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Herein we show that non-resonant inelastic x-ray scattering involving an $s$core level is a powerful spectroscopic method to characterize the excitedstates of transition metal compounds. The spherical charge distribution of the$s$ core hole allows the orientational dependence of the intensities of thevarious spectral features to produce a spatial charge image of the associatedmultiplet states in a straightforward manner, thereby facilitating theidentification of their orbital character. In addition, the $s$ core hole doesnot add an extra orbital angular momentum component to the multiplet structureso that the well-established Sugano-Tanabe-Kamimura diagrams can be used forthe analysis of the spectra. For $\alpha$-MnS we observe the spherical chargedensity corresponding to its high spin $3d^5$ ($^6A_1$) ground stateconfiguration and we were able to selectively image its excited states andidentify them as $t_{2g}$ ($^5T_2$) and $e_g$ ($^5E$) with an energy splitting$10Dq$ of 0.78\,eV.

Selective orbital imaging of excited states with x-ray spectroscopy: the example of $\alpha$-MnS