Abstract:
Effective symmetry-based transition operators for resonant inelastic X-ray scattering (RIXS) are derived that show how the scattering between different states depends on the polarization of the incoming and outgoing X-rays. In spherical symmetry, the effective operators can be rewritten in terms of spin operators, although the expressions depend on the nature of the ground state. For lower symmetries, the combined action of the crystal field and the spin-orbit interaction breaks up the spin space and spin operators are no longer appropiate operators. By taking iridium compounds as an example, it is demonstrated that effective scattering operators can still be obtained. These effective transition operators facilitate our understanding how RIXS couples to elementary excitations.

Abstract:
This paper makes a comparison between x-ray absorption (XAS) and resonant inelastic x-ray scattering (RIXS) in the rare earths. Atomic calculations are given for 2p -> 4f and 2p -> 5d XAS. The latter calculation includes the contraction and expansion of the 5d orbitals resulting from the complete exchange interaction with the 4f electrons. The radiative decay of the XAS final states is described for the situations where the core hole created in the absorption process is filled by a valence electron or by an electron from a shallower core level. RIXS spectra, 4f^n -> _{3d} 4f^{n+1} -> 4f^n,integrated over the outgoing photon energy (fluorescence yield) are compared with 3d -> 4f XAS. Sum rules related to XAS and RIXS and their applicability are discussed.

Abstract:
The photoinduced magnetism in manganese-tetracyanoethylene (Mn-TCNE) molecule-based magnets is ascribed to charge-transfer excitations from manganese to TCNE. Charge-transfer energies are calculated using Density Functional Theory; photoinduced magnetization is described using a model Hamiltonian based on a double-exchange mechanism. Photoexciting electrons from the manganese core spin into the lowest unoccupied orbital of TCNE with photon energies around 3 eV increases the magnetization through a reduction of the canting angle of the manganese core spins for an average electron density on TCNE less than one. When photoexciting with a smaller energy, divalent TCNE molecules are formed. The delocalization of the excited electron causes a local spin flip of a manganese core spin.

Abstract:
We express the cross section for indirect resonant inelastic X-ray scattering in terms of an intrinsic dynamic correlation function of the system that is studied with this technique. The cross section is a linear combination of the charge response function and the dynamic longitudinal spin density correlation function. This result is asymptotically exact for both strong and weak local core-hole potentials. We show that one can change the relative charge and spin contribution to the inelastic spectral weight by varying the incident photon energy.

Abstract:
Recent experiments by Larson et al. demonstrate the feasibility of measuring local $dd$ excitations using nonresonant inelastic X-ray scattering (IXS). We establish a general framework for the interpretation where the $dd$ transitions created in the scattering process are expressed in effective one-particle operators that follow a simple selection rule. The different operators can be selectively probed by employing their different dependence on the direction and magnitude of the transferred momentum. We use the operators to explain the presence of nodal directions and the nonresonant IXS in specific directions and planes. We demonstrate how nonresonant IXS can be used to extract valuable ground state information for orbiton excitations in manganite.

Abstract:
Although the Ni_4 cluster includes more information regarding the Ni band structure with respect to the Anderson impurity model, it also favors very peculiar ground states which are incompatible with a coherent picture of all dichroism experiments.

Abstract:
First-principles density functional theory calculations have been performed to understand the electronic structure and orbital polarization of LaNiO$_3$ with a reduced coordination and under strain. From the slab calculation to simulate [001] surface, it is found that $d_{3z^2-r^2}$ orbital occupation is significantly enhanced relative to $d_{x^2-y^2}$ occupation owing to the reduced coordination along the perpendicular direction to the sample plane. Furthermore, the sign of the orbital polarization does not change under external strain. The results are discussed in comparison to the bulk and heterostructure cases, which sheds new light on the understanding of the available experimental data.

Abstract:
Density functional band calculations have been performed to study LaNiO$_3$/LaAlO$_3$ superlattices. Motivated by recent experiments reporting the magnetic and metal-insulator phase transition as a function of LaNiO$_3$ layer thickness, we examined the electronic structure, magnetic properties, and orbital occupation depending on the number of LaNiO$_3$ layers. Calculations show that the magnetic phase is stabler than the nonmagnetic for finite and positive $U$ values. The orbital polarization is significantly reduced by $U$ even in the magnetic regions. The implications of the results are discussed in comparison to recent experimental and theoretical studies within the limitations of the LDA$+U$ method.

Abstract:
By using first-principles density functional theory calculations for (LaNiO3)m/(SrTiO3)n superlattices, we report a systematic way of electronic response to the interface geometry. It is found that Fermi level density of states of metallic nickelate layers is significantly reduced without charge transfer in the vicinity of interface to the insulating SrTiO3. This type of electronic state redistribution is clearly distinctive from other interface phenomena such as charge and orbital reconstruction. Our result sheds new light towards understanding the nickelates and other transitionmetal oxide heterostructures.

Abstract:
The mechanism behind fast intersystem crossing in transition-metal complexes is shown to be a result of the dephasing of the photoexcited state to the phonon continuum of a different state with a significantly different transition metal-ligand distance. The coupling is a result of the spin-orbit interaction causing a change in the local moment. Recurrence to the initial state is prevented by the damping of the phonon oscillation. The decay time is faster than the oscillation frequency of the transition metal-ligand stretch mode, in agreement with experiment. For energies above the region where the strongest coupling occurs, a slower "leakage-type" decay is observed. If the photoexcited state is lower in energy than the state it couples to, then there is no decay.