**6. Some applications of RIXS**

#### **6.1. Soft X-ray RIXS on cuprates**

In the early days, soft X-ray RIXS with moderate resolution was performed a lot on standard compounds such as manganese oxide (MnO) [37, 40], cobalt oxide (CoO) [40], and nickel oxide (NiO) [40–43]. Interestingly, in the soft X-ray regime when the SAXES spectrometer [44] became available with a much better energy resolution, and the general improved resolution was established on MnO [45], CoO [46], and NiO [47], high-energy resolution RIXS was focused mostly on the Cu L-edge of high-temperature superconductors (HT-SC) and representative HT-SC model compounds and as well with some measurements at the oxygen K-edge to gain understanding of superconducting properties related to phonon, magnon, and electronic structure, for example, Refs [48–52] for Cu L-edge and Refs. [53, 54] for the oxygen K-edge RIXS of HT-SC (model) compounds.

Nowadays, with more high-resolution RIXS spectrometers becoming available with even advanced features [55], high-resolution soft X-ray RIXS studies toward other 3d- (e.g., iron selenides, manganites, nickelates, or cobalt), 4d-, and 5d-metal (e.g., iridium) materials and to 4f-materials are expected for investigations into solid-state applications like superconductivity (FeSe-related), multiferroics, topological insulators, etc.

#### **6.2. RIXS on metal organics – hard X-ray RIXS: 1s2p and 1s3p RIXS**

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

**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

In the early days, soft X-ray RIXS with moderate resolution was performed a lot on standard compounds such as manganese oxide (MnO) [37, 40], cobalt oxide (CoO) [40], and nickel oxide (NiO) [40–43]. Interestingly, in the soft X-ray regime when the SAXES spectrometer [44] became available with a much better energy resolution, and the general improved resolution was established on MnO [45], CoO [46], and NiO [47], high-energy resolution RIXS was focused mostly on the Cu L-edge of high-temperature superconductors (HT-SC) and representative HT-SC model compounds and as well with some measurements at the oxygen K-edge to gain understanding of superconducting properties related to phonon, magnon, and electronic structure, for example, Refs [48–52] for Cu L-edge and Refs. [53, 54] for the oxygen K-edge

the system before the X-ray excitation is already in an excited state.

be found in Refs. [5, 38, 39].

234 Raman Spectroscopy and Applications

**6. Some applications of RIXS**

RIXS of HT-SC (model) compounds.

**6.1. Soft X-ray RIXS on cuprates**

In general, organic materials suffer from the X-ray probe, for example, the X-rays create beam damage. Hard X-rays have a lower cross section with metallic components in metal organics, such as proteins and homogeneous metal-containing catalysts than soft X-rays. In order to decrease the chances of beam damage, hard X-ray RIXS is often applied on these biologically/ homogeneous catalysis relevant materials, especially focusing on properties concerning the active metal center of these systems.

In line with XRS, hard X-ray RIXS can also be used to study the edges with best chemical resolution indirectly [56, 57]. For example, for iron one can excite the (pre-)K-edge (1s core hole with excitation into the 3d-shell-related states) and probe the Ka (2p emission) or Kb (3p) emission. In these cases, the final state of the RIXS process is similar to the normal 2p XAS or 3p XAS (a hole in the 2p/3p and an additional electron in 3d). The emission resembles then the normal 2p (3p) XAS measured in the soft X-ray regime, but the spectrum measured via 1s2p (1s3p) RIXS may have additional features [58] due to quadrupole and monopole contributions, since with RIXS as a two-photon process the dipole selection rule has to be twice taken into account.

#### **6.3. RIXS on simple semiconductors: electron-phonon coupling, band gap properties**

In the hard X-ray regime, RIXS has been applied as well to study electron-phonon interactions of cuprates by focusing on the phonon progression [59], and in essence, the same technique can be performed in soft X-ray RIXS with high-energy resolution as long as there are not too many different phonon modes interfering. In the soft X-ray regime, electron-phonon scattering properties have been analyzed by measuring both RIXS and X-ray emission spectroscopy (XES) with a relatively low-energy resolution RIXS spectrometer [60] compared to the current standard as function of temperature for silicon and silicon carbide.

Resonant inelastic X-ray scattering and X-ray emission are very often applied in a similar fashion. Above certain energies, for example, well above the X-ray resonances, in the ionization regime, when one observes emitted X-ray photons, one speaks simply of *normal* XES.

By applying the combination of RIXS and XES, one could get (relative) measures on the angular and crystal momentum transfer due to electron-phonon scattering. This gives you an average electron-phonon scattering picture, so it is perfectly fine if there are many phonon modes. Comparing the different results on these compounds, a form of silicon carbide (6H-SiC) showed a much stronger electron-phonon scattering effect than pure silicon for both crystal momentum transfer and angular momentum transfer [61, 62]. In **Figure 5**, comparison of calculated silicon partial density of states (DOS) of 6H-SiC with the difference in XES as function of temperature with reference to room temperature is given. One sees that as function of temperature, the XES difference shows a decrease related to s-DOS and an increase related to p-DOS, while the core hole is of 2p character. In general, s-(and d-)DOS is expected in the XES with a Si 2p core hole and the increase in p-DOS with temperature is therefore a measure for the amount of angular momentum transfer events in the core-hole lifetime.

**Figure 5.** Top: calculated Si s-DOS and p-DOS for silicon carbide (6H-SiC). Bottom: difference in the XES with the XES at room temperature for 6H-SiC. This figure was adapted from Ref. [62] and is taken with permission.

For insulators and semiconductors, the first electronic energy loss observed in RIXS is directly related to the (element-specific) band gap, and by combining the information of RIXS with XAS and XES, one is able to identify the valence and conduction band behavior as a function of temperature [63, 64], which is important to know for semiconductor applications under extreme temperature conditions.

