Many of the questions below can be answered by experimenting with the theory. If you turn off sussesively interactions (Echange interaction, Ni-3d spin-orbit coupling, 2p-3d Coulomb interaction, 3-d Coulomb interaction, ...) you can find which interactions are responsible for the effect we describe. Combining this with looking at the right expectation values (including partial excitations and spectrosocpy in tensor form) can give insight into the physics behind the observation. Good luck

*) The groundstate of NiO is given by a spin triplet, that branched from the ^3F multiplet. If you look at the expectation values you should expect that S=1 and L=3. This is only roughly the case. Why is there a deviation. 

*) Compare the groundstate of NiO in crystal-field theory for 10Dq=0.5, 1 and 2 eV. (you can either compare expectation values or look at the overlap of these functions <psi_0.5 | psi_1>. Do the same for CoO. Why is there such a big difference in behaviour? How does this influence the Bulk modulus (isotropic pressure v.s. volume curves)? While you're at it: Also the Youngs modulus (deformation due to uni-axel pressure) is very different between CoO and NiO. Do you know why? The explanation for the Youngs modulus is different from the explanation of the Bulk modulus. 

*) Excitations from the 2p shell to the 3d shell of Ni in NiO can either be into the t2g or into the eg orbitals. At the same time they can come from either the j=1/2 of j=3/2 orbitals. If you calculate the spectrum where you can excite only into the t2g orbitals and the spectrum where you can excite only into the eg orbitals then their sum is not the same as the spectrum where one can excite into both the t2g and eg orbitals. The same is true for excitations from the j=1/2 and j=3/2 orbitals (See the example on partial excitations in XAS). Why is this the case?

In RIXS of NiO we can see single and double "magnon" excitations. THe word magnon is here  a bit strange as we only have one Ni atom, but letts (mis) use this term anyhow. We enter with one photon, which can transfer an angular momentum of unit one to the crystal and leave with a photon that can take an angular momentum one from the crystal. In total an angular momentum transfer of two, i.e. a transition from Sz=-1 to Sz=1. If you redo the calculation for MnO (locally d5) you find that there are also 3,4 and 5 spin-flips or magnon excitations possible. A single photon can excite from Sz=-5/2 to Sz=+5/2. Why is this the case?





