RESCOR · Exploiting RESonant processes to understand CORrelations

Exploiting RESonant processes to understand CORrelations

The aim of this Marie Curie project was to gain a better understanding of electronic/magnetic properties of materials by looking at the elementary excitations probed by two very powerful and challenging spectroscopies, angle resolved Resonant PhotoEmission Spectroscopy (RPES) [1] and Resonant Inelastic X-ray Scattering (RIXS) [2]. An ab-initio model (i.e., not relying on any adjustable parameter) able to describe with predictive power these spectroscopies is/was still lacking, although some first steps exist for a more robust and consistent theoretical treatment. These first steps are represented by some previous work performed by the candidate for RPES [3], and by world leading experts in X-ray spectroscopy for RIXS [4,5,6], with whom a joint effort together with the host group was envisaged in this proposal. The huge amount of experimental output from different European synchrotron radiation sources, on both RIXS and RPES, called and is calling for an urgent advance in their theoretical description. The two main objectives were: 1) to extend the capabilities of the model for RPES previously developed by the author (based on a modification of the known one-step theory of photoemission by Pendry [7]), in order a) to use as input more sophisticated (beyond LDA/GGA) potentials by common all-electron codes and b) to study magnetic excitations in the spin and orbital channel; 2) to explore different routes/codes to study RIXS, and invest in one of them to provide to the community a consistent robust approach (possibly interfaced with common electronic structure codes) able to describe electronic but also (some) magnetic excitations, on the basis of a quasi-particle (or beyond quasi-particle) description. This Marie Curie fellowship has had an effective duration of one year and three months. This period of one year and three months has not been consecutive, but it has had an interruption of 6 months. The work performed is here outlined: - extension of the RPES code to receive all-electron self-consistent potentials from known modern electronic structure codes; study of spin flip and orbital flip excitations in angle resolved RPES spectra and resonant photoelectron diffraction patterns on bcc Fe, a system whose origin of magnetism is nowadays seen as a correlation effect - exploring different routes for RIXS; this has been done by a critical reading of the literature and through exchanges with the many contacts that this fellowship has allowed to start with other researchers; the final choice has been starting testing the code for RIXS developed in the past by Dr. E. Shirley (NIST, USA) and now mainly maintained by Dr. J. Vinson (NIST, USA) and Dr. K. Gilmore (ESRF, Grenoble, France) [5,6]. The main results achieved have been: - the study of the spin and orbital flip excitations in a magnetic system has allowed to assees the capability of RPES and related diffration patterns as a new tool for full tomographic photoemission, i.e. to fully map the local (atomic-scale) spin and orbital nature of the ground state of the system. This is shown in a single-author paper by the fellow [8]. Fe is a paradigmatic weak itinerant ferromagnet, whose magnetism, a correlation phenomenon given by the coexistence of localized moments and itinerant electrons, and the observed non-Fermi-Liquid behaviour at extreme conditions both remain unclear. Pure spin-flip, entangled spin-flip–orbital-flip excitations and chiral transitions with vortex-like wave fronts of photoelectrons have been found depending on the valence orbital symmetry and the direction of the local magnetic moment, making a distinction between eg and t2g orbitals, which in Fe do indeed play a different role in the rise of magnetism. Overall, the results have shown that RPES is a promising tool to perform a full tomography of the local magnetic properties even in itinerant ferromagnets or macroscopically nonmagnetic systems. - the first tests on RIXS have shown that the code was still not fully working and that further modifications (in the code itself and also in the interface with common electronic structure codes like ABINIT and QuantumEspresso) still had to be done. Problems where encountered when calculating twice the excitonic effects (in the first core excitation and then also for valence excitons). At the very end of the contract the code started to work and calculations were starting to run on iron-based superconductor FeSe and plans were done to study Co-substituted FeSe. Despite the end of the contract, the fellow is still in contact with Dr. K. Gilmore and still providing some GW calculations to correct self energies to be plugged into the RIXS code. Calculations are now running for Fe, in which case the quality of the self energy might affect even the XAS spectrum. In conclusion, while the results are obviously only partial because of the limited duration of the fellowship, but extremly encouraging. Angle-resolved RPEs has been assessed a new photoemission-based tomographic tool able to map properties at the atomic scale. This pushes experimentalists to invest into spectromicroscopy at core edges and to look at energies of magnetic excitations in different channels. For RIXS, the route to obtain a full robust ab-initio description of RIXS (based on a quasi-particle and even more for a beyond quasi-particle picture) is still long, but first encouraging runs of the chosen computational tool are now paving the way for a full exploration of the improvements to be done in the future to the theoretical description of this spectroscopy. [1] W. R. Flavell, J. Hollingworth, J. F. Howlett, A. G. Thomas, Md. M. Sarker, S. Squire, Z.Hashim, M. Mian, P. L. Wincott, D. Teehan, S. Downes and F. E. Hancock, J. Synchrotron Rad. 2,264-271 (1995) [2] L.J.P. Ament, M. van Veenendaal, T. P. Devereaux, J. P. Hill, and J. van den Brink, Rev. Mod.Phys. 83, 705 (2011) [3] F. Da Pieve and P. Krüger Phys. Rev. Lett. 110, 127401 (2013) [4] J. J. Kas, J. J. Rehr, J. A. Soininen, and P. Glatzel, Phys. Rev. B 83, 235114 (2011) [5] E. L. Shirley, J. Elec. Spec. 136, 77 (2004) [6] J.Vinson, J.J.Rehr, J.J. Kas and E.L.Shirley, Phys.Rev. B 83, 11506 (2011) [7] J. B. Pendry, Surf. Sci. 57, 679 (1976).; J. Braun, Rep. Prog. Phys. 59, 1267 (1996). [8] F. Da Pieve, Phys. Rev. B 93, 035106 (2016)

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