Dynamical screening in ${\mathrm{SrVO}}_3$: Inelastic x-ray scattering experiments and ab initio calculations

We characterize experimentally and theoretically the high-energy dielectric screening properties of the prototypical correlated metal ${\mathrm{SrVO}}_3$. The dynamical structure factor measured by inelastic x-ray scattering spectroscopy as a function of momentum transfer is in very good agreement with first-principles calculations in the adiabatic local-density approximation to time-dependent density-functional theory. Our results reveal the crucial importance of crystal local fields in the charge response function of correlated materials: They lead to depolarization effects for localized excitations and couple spectra from different Brillouin zones.

Figure 1

Comparison between experimental IXS spectra (black) and theoretical dynamic structure factors calculated within the ALDA (blue) and the RPA (green). ${\mathbf{q}}_{\text{e(t)}}$ denotes the experimental (theoretical) momentum transfer value in reciprocal lattice units (r.l.u.) and $\hslash \omega$ is the energy transfer (${\mathbf{q}}_{\text{t}}$ is the wave vector in the $12\times 12\times 12$ grid that is the closest to ${\mathbf{q}}_{\text{e}}$). The experimental and theoretical spectra have been normalized to the area under the curve between 5 and 40 eV. A vertical offset has been added to the spectra for improved clarity. (a) Low $q$. (b) Intermediate $q$. (c) High $q$. The theoretical spectra have been broadened by 0.17 (0.4) eV for panel (a) [panels (b) and (c)]) to match the experimental resolution.

Figure 2

Dispersion of the calculated dynamic structure factor $S(\mathbf{q},\omega )$ for $\mathbf{q}$ along the (100) direction. The size of $\mathbf{q}$ ranges from $\mathrm{q}=0.083$ (bottom curve) to $\mathrm{q}=4.083$ (top curve) by steps equal to 0.166 reciprocal lattice units. (a) Full calculations within the ALDA. (b) Calculations within the RPA neglecting local field effects.

Figure 3

Analysis of the contribution from O $2p$ valence electrons and different semicore states to the spectra: (left) $\text{Im}{\epsilon }_M(\mathbf{q},\omega )$ in the independent-particle approximation (i.e., without LFEs), see Eq. (7), (center) the corresponding loss function $-\text{Im}{\epsilon }_M^{-1}(\mathbf{q},\omega )$, and (right) the full ALDA calculation for (upper row) a small $q=0.083$, (middle row) an intermediate $q=1.916$, and (bottom row) a high $q=3.916$ for momentum transfers $\mathbf{q}$ along the (100) direction.

Figure 4

Loss function at $q=(13/12)$ $\left|\mathbf{G}\right|$ along the (100) direction calculated with or without LFEs.

Figure 5

Loss functions calculated at $\mathbf{q}=\mathbf{G}+\mathit{\eta }$, where $\mathbf{G}=\left(100\right)$ and $\mathit{\eta }$ has a very small size $\left|\eta \right|={10}^{-3}$ and forms an angle $\alpha$ with $\mathbf{G}$ that varies from $0{}^{\circ }$ when $\mathit{\eta }$ is along (100) to $90{}^{\circ }$ when $\mathit{\eta }$ is along (010). The spectra calculated without LFEs (gray curve) are independent of $\alpha$, while spectra that include LFEs are sensitive to the angle $\alpha$ with the small-$\eta$ component.