Orbital superