Experimental Determination of Momentum-Resolved Electron-Phonon Coupling

We provide a novel experimental method to quantitatively estimate the electron-phonon coupling and its momentum dependence from resonant inelastic x-ray scattering (RIXS) spectra based on the detuning of the incident photon energy away from an absorption resonance. We apply it to the cuprate parent compound NdBa$_2$Cu$_3$O$_6$ and find that the electronic coupling to the oxygen half-breathing phonon mode is strongest at the Brillouin zone boundary, where it amounts to $\sim 0.17$ eV, in agreement with previous studies. In principle, this method is applicable to any absorption resonance suitable for RIXS measurements and will help to define the contribution of lattice vibrations to the peculiar properties of quantum materials.Comment: 6 pages, 3 figure

Charge response function probed by resonant inelastic x-ray scattering: the signature of electronic gaps of YBa2_2Cu3_3O7−δ_{7-\delta}

In strongly correlated systems the complete determination of the dynamical susceptibility $\chi(\textbf{q}, \omega)$ is of special relevance because of the entwinement of the spin and charge components. Although Resonant Inelastic X-Ray Scattering (RIXS) spectra are directly related to both the charge ($\chi''_c(\textbf{q}, \omega)$) and the spin ($\chi''_s(\textbf{q}, \omega)$) contributions, only the latter has been extensively studied with RIXS so far. Here we show how to extract from RIXS spectra of high-$T_c$ superconducting cuprates relevant properties of $\chi''_c$, such as the presence of the superconducting gap and of the pseudogap. In particular, we exploit the temperature dependence of the Cu L$_3$ edge RIXS spectra of underdoped YBa$_2$Cu$_3$O$_{7-\delta}$ at specific wave-vectors q. The signature of the two gaps is in the departure of the low energy Bosonic excitation continuum from the statistical temperature-dependence. This approach can be immediately used to investigate systematically the nature of the pseudogap in cuprates, thereby taking advantage of the RIXS technique that does not suffer the limitations of surface-sensitive electron spectroscopies. Its extension to other interesting materials is foreseen.Comment: 11 pages, 9 figure

Fractional Spin Excitations in the Infinite-Layer Cuprate CaCuO2

We use resonant inelastic x-ray scattering (RIXS) to investigate the magnetic dynamics of the infinite-layer cuprate CaCuO2. We find that close to the (1/2,0) point, the single magnon decays into a broad continuum of excitations accounting for about 80% of the total magnetic spectral weight. Polarization-resolved RIXS spectra reveal the overwhelming dominance of the spin-flip (Delta S = 1) character of this continuum with respect to the Delta S = 0 multimagnon contributions. Moreover, its incident-energy dependence is identical to that of the magnon, supporting a common physical origin. We propose that the continuum originates from the decay of the magnon into spinon pairs, and we relate it to the exceptionally high ring exchange J(c) similar to J(1) of CaCuO2. In the infinite-layer cuprates, long-range and multisite hopping integrals are very important, and they amplify the 2D quantum magnetism effects in spite of the 3D antiferromagnetic Neel order

Mobile orbitons in Ca2_2CuO3_3: crucial role of the Hund's exchange

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 increase in orbiton velocities, so that their theoretically calculated values match those observed experimentally. Even though Hund's exchange also mediates some interaction between spinon and orbiton, the picture of spin-orbit separation remains intact and describes orbiton motion in this compound.Comment: 13 pages, 10 figure

Determining the Electron-Phonon Coupling in Superconducting Cuprates by Resonant Inelastic X-ray Scattering: Methods and Results on Nd1+x_{1+x}Ba2−x_{2-x}Cu3_3O7−δ_{7-\delta}

The coupling between lattice vibration quanta and valence electrons can induce charge density modulations and decisively influence the transport properties of materials, e.g. leading to conventional superconductivity. In high critical temperature superconductors, where electronic correlation is the main actor, the actual role of electron-phonon coupling (EPC) is being intensely debated theoretically and investigated experimentally. We present an in-depth study of how the EPC strength can be obtained directly from resonant inelastic x-ray scattering (RIXS) data through the theoretical approach derived by Ament et al. [EPL 95, 27008 (2011)]. The role of the model parameters (e.g. phonon energy $\omega_0$, intermediate state lifetime $1/\Gamma$, EPC matrix element $M$, and detuning energy $\Omega$) is thoroughly analyzed, providing general relations among them that can be used to make quantitative estimates of the dimensionless EPC $g = (M/\omega_0)^2$ without detailed microscopic modeling. We then apply these methods to very high resolution Cu $L_3$ edge RIXS spectra of three Nd$_{1+x}$Ba$_{2-x}$Cu$_3$O$_{7-\delta}$ films. For the insulating antiferromagnetic parent compound the value of $M$ as a function of the in-plane momentum transfer is obtained for Cu-O bond-stretching (breathing) and bond-bending (buckling) phonon branches. For the underdoped and the nearly optimally doped samples, the effects of Coulomb screening and of charge-density-wave correlations on $M$ are assessed. In light of the anticipated further improvements of the RIXS experimental resolution, this work provides a solid framework for an exhaustive investigation of the EPC in cuprates and other quantum materials.Comment: 21 pages, 16 figure

