. The incident photon energy dependent coefficients help to pinpoint main RIXS contributions from different degrees of freedom. We show in particular that, with parameters pertaining to cuprate superconductors, local spin excitation dominates the RIXS spectral weight over a wide doping range in the cross-polarization channel.

Quenched Magnon excitations by oxygen sublattice reconstruction in (SrCuO2)n/(SrTiO3)2 superlattices

The recently discovered structural reconstruction in the cuprate superlattice (SrCuO2)n/(SrTiO3)2 has been investigated across the critical value of n = 5 using resonant inelastic x-ray scattering (RIXS). We find that at the critical value of n, the cuprate layer remains largely in the bulk-like two-dimensional structure with a minority of Cu plaquettes being reconstructed. The partial reconstruction leads to quenching of the magnons starting at the Γ-point due to the minority plaquettes acting as scattering points. Although comparable in relative abundance, the doped charge impurities in electron-doped cuprate superconductors do not show this quenching of magnetic excitations.

Persistent Paramagnons Deep in the Metallic Phase of Sr_{2-x}La_{x}IrO_{4}

We have studied the magnetic excitations of electron-doped Sr_{2-x}La_{x}IrO_{4} (0≤x≤0.10) using resonant inelastic x-ray scattering at the Ir L_{3} edge. The long-range magnetic order is rapidly lost with increasing x, but two-dimensional short-range order (SRO) and dispersive magnon excitations with nearly undiminished spectral weight persist well into the metallic part of the phase diagram. The magnons in the SRO phase are heavily damped and exhibit anisotropic softening. Their dispersions are well described by a pseudospin-1/2 Heisenberg model with exchange interactions whose spatial range increases with doping. We also find a doping-independent high-energy magnetic continuum, which is not described by this model. The spin-orbit excitons arising from the pseudospin-3/2 manifold of the Ir ions broaden substantially in the SRO phase, but remain largely separated from the low-energy magnons. Pseudospin-1/2 models are therefore a good starting point for the theoretical description of the low-energy magnetic dynamics of doped iridates.

Fractional excitations in the square lattice quantum antiferromagnet

Quantum magnets have occupied the fertile ground between many-body theory and low-temperature experiments on real materials since the early days of quantum mechanics. However, our understanding of even deceptively simple systems of interacting spins-1/2 is far from complete. The quantum square-lattice Heisenberg antiferromagnet (QSLHAF), for example, exhibits a striking anomaly of hitherto unknown origin in its magnetic excitation spectrum. This quantum effect manifests itself for excitations propagating with the specific wave vector (π, 0). We use polarized neutron spectroscopy to fully characterize the magnetic fluctuations in the metal-organic compound CFTD, a known realization of the QSLHAF model. Our experiments reveal an isotropic excitation continuum at the anomaly, which we analyse theoretically using Gutzwiller-projected trial wavefunctions. The excitation continuum is accounted for by the existence of spatially-extended pairs of fractional S=1/2 quasiparticles, 2D analogues of 1D spinons. Away from the anomalous wave vector, these fractional excitations are bound and form conventional magnons. Our results establish the existence of fractional quasiparticles in the high-energy spectrum of a quasi-two-dimensional antiferromagnet, even in the absence of frustration.

Prospects of high-resolution resonant X-ray inelastic scattering studies on solid materials, liquids and gases at diffraction-limited storage rings

The spectroscopic technique of resonant inelastic X-ray scattering (RIXS) will particularly profit from immensely improved brilliance of diffraction-limited storage rings (DLSRs). In RIXS one measures the intensities of excitations as a function of energy and momentum transfer. DLSRs will allow for pushing the achievable energy resolution, signal intensity and the sampled spot size to new limits. With RIXS one nowadays probes a broad range of electronic systems reaching from simple molecules to complex materials displaying phenomena like peculiar magnetism, two-dimensional electron gases, superconductivity, photovoltaic energy conversion and heterogeneous catalysis. In this article the types of improved RIXS studies that will become possible with X-ray beams from DLSRs are envisioned.