Determining the Electron-Phonon Coupling Strength in Correlated Electron Systems from Resonant Inelastic X-ray Scattering

We show that high resolution Resonant Inelastic X-ray Scattering (RIXS) provides direct, element-specific and momentum-resolved information on the electron-phonon (e-p) coupling strength. Our theoretical analysis demonstrates that the e-p coupling can be extracted from RIXS spectra by determining the differential phonon scattering cross section. An alternative, very direct manner to extract the coupling is to use the one and two-phonon loss ratio, which is governed by the e-p coupling strength and the core-hole life-time. This allows measurement of the e-p coupling on an absolute energy scale.Comment: 4 pages, 3 figure

Magnetic Excitations in La2CuO4 probed by Indirect Resonant Inelastic X-ray Scattering

Recent experiments on La$_2$CuO$_4$ suggest that indirect resonant inelastic X-ray scattering (RIXS) might provide a probe for transversal spin dynamics. We present in detail a systematic expansion of the relevant magnetic RIXS cross section by using the ultrashort core-hole lifetime (UCL) approximation. We compute the scattering intensity and its momentum dependence in leading order of the UCL expansion. The scattering is due to two-magnon processes and is calculated within a linear spin-wave expansion of the Heisenberg spin model for this compound, including longer range and cyclic spin interactions. We observe that the latter terms in the Hamiltonian enhance the first moment of the spectrum if they strengthen the antiferromagnetic ordering. The theoretical spectra agree very well with experimental data, including the observation that scattering intensity vanishes for the transferred momenta ${\bf q} = (0,0)$ and ${\bf q} = (\pi,\pi)$. We show that at finite temperature there is an additional single-magnon contribution to the scattering with a spectral weight proportional to $T^3$. We also compute the leading corrections to the UCL approximation and find them to be small, putting the UCL results on a solid basis. All this univocally points to the conclusion that the observed low temperature RIXS intensity in La$_2$CuO$_4$ is due to two-magnon scattering.Comment: 11 pages, 13 figures, Phys. Rev. B 77, 134428 (2008) (v4: corrected figs 7

Bimagnon studies in cuprates with Resonant Inelastic X-ray Scattering at the O K edge. I - An assessment on La2CuO4 and a comparison with the excitation at Cu L3 and Cu K edges

We assess the capabilities of magnetic Resonant Inelastic X-ray Scattering (RIXS) at the O $K$ edge in undoped cuprates by taking La_{2}CuO_{4} as a benchmark case, based on a series of RIXS measurements that we present here. By combining the experimental results with basic theory we point out the fingerprints of bimagnon in the O $K$ edge RIXS spectra. These are a dominant peak around 450 meV, the almost complete absence of dispersion both with $\pi$ and $\sigma$ polarization and the almost constant intensity vs. the transferred momentum with $\sigma$ polarization. This behavior is quite different from Cu $L_3$ edge RIXS giving a strongly dispersing bimagnon tending to zero at the center of the Brillouin zone. This is clearly shown by RIXS measurements at the Cu $L_3$ edge that we present. The Cu $L_3$ bimagnon spectra and those at Cu $K$ edge - both from the literature and from our data - however, have the same shape. These similarities and differences are understood in terms of different sampling of the bimagnon continuum. This panorama points out the unique possibilities offered by O $K$ RIXS in the study of magnetic excitations in cuprates near the center of the BZ

Momentum dependence of orbital excitations in Mott-insulating titanates

High-resolution resonant inelastic x-ray scattering has been used to determine the momentum dependence of orbital excitations in Mott-insulating LaTiO$_3$ and YTiO$_3$ over a wide range of the Brillouin zone. The data are compared to calculations in the framework of lattice-driven and superexchange-driven orbital ordering models. A superexchange model in which the experimentally observed modes are attributed to two-orbiton excitations yields the best description of the data.Comment: to appear in PR

Measurement of magnetic excitations in the two-dimensional antiferromagnetic Sr2CuO2Cl2 insulator using resonant x-ray scattering:Evidence for extended interactions

Using high-resolution resonant inelastic x-ray scattering (RIXS), we performed a momentum-resolved study of magnetic excitations in the model spin-1/2 2D antiferromagnetic insulator Sr_2CuCl_2O_2. We identify both a single-spin-wave feature and a multi-magnon continuum, and show that the X-ray polarization can be used to distinguish these two contributions in the cross-section. The spin-waves display a large (70 meV) dispersion between the zone-boundary points ($\pi$,0) and ($\pi$/2,$\pi$/2). Employing an extended $t$-$t'$-$t"$-$U$ one-band Hubbard model, we find significant electronic hopping beyond nearest-neighbor Cu ions. We conclude that sizeable extended magnetic interactions are present in \scoc{} and probably important in all undoped cuprates.Comment: 4 pages, 4 figure

Effectiveness of private land conservation areas in maintaining natural land cover and biodiversity intactness

CITATION: Shumba, T. et al. 2020. Effectiveness of private land conservation areas in maintaining natural land cover and biodiversity intactness. Global Ecology and Conservation, 22:e00935, doi:10.1016/j.gecco.2020.e00935.The original publication is available at https://www.journals.elsevier.com/global-ecology-and-conservationPrivate land conservation areas (PLCAs) are increasingly looked to for meeting the deficit left by state-owned protected areas in reaching global conservation targets. However, despite the increasing extent and recognition of PLCAs as a complementary conservation strategy, little research has been done to quantify their effectiveness; a critical consideration if they are to be counted towards international biodiversity conservation targets. The long history of PLCAs in South Africa provides an interesting case study to address this knowledge gap. Here, we quantified the effectiveness of South African PLCAs by comparing losses in natural land cover and biodiversity intactness within PLCAs with different levels of protection to that of unprotected control points. Points within PLCAs were matched with unprotected control points to test the prediction that if PLCAs offer effective protection, losses in natural land cover and biodiversity intactness would be significantly lower within their boundaries in comparison to unprotected controls exposed to similar conditions. Consequences of natural land cover loss on biodiversity intactness were thus assessed, thus advancing standard approaches for quantifying effectiveness. Between 1990 and 2013, PLCAs lost significantly less natural land cover (3%) and biodiversity intactness (2%) than matched unprotected areas (6% and 4%, respectively). Of the natural land cover lost within PLCAs, most was converted to cultivated land. Farms can support more species than other land uses (e.g. mines), a likely explanation for why losses in biodiversity intactness were less than losses in natural land cover. Contrary to the predicted pattern, effectiveness did not increase with level of protection; informal PLCAs with no legal protection had comparable natural land cover and biodiversity intactness retention to strictly protected PLCAs, with most losses recorded among PLCAs with moderate protection. This study provides the first national-scale evidence that PLCAs can be an effective mechanism for conserving natural land cover and biodiversity intactness, which is highly relevant given current discussions around their likely long-term biodiversity conservation capacity.Publisher's versio

Dispersive charge density wave excitations and temperature dependent commensuration in Bi2Sr2CaCu2O8+{\delta}

Experimental evidence on high-Tc cuprates reveals ubiquitous charge density wave (CDW) modulations, which coexist with superconductivity. Although the CDW had been predicted by theory, important questions remain about the extent to which the CDW influences lattice and charge degrees of freedom and its characteristics as functions of doping and temperature. These questions are intimately connected to the origin of the CDW and its relation to the mysterious cuprate pseudogap. Here, we use ultrahigh resolution resonant inelastic x-ray scattering (RIXS) to reveal new CDW character in underdoped Bi2Sr2CaCu2O8+{\delta} (Bi2212). At low temperature, we observe dispersive excitations from an incommensurate CDW that induces anomalously enhanced phonon intensity, unseen using other techniques. Near the pseudogap temperature T*, the CDW persists, but the associated excitations significantly weaken and the CDW wavevector shifts, becoming nearly commensurate with a periodicity of four lattice constants. The dispersive CDW excitations, phonon anomaly, and temperature dependent commensuration provide a comprehensive momentum space picture of complex CDW behavior and point to a closer relationship with the pseudogap state

Resonant Inelastic X-ray Scattering Studies of Elementary Excitations

In the past decade, Resonant Inelastic X-ray Scattering (RIXS) has made remarkable progress as a spectroscopic technique. This is a direct result of the availability of high-brilliance synchrotron X-ray radiation sources and of advanced photon detection instrumentation. The technique's unique capability to probe elementary excitations in complex materials by measuring their energy-, momentum-, and polarization-dependence has brought RIXS to the forefront of experimental photon science. We review both the experimental and theoretical RIXS investigations of the past decade, focusing on those determining the low-energy charge, spin, orbital and lattice excitations of solids. We present the fundamentals of RIXS as an experimental method and then review the theoretical state of affairs, its recent developments and discuss the different (approximate) methods to compute the dynamical RIXS response. The last decade's body of experimental RIXS data and its interpretation is surveyed, with an emphasis on RIXS studies of correlated electron systems, especially transition metal compounds. Finally, we discuss the promise that RIXS holds for the near future, particularly in view of the advent of x-ray laser photon sources.Comment: Review, 67 pages, 44 figure