**5. RIXS**

Resonant X-ray Raman spectroscopy is now more commonly known as RIXS, but other terms such as resonant X-ray fluorescence spectroscopy (RXFS) and resonant X-ray emission spectroscopy (RXES) have also been used in the past. With RIXS, the incoming X-ray photon energy corresponds (or is close) to an X-ray edge in contrast to XRS. The RIXS process is schematically shown with an one-electron scheme in **Figure 3** next to schematically shown XAS and XES process. The first step of the RIXS process is the same as the XAS process. The second transition is emission from some state, and here it is shown as emission from an occupied state. The XES process is similar to that second step. The processes of RIXS are here only shortly described. For more details on (theory of) RIXS one is referred to Refs. [1, 32–35]. However, for RIXS, the excited electron can relax back into the core hole (elastic emission) and in parallel create an additional excitation from the occupied valence into the unoccupied valence with some energy loss related to this valence excitation as opposed to XES: following the X-ray excitation, subsequent X-ray emission may take place (side-note: Auger decay is stronger than emission decay in the soft X-ray regime). There are a few possibilities that the excited electron decays itself (participator decay channel), which may lead to elastic X-ray scattering, but the excited electron could also have traveled over some excited potential energy surface during the core-hole lifetime which may lead to emission to a vibrationally excited state. Another option for the participator channel is that the excited electron decays itself and transfers energy to an electron in the valence band which gets excited into some unoccupied state (e.g., a so-called charge transfer state or a valence-valence excitation). Also an electron from the valence band (spectator decay channel) may decay instead of the excited electron (participator channel). This may lead effectively to the same final situation from this oneelectron picture of **Figure 3**.

where the B K-edge XRS (and in addition the Mg L-edge XRS) has recently been measured for

Although the previously mentioned hydrogen storage materials were only under 1 bar of nitrogen/hydrogen, XRS is also applied in studies with even higher pressures to study the effect of it on materials [25], for example, on iron to gain information on the behavior of it in the inner core of earth [26]. In these higher-pressure studies, phonon scattering is often studied with XRS [27, 28] (NIXS or IXS mentioned in the previous section) to study pressure-induced phase transitions and how the phonon spectrum changes. Since XRS is applied in the hard Xray regime, it is also easier to get electronic structure measures, similar to direct XAS, on liquid

In Section 3, it was mentioned that XRS and XAS may give similar results, but with XRS one is as well able to obtain higher-order transitions above the dipole transition. It has been shown in Ref [31] that octupole transitions can be observed in XRS on rare earth phosphates RePO4 with Re = La, Ce, Pr, and Nd. In this respect, XRS might potentially be used in measuring

In summary, XRS has been mostly used for (*in situ*) electronic structure studies on light elements as the alternative to XAS, and there is a strong focus on materials under high-pressure conditions. In general, XRS studies may become important as well for studies on (heterogenous) catalysts under (close to) industrial operation conditions, because of the advantage of the edge with best chemical resolution without the constraints of the soft X-ray regime (vacuum). As well, XRS is used to gain understanding of the momentum space of phonons of

Resonant X-ray Raman spectroscopy is now more commonly known as RIXS, but other terms such as resonant X-ray fluorescence spectroscopy (RXFS) and resonant X-ray emission spectroscopy (RXES) have also been used in the past. With RIXS, the incoming X-ray photon energy corresponds (or is close) to an X-ray edge in contrast to XRS. The RIXS process is schematically shown with an one-electron scheme in **Figure 3** next to schematically shown XAS and XES process. The first step of the RIXS process is the same as the XAS process. The second transition is emission from some state, and here it is shown as emission from an occupied state. The XES process is similar to that second step. The processes of RIXS are here only shortly described. For more details on (theory of) RIXS one is referred to Refs. [1, 32–35].

otherwise spectroscopically unavailable excited states or "optically dark states."

materials of interest (which was not covered in this section).

another possible hydrogen storage material, Mg(BH4)2 [24].

**4.2. Materials under pressure and in the liquid phase**

phase systems [29, 30].

232 Raman Spectroscopy and Applications

**4.4. Summary**

**5. RIXS**

**4.3. Higher-order electronic transitions**

**Figure 3.** Schematic representation of the different core spectroscopies: X-ray absorption spectroscopy (XAS), resonant inelastic X-ray scattering (RIXS), and (nonresonant) X-ray emission spectroscopy (XES). FE indicated the Fermi level. Solid horizontal lines indicate unoccupied states within the system, while the dotted line indicates a virtual state for electrons ("free electrons"). Red lines indicate incident and emitted radiation.

So, **Figure 3** showed the XAS, XES, and RIXS processes by single-electron movements. However, one should think about these processes in total energy terms. The case for the combination of XAS, RIXS, and XES is shown in **Figure 4**.

As simplified above, RIXS is a combination of XAS (the absorption of the photon) and XES (the emission of a photon), and **Figure 4** shows that with RIXS it is then possible to reach excited states of the material. Here it is not stressed what kind of excited states these are, since this can be any type of excited state. That means that with RIXS (and sufficient resolution in the emission spectrometer) one can obtain information on electronic excited states (e.g., dd excitations in 3d-materials) but as well on vibrationally and magnetically excited states [36]. The figure does not show energy gains (anti-Stokes Raman), but in principle this is possible if the system before the X-ray excitation is already in an excited state.

**Figure 4.** Total energy scheme of the processes of X-ray absorption (XAS), X-ray emission (XES) and resonant inelastic X-ray scattering (RIXS) with X-ray absorption resonances and the continuum as possible excitation channels (intermediate state for RIXS/XES) and final states for RIXS at different energy (energy loss) than the original ground state.

In the earlier days of RIXS, Butorin showed advantages of the RIXS technique, such as clear band showing allowed dd excitations compared to EELS and UV-VIS absorption spectra where dd transitions often appear as weak structures [37]. RIXS spectroscopy gained increased interest with the advances on the brilliance of synchrotrons and X-ray free-electron lasers as well as advances in more efficient detectors. More information on RIXS and its capabilities can be found in Refs. [5, 38, 39].