Scientific Opinion on an application (Reference EFSA-GMO-NL-2011-100) for the placing on the market of the herbicide-tolerant, increased oleic acid genetically modified soybean MON 87705$ MON 89788 for food and feed uses, import and processing under Regulation (EC) No 1829/2003 from Monsanto

The EFSA GMO Panel previously assessed the two single events combined to produce soybean MON 87705 × MON 89788 and did not identify safety concerns. No new data on the single events affecting the previous conclusions were identified. No differences in composition requiring further assessment were observed between soybean MON 87705 × MON 89788 and its comparator, except for the intended trait i.e. an altered fatty acid profile. Nutritional assessment on soybean MON 87705 × MON 89788 oil and oil-containing food products did not identify concerns on human health and nutrition. There are no concerns regarding the use of feedingstuffs from defatted soybean meal MON 87705 × MON 89788. The EFSA GMO Panel is of the opinion that soybean MON 87705 × MON 89788 is as safe, and at least as nutritious, as its comparator and commercial soybean varieties. There is no reason to expect interactions between the single events that could impact on the food and feed safety and the nutritional properties of soybean MON 87705 × MON 89788. There are no indications of an increased likelihood of establishment and spread of feral soybean plants. Potential interactions with the biotic and abiotic environment were not considered to be a relevant issue. The unlikely but theoretically possible transfer of the recombinant genes from soybean MON 87705 × MON 89788 to environmental bacteria does not give rise to any safety concern. The post-market environmental monitoring plan and reporting intervals are in line with the scope of the application. The EFSA GMO Panel considers that the information available for soybean MON 87705 × MON 89788 addresses the scientific comments raised by Member States. The EFSA GMO Panel concludes, considering the scope of the application, that soybean MON 87705 × MON 89788 is as safe as its comparator and non-GM soybean reference varieties with respect to potential effects on human and animal health and the environment. The GMO Panel recommends a post-market monitoring plan, focusing on import data and, if needed, on consumption data for the European population, for the marketed foods and feed

Determining the electron-phonon coupling in superconducting cuprates by resonant inelastic x-ray scattering: Methods and results on Nd1+xBa2-xCu3O7-δ

The coupling between lattice vibration quanta and valence electrons can induce charge-density modulations and decisively influence the transport properties of materials, e.g., leading to conventional superconductivity. In high-critical-temperature superconductors, where electronic correlation is the main actor, the actual role of electron-phonon coupling (EPC) is being intensely debated theoretically and investigated experimentally. We present an in-depth study of how the EPC strength can be obtained directly from resonant inelastic x-ray scattering (RIXS) data through the theoretical approach derived by Ament et\ua0al. [Europhys. Lett. 95, 27008 (2011)]. The role of the model parameters (e.g., phonon energy ω0, intermediate state lifetime 1/Γ, EPC matrix element M, and detuning energy Ω) is thoroughly analyzed, providing general relations among them that can be used to make quantitative estimates of the dimensionless EPC g=(M/ω0)2 without detailed microscopic modeling. We then apply these methods to very high-resolution Cu L3-edge RIXS spectra of three Nd1+xBa2−xCu3O7−δ films. For the insulating antiferromagnetic parent compound, the value of M as a function of the in-plane momentum transfer is obtained for Cu-O bond-stretching (breathing) and bond-bending (buckling) phonon branches. For the underdoped and the nearly optimally doped samples, the effects of Coulomb screening and of charge-density-wave correlations on M are assessed. In light of the anticipated further improvements of the RIXS experimental resolution, this work provides a solid framework for an exhaustive investigation of the EPC in cuprates and other quantum materials

Collective nature of orbital excitations in layered cuprates in the absence of apical oxygens

We have investigated the 3d orbital excitations in CaCuO2 (CCO), Nd2CuO4 (NCO) and La2CuO4 (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 dxy orbital clearly disperse, 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 orbiton from its coupling to magnons, which is associated with the orbiton hopping between nearest neighbor copper sites. We show that the exceptionally large NNN orbital superexchange can be traced back to the absence of apical oxygens suppressing the charge transfer energy.Comment: 18 pages, 7 figure