Program

Monday 9:00 - Robert Green Solving the full Hamiltonian of a correlated solid is hopeless, but core-level spectroscopy is local, and that suggests a way forward: treat a small region exactly and replace the rest of the crystal by an effective environment. Using NiO as a running example, this lecture builds up the hierarchy from atomic multiplets through crystal-field, ligand-field and Anderson impurity models to DMFT, showing that they are all the same Hamiltonian with an increasingly faithful description of that environment.

Tuesday 9:00 - Marie-Anne Arrio The open 3d or 4f shell of a transition-metal or rare-earth ion determines many of its chemical and physical properties. This lecture first builds the free-ion Hamiltonian: the Coulomb interaction expressed through Slater integrals, the resulting spectroscopic terms, and spin-orbit coupling, including the two open shells created by a core hole. It then places the ion in a crystal, using point-group symmetry to derive crystal-field splittings and Tanabe-Sugano diagrams, with spin crossover as an example. Finally, a magnetic field is added to show how the crystal field shapes magnetic moments, paramagnetic susceptibility and magnetic anisotropy.

Wednesday 9:00 - Robert Green The single-site models of the first two days assume that a transition-metal ion's neighbours act only as a bath. This lecture shows what happens when that assumption breaks down. Double-cluster models capture intersite charge fluctuations and bond disproportionation in negative charge-transfer perovskite nickelates, and Anderson impurity models with a band-like bath explain the dispersing charge-transfer features in the RIXS of NiO.

Thursday 9:00 Kevin Ackerman and Sina Shokri An introduction to Kohn-Sham density functional theory and its use for spectroscopic applications. Practical consideration when DFT might be sufficient and when not. Followed by a hands-on introduction to FPLO for the example of fcc Al, laying the groundwork for the Wannier downfolding and DFT+DMFT sessions thereafter.

Monday 13:30 - Frank de Groot In order to perform simulations of x-ray spectroscopies, it is important to have a good understanding in the experimental procedures that are used to obtain x-ray spectra. In this lecture first an overview is given of the core level spectroscopies that can be performed with x-rays and with electrons. We discuss the basic interpretation of x-ray absorption spectra. The last part of the lecture discuss the different methods to measure an XAS spectrum, where the three main methods are transmission, electron yield and fluorescence yield.

Tuesday - 13:30 Frank de Groot Based on the atomic multiplet theory and crystal field theory, the 2p x-ray absorption spectral shape is explained, where we analyze the symmetry aspects of some XAS and X-MCD spectra. The effects of screening are discussed in the charge transfer multiplet theory of XAS and XPS spectral shapes.

Wednesday 13:00 - Michelangelo Tagliavini Measuring how an x-ray spectrum depends on the polarisation of the light and the orientation of the sample reveals properties that an averaged measurement hides. There are infinitely many possible measurement geometries, but not all of them give different information. Starting from the dipole and quadrupole transition operators, this lecture explains x-ray linear and magnetic circular dichroism, and the sum rules that relate XMCD to the spin and orbital magnetic moments. It then shows that all of these effects are contained in a single conductivity tensor, whose form follows from the local point-group symmetry. There are straightforward relations between the tensor elements, the point-group symmetry and the material properties. In the second part, the tensor formulation is extended to RIXS. The 3 by 3 conductivity tensor of absorption (a three-dimensional rank-2 tensor) becomes a three-dimensional rank-4 tensor for RIXS. We can write it as a 9 by 9 matrix, using spherical tensors as its basis. As for absorption, this allows us to relate the tensor elements to the point-group symmetry and to material-specific properties.