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Register a new userBeyond the single-site approximation modeling of electron-phonon coupling effects on resonant inelastic X-ray scattering spectra
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Resonant inelastic X-ray scattering (RIXS) is used increasingly for characterizing low-energy collective excitations in materials. RIXS is a powerful probe, which often requires sophisticated theoretical descriptions to interpret the data. In particular, the need for accurate theories describing the influence of electron-phonon ($e$-p) coupling on RIXS spectra is becoming timely, as instrument resolution improves and this energy regime is rapidly becoming accessible. To date, only rather exploratory theoretical work has been carried out for such problems. We begin to bridge this gap by proposing a versatile variational approximation for calculating RIXS spectra in weakly doped materials, for a variety of models with diverse $e$-p couplings. Here, we illustrate some of its potential by studying the role of electron mobility, which is completely neglected in the widely used local approximation based on Lang-Firsov theory. Assuming that the electron-phonon coupling is of the simplest, Holstein type, we discuss the regimes where the local approximation fails, and demonstrate that its improper use may grossly textit{underestimate} the $e$-p coupling strength.
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We compute the effects of magnon-phonon coupling on the indirect K-edge bimagnon resonant inelastic x-ray scattering (RIXS) intensity spectrum of a square lattice Heisenberg antiferromagnet. We analyze the effects of competing nearest and next--nearest magnetic and magnon-phonon coupling interaction in the RIXS spectrum, for both the antiferromagnetic (AF) and the collinear antiferromagnetic (CAF) phases of the model. Utilizing the Dyson-Maleev representation of spin operators, the Bethe-Salpeter ladder approximation scheme for the bimagnon interacting channel, and considering the lowest order magnon-phonon-magnon scattering interaction we highlight distinct features in the X-ray spectrum. Considering damping effects, arising due to the presence of phonons, we find that in the AF phase the RIXS intensity spectrum attains a maximum value primarily localized around the K $left(pmfrac{pi}{2}, pm frac{pi}{2}right)$ - point. For the CAF phase the intensity is broadly distributed with a significant scattering intensity located around the Y $left(pmfrac{pi}{2}, 0right)$ - point. Furthermore, in the CAF phase for suitable anisotropy, nearest-, and next-nearest neighbor interaction parameters the phonon effects can manifest itself as a distinct peak both below and above the bimagnon peak. Such a feature is in contrast to the antiferromagnetic spectrum where the effect due to the phonon peak was located consistently beyond the bimagnon peak in the high energy end of the spectrum. Additionally, in the CAF phase we find the RIXS bimagnon-phonon spectrum to be more sensitive to anisotropy compared to its antiferromagnetic counterpart. We conclude that the ultimate effect of magnon-phonon effects in the indirect K-edge RIXS spectrum, in both the antiferromagnetic and the collinear antiferromagnetic phase, is an observable effect.
The coupling between lattice and charge degrees of freedom in condensed matter materials is ubiquitous and can often result in interesting properties and ordered phases, including conventional superconductivity, charge density wave order, and metal-insulator transitions. Angle-resolved photoemission spectroscopy and both neutron and non-resonant x-ray scattering serve as effective probes for determining the behavior of appropriate, individual degrees of freedom -- the electronic structure and lattice excitation, or phonon dispersion, respectively. However, each provides less direct information about the mutual coupling between the degrees of freedom, usual through self-energy effects, which tend to renormalize and broaden spectral features precisely where the coupling is strong, impacting ones ability to quantitively characterize the coupling. Here we demonstrate that resonant inelastic x-ray scattering, or RIXS, can be an effective tool to directly determine the relative strength and momentum dependence of the electron-phonon coupling in condensed matter systems. Using a diagrammatic approach for an 8-band model of copper oxides, we study the contributions from the lowest order diagrams to the full RIXS intensity for a realistic scattering geometry, accounting for matrix element effects in the scattering cross-section as well as the momentum dependence of the electron-phonon coupling vertex. A detailed examination of these maps offers a unique perspective into the characteristics of electron-phonon coupling, which complements both neutron and non-resonant x-ray scattering, as well as Raman and infrared conductivity.
We report the observation of multiple phonon satellite features in ultra thin superlattices of form $n$SrIrO$_3$/$m$SrTiO$_3$ using resonant inelastic x-ray scattering. As the values of $n$ and $m$ vary the energy loss spectra show a systematic evolution in the relative intensity of the phonon satellites. Using a closed-form solution for the cross section, we extract the variation in the electron-phonon coupling strength as a function of $n$ and $m$. Combined with the negligible carrier doping into the SrTiO$_3$ layers, these results indicate that tuning of the electron-phonon coupling can be effectively decoupled from doping. This work showcases both a feasible method to extract the electron-phonon coupling in superlattices and unveils a potential route for tuning this coupling which is often associated with superconductivity in SrTiO$_3$-based systems.
The excitations in honeycomb $alpha$-Li$_2$IrO$_3$ have been investigated with high-resolution resonant inelastic x-ray scattering (RIXS) at the O K edge. The low-energy response is dominated by a fully resolved ladder of excitations, which we interpret as being due to multi-phonon processes in the presence of strong electron-phonon coupling (EPC). At higher energies, the orbital excitations are shown to be dressed by phonons. The high quality of the data permits a quantitative test of the analytical model for the RIXS cross-section, which has been proposed to describe EPC in transition metal oxides (TMOs). We find that the magnitude of the EPC is comparable to that found for a range of 3d TMOs. This indicates that EPC may be of equal importance in determining the phenomenology displayed by corresponding 5d based systems.
The ladder compound Sr$_{14}$Cu$_{24}$O$_{41}$ is of interest both as a quasi-one-dimensional analog of the superconducting cuprates and as a superconductor in its own right when Sr is substituted by Ca. In order to model resonant inelastic x-ray scattering (RIXS) spectra for this compound, we investigate the simpler SrCu$_{2}$O$_{3}$ system in which the crystal structure contains very similar ladder planes. We approximate the LDA dispersion of SrCu$_{2}$O$_{3}$ by a Cu only two-band tight-binding model. Strong correlation effects are incorporated by assuming an anti-ferromagnetic ground state. The available angle-resolved photoemission (ARPES) and RIXS data on the ladder compound are found to be in reasonable accord with our theoretical predictions.
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