Combining $M$- and $L$-edge resonant inelastic x-ray scattering for studies of $3d$ transition metal compounds

Resonant inelastic x-ray scattering (RIXS) measurements performed jointly across the $M_{2,3}$ and $L_3$ absorption thresholds are used to study CoO local electronic structure and are supported by model calculations. The high-resolution experimental data provide a precise set of parameters to describe the correlated response of valence electrons. The same core-hole independent set of parameters within the single impurity Anderson model is used to describe both the $M$ $\left(3p\text{−}3d\right)$ and $L$ $\left(2p\text{−}3d\right)$ resonances. This work shows that combining $M$ and $L$ scattering data provides an enhanced contrast view of the spectral weights. Measured $M_{2,3}$-RIXS spectra are observed to be free of charge-transfer or normal fluorescence contributions. Moreover the cross section of $M$-RIXS final states with change in spin multiplicity is low. Combining this information with $L$-edge studies establishes an appealing means of making a better separation between on-site and intersite (ligand to metal) electronic excitations. Experimental and theoretical features specific to RIXS studies performed at $M$ and $L$ edges are summarized as a basis for future studies on complex transition metal compounds.

Figure 1

Schematic view of the scattering geometry.

Figure 2

RIXS spectra measured at the $\text{Co}M$ threshold in CoO. Vertical dashed lines are a guide to help identify the spectral features (see text for further information). All spectra are normalized to the acquisition time and incoming photon flux, the average recording time per spectrum being about 2 h. The abscissa represents the difference between the energies of incoming and scattered photons $h{\nu }_{\text{in}}-h{\nu }_{\text{out}}$. The left inset reproduces the shape of the $\text{Co}{M}_{2,3}$ absorption spectra deduced from reflectivity measurements (Ref. 14). The right inset shows the shape of the spectrum measured for 57.5 eV incoming x rays and displays the FWHM of the elastic peak.

Figure 3

Representative $L_3$-RIXS experimental data set along with the corresponding x-ray absorption curve detected in total electron yield mode (inset). The excitations energies used for scattering measurements are indicated with vertical bars. The notation of observed losses (vertical dashed lines) was made in compliance with the one used in Fig. 2 (see text also).

Figure 4

Calculated x-ray absorption cross section (top) and RIXS intensities for four selected incoming photon energies (bottom).

Figure 5

Computational results for the RIXS cross section for $M$ resonances of Co in CoO. The levels of the contour plot (identical with the ticks of lateral color bar) are chosen in order to emphasize the states below $-3\text{eV}$ relative energy. The map was generated by incrementing the incoming photon energy with 0.5 eV steps and convoluting each spectrum with 0.15 eV FWHM Gaussian to account for experimental broadening. Points along constant transferred energy lines were generated by spline interpolation.

Figure 6

Results of theoretical simulations performed for $L_3$-RIXS case. The inset displays the corresponding absorption edge.

Figure 7

Experimental results obtained at the $\text{Co}M$ resonances in CoO presented as a two-dimensional map. We considered the spectra from Fig. 2 and subtracted the background fitting the tail of the elastic peak. The points along constant transfer energy lines were calculated by spline interpolation.