Probing the Electronic Structure of Warm Dense Nickel via Resonant Inelastic X-Ray Scattering

The development of bright free-electron lasers (FEL) has revolutionized our ability to create and study matter in the high-energy-density (HED) regime. Current diagnostic techniques have been successful in yielding information on fundamental thermodynamic plasma properties, but provide only limited or indirect information on the detailed quantum structure of these systems, and on how it is affected by ionization dynamics. Here we show how the valence electronic structure of solid-density nickel, heated to temperatures of around 10 of eV on femtosecond timescales, can be probed by single-shot resonant inelastic x-ray scattering (RIXS) at the Linac Coherent Light Source FEL. The RIXS spectrum provides a wealth of information on the HED system that goes well beyond what can be extracted from x-ray absorption or emission spectroscopy alone, and is particularly well suited to time-resolved studies of electronic-structure dynamics.

Figure 1

Experimental RIXS map of the electronic valence structure of warm-dense Ni, irradiated at $1.2\times {10}^{17}\mathrm{W}{\mathrm{cm}}^{-2}$. Spurious Fe ${\mathrm{K}}_{\beta }$ emission at $\sim 7060\mathrm{eV}$ is due to small amounts of Fe impurities. The schematic shows the two RIXS channels, for excitations into $M$-shell states and into the continuum.

Figure 2

RIXS map as a function of irradiation x-ray intensity. The x-ray pulse drives isochoric heating so higher intensities create hotter, more ionized plasma conditions. The intensity of the $M$-shell feature is strongly dependent on the x-ray intensity.

Figure 3

(a) RIXS spectrum measured from the $K_{\alpha }$ resonance (FEL photon energy of 8160 eV, peak intensity $1.2\times {10}^{17}\mathrm{W}{\mathrm{cm}}^{-2}$). Features from the $K$-edge and vacant $3p$ states are highlighted, alongside the envelope of the $K_{\alpha }$ emission, for reference. (b) Absorption part of the RIXS spectrum after removing the $K_{\alpha }$ emission contribution [see Eq. (2)], compared with DFT simulations. Also shown is the Ni $p$-like LDOS before experimental broadening, illustrating the contributing RIXS states. Zero energy is set to the bottom of the valence band.

Figure 4

(a) Temperature and (b) $K$-edge position extracted from the RIXS dataset at different irradiation intensities. $K$-edge energies are compared with finite-temperature DFT calculations. Temperature uncertainties are $\pm 1–2\mathrm{eV}$, not plotted for clarity.