#### **6.4. RIXS on liquids and on ions and organic molecules solved in liquid**

In general, liquids at synchrotrons are measured by flow cells or liquid jets. For hard X-ray RIXS measurements, there are in principal no side conditions, but for soft X-ray RIXS measurements, you need to stay below a certain pressure in order to still be able to get X-rays on the liquid and to measure the emitted X-rays. There are a few setups in the world that can perform these measurements routinely, for example, the setups explained in Refs. [6, 65]. For liquids, the soft X-ray regime of RIXS [66, 67] is more important because often you want to study resonantly the oxygen K-edge and nitrogen K-edges which are at about 500 and 400 eV in the soft X-ray regime, respectively. Liquid jet RIXS with relatively low-energy resolution (~500 meV) has now, for example, been successfully employed on liquid and gas phase water [68, 69], methanol and other alcohols [70], 3d-metal ions solved in water, for example, Mn2+ (and Mn2+ organic complexes) [71] and Ni2+ in water [72], Fe(CO)5 solved in ethanol [73, 74], Fe(CN)6 solved in water [74–76], 2-mercaptopyridine solved in water [77] and (models for) biologically relevant proteins in solution [71, 78–80].

function of temperature with reference to room temperature is given. One sees that as function of temperature, the XES difference shows a decrease related to s-DOS and an increase related to p-DOS, while the core hole is of 2p character. In general, s-(and d-)DOS is expected in the XES with a Si 2p core hole and the increase in p-DOS with temperature is therefore a measure

**Figure 5.** Top: calculated Si s-DOS and p-DOS for silicon carbide (6H-SiC). Bottom: difference in the XES with the XES

For insulators and semiconductors, the first electronic energy loss observed in RIXS is directly related to the (element-specific) band gap, and by combining the information of RIXS with XAS and XES, one is able to identify the valence and conduction band behavior as a function of temperature [63, 64], which is important to know for semiconductor applications under

In general, liquids at synchrotrons are measured by flow cells or liquid jets. For hard X-ray RIXS measurements, there are in principal no side conditions, but for soft X-ray RIXS measurements, you need to stay below a certain pressure in order to still be able to get X-rays on the liquid and to measure the emitted X-rays. There are a few setups in the world that can perform these measurements routinely, for example, the setups explained in Refs. [6, 65]. For liquids, the soft X-ray regime of RIXS [66, 67] is more important because often you want to study resonantly the oxygen K-edge and nitrogen K-edges which are at about 500 and 400 eV in the soft X-ray regime, respectively. Liquid jet RIXS with relatively low-energy resolution (~500 meV) has now, for example, been successfully employed on liquid and gas phase water [68, 69], methanol and other alcohols [70], 3d-metal ions solved in water, for example, Mn2+ (and Mn2+ organic complexes) [71] and Ni2+ in water [72], Fe(CO)5 solved in ethanol [73, 74],

at room temperature for 6H-SiC. This figure was adapted from Ref. [62] and is taken with permission.

**6.4. RIXS on liquids and on ions and organic molecules solved in liquid**

extreme temperature conditions.

236 Raman Spectroscopy and Applications

for the amount of angular momentum transfer events in the core-hole lifetime.

As an example of RIXS on liquids, **Figure 6** shows the oxygen K-edge RIXS on resonance and far above the resonance (nonresonant X-ray emission) for methanol, ethanol, propanol, butanol, pentanol, and hexanol. It shows the main double-peak structure for all these alcohols, where the interpretation of this double-peak structure has been under debate for oxygen Kedge of water. As explained by Schreck et al., the relative ratio of this main double-peak structure corresponds to the amount of hydrogen bonds (expected from simulations) [70].

**Figure 6.** From top to bottom: oxygen K-edge on resonance (a) and oxygen K-edge nonresonant X-ray emission (b) of liquid hexanol, pentanol, butanol, propanol, ethanol and methanol. Figure taken from Ref. [70].

For the more sophisticated RIXS spectrometers with high resolution (~50 meV), flow cells are preferred in order to keep good vacuum conditions in the overall vacuum chamber and in the spectrometer. With the first high-resolution RIXS spectrometer available at the Swiss Light Source [44, 81], RIXS with vibrational-resolved resolution was acquired and analyzed for water [68] and acetone and the acetone-chloroform complex [82], and for the latter, two systems ground state potential energy surfaces could be reconstructed from the vibrational progression observed with vibrationally resolved RIXS.

By combining pump-laser probe-X-ray photons, one can get time-resolved information on materials. In this case, it is possible that the pump-laser excites the material to some excited state and the probe X-ray followed by X-ray scattering may lead to anti-stokes RIXS features (that is features observed at X-ray emission energies higher than the probe X-ray excitation energy). The first indications have been shown in X-ray free-electron laser experiments on Fe(CO)5 solved in ethanol [74].

#### **7. Summary**

A short overview of X-ray Raman spectroscopy and resonant X-ray Raman spectroscopy (RIXS) has been given with special attention to what these element-specific spectroscopies can contribute to a better understanding of materials, or in other words how chemistry might benefit from Raman spectroscopy studies in the X-ray regime. Here it was shown that XRS and RIXS can supply information on (local, occupied, and unoccupied valence) electronic structure relevant to chemical activity, as well as supplying data to coupling of electronic structure with vibrational (electron-phonon interaction) and spin structure (electron-magnon interaction). In addition, with X-ray FELs, XRS and RIXS can be applied to (optically) excited states, and in particular the shift of these spectroscopies from synchrotrons to X-ray free-electron lasers [83] may become an important transition for time-dependent electronic and phononic structure studies. As well, (future) diffraction-limited storage rings will enhance the energy resolution for XRS and RIXS [84].
