Reply to “Comment on ‘Resonant inelastic x-ray scattering of MnO: $L_{2,3}$ edge measurements and assessment of their interpretation’ ”

In their Comment to our recent paper [Phys. Rev. B 73, 035111 (2006)], Müller and Hüfner proposed a comparison of our $\text{Mn}{L}_{2,3}$ resonant inelastic x-ray scattering (RIXS) data with low-energy electron energy-loss spectroscopy (EELS) measurements. The differences in the experimental spectra highlighted by the authors can be easily ascribed to the different cross sections in the two techniques, even when they probe the same subset of excited states, namely, the $dd$ excitations. One important difference is that EELS is limited to quartet final states only, whereas RIXS can lead to doublets, too. Thus our theoretical interpretation of the RIXS spectra, made within two different models, is compatible with the traditional crystal-field analysis of EELS. As the Sugano-Tanabe diagram usually do not include the $3d$ spin-orbit and the interatomic superexchange interactions, their accuracy is limited to hundreds of meV and they should be utilized only for rough assignments of the spectral features. On the contrary, by calculating the RIXS spectral shape we could address more sophisticated models with remarkable agreement to the experimental results. This is hardly possible in the case of low-energy EELS, for which reliable simulations of the spectra are much more difficult.

Figure 1

(Color online) Comparing the Sugano-Tanabe diagram for $3d^5$ configuration to the experimental RIXS spectra measured at two excitation energies (c) at $L_3$ and (g) at $L_2$. Top panel, RIXS spectra: black solid (red dashed) lines for linear polarization perpendicular (parallel) to the scattering plane; same spectra presented in Fig. 1 of Ref. 2. Middle and bottom panels: Sugano-Tanabe diagrams. We have rescaled the Slater integrals to 75% of the value calculated by Cowan’s code (Ref. 6), as in our original calculations with CFM. We separate here the quartet from the doublet final states to highlight that RIXS can reach both types of final states and that at $L_2$ doublets seem to be more intense than quartets.

Figure 2

(Color online) Comparing the Sugano-Tanabe diagrams for $3d^5$ configuration obtained with our Slater integrals to those suggested by MH. In the bottom panel we show the energy diagrams of quartet states only: for our parameters up to $10Dq=1.0\text{eV}$ (red solid lines, right-hand scale), for MH’s parameters up to $10Dq=1.3\text{eV}$ (dashed blue lines, left-hand scale). We notice that some energy can be obtained by either parameter combinations. In the top panel the full multiplet is presented having included the $3d$ spin-orbit interaction and the interatomic superexchange interaction. The states have there mixed character and they cannot be separated into doublets and quartets anymore.