Magnetic circular dichroism in the dd excitation in the van der Waals magnet CrI3 probed by resonant inelastic x-ray scattering

We report on a combined experimental and theoretical study on ${\mathrm{CrI}}_{3}$ single crystals by employing the polarization dependence of resonant inelastic x-ray scattering (RIXS). Our investigations reveal multiple Cr $3d$ orbital splitting ($dd$ excitations) as well as magnetic dichroism (MD) in the RIXS spectra. The $dd$ excitation energies are similar on the two sides of the ferromagnetic transition temperature, ${T}_{C}\ensuremath{\sim}61$ K, although MD in RIXS is predominant at 0.4 T magnetic field below ${T}_{C}$. This demonstrates that the ferromagnetic superexchange interaction that is responsible for the interatomic exchange field is vanishingly small compared with the local exchange field that comes from exchange and correlation interaction among the interacting Cr $3d$ orbitals. The recorded RIXS spectra reported here reveal clearly resolved Cr $3d$ intraorbital $dd$ excitations that represent transitions between electronic levels that are heavily influenced by dynamic correlations and multiconfiguration effects. Our calculations taking into account the Cr $3d$ hybridization with the ligand valence states and the full multiplet structure due to intra-atomic and crystal field interactions in ${\mathrm{O}}_{h}$ and ${\mathrm{D}}_{3d}$ symmetry clearly reproduced the dichroic trend in experimental RIXS spectra.