Measurement of the spectral line shapes for orbital excitations in the Mott insulator CoO using high-resolution resonant inelastic x-ray scattering

We establish the spectral line shape of orbital excitations created by resonant inelastic x-ray scattering for the model Mott insulator CoO. Improved experimental energy resolution reveals that the line shapes are strikingly different from expectations in a first-principles-based atomic multiplet model. Extended theoretical simulations are performed to identify the underlying physical origins, which include a pronounced thermal tail reminiscent of anti-Stokes scattering on the energy gain side of excitations, and an essential contribution from interatomic many-body dynamics on the energy loss side of excitations.

Figure 1

Resonant inelastic scattering at the M-edge. (a) The scattering geometry is shown. (b) The penetration length of x rays in CoO is estimated from Ref. 24. (c) (left) CoO RIXS spectra measured at 320 K with incident energies from 55 to 70 eV (0.5 eV steps) are compared with (right) an atomic multiplet model.

Figure 2

Thermal changes in experimental line shapes. (a) (red) A fluorescence spectrum of CoO is compared with (black) an atomic multiplet simulation. (b) RIXS data obtained at energies labeled A to E in panel (a) are overlaid with black background curves obtained by an automated fitting function described in the text. Red data points are measured at 320 K and blue points at 90 K, and a dashed vertical line indicates the onset of ${}^4{T}_2$ excitation intensity at 90 K. (c) The data from panel (b) are shown after background subtraction, and normalized so that all 90 K measurements have the same height. Curves represent multiplet simulations for (dark blue) $T=90$ K, (light red) $T=320$ K, and (green) $T=90$ K electronic Boltzmann occupation with the $T=320$ K lattice constant, and are normalized to align the blue simulation curve with the low energy line shape of $T=90$ K data points. An inset at upper right illustrates how thermally populated states (shaded red) reduce the excitation energy gap.

Figure 3

Pseudo-anti-Stokes features from thermally populated modes. (a) A schematic shows a typical anti-Stokes scattering process. Thermal fluctuations cause the scattering site to start in a spin flip excited state[2, 5, 9] with energy $E_S$, within the ${}^4{T}_1$ ground state manifold. An incident photon excites the system into intermediate resonance states ($m$), and a scattered photon is emitted as the system decays into the lowest energy state of the ground state manifold. The resulting RIXS feature appears at a negative energy loss ($E=-E_S$). (b) In a pseudo-anti-Stokes scattering process, the system evolves through the same initial and intermediate states as in anti-Stokes scattering, but the final state is the lowest energy state of a higher energy multiplet manifold (e.g., ${}^4{T}_2$). (c) Spectral line shapes of low energy multiplet excitations are compared at (blue) $T=90$ K and (red) $T=320$ K using the same 10 Dq value. Anti-Stokes and pseudo-anti-Stokes tails appear on the energy gain side of all multiplet features. The spectra are averaged over incident energy, and the $T=90$ K curve intensity has been enhanced by 13$\%$ to roughly align peak heights.

Figure 4

Intersite electronic shakeup interactions. (a) The scattering site is highlighted in red in a [001] plane of the CoO lattice, with relative antiferromagnetic spin orientations indicated by “$+$” and “$-$” signs. Parameters describing intersite interactions are labeled for (vector 1, [110] direction) nearest and (vector 2, [100] direction) next-nearest cobalt neighbors of the scattering site. (b) The effect of (top) $V$ and (bottom) $J$ shakeup parameters is simulated. Green curves representing nearest neighbor interactions (the simulation results for $J_2=0$ and $J_2=-1.4$ meV are nearly identical) to (black) the trivial curves with no shakeup parameters applied. (c) Data points obtained by averaging the five $T=90$ K curves in Fig. 2c are compared with (top) a shakeup simulation and (bottom) a Poisson distribution.

Figure 5

Merging shakeup and multiplet models. A simulation of the scattering site and its 12 nearest Co neighbors is thermalized to (dark blue curves) $T=90$ K and (light red curves) $T=320$ K to match experimental data. Data curves are reproduced from Fig. 2c, and are measured at the incident energies labeled.

Figure 6

RIXS on a spectator atom. (black, diamonds) The CoO ${}^4{T}_2$ excitation measured at $h\nu =61.5$ eV and $T=320$ K is overlaid with (gray, circles) a room temperature $ff$ RIXS excitation spectrum from Nd spectator atoms in Nd${}_{1.67}$Sr${}_{0.33}$NiO${}_{4+\delta }$ (NSNO). Energy loss for NSNO is displayed on the top axis, and is shifted by 1.2 eV relative to the CoO incident energy axis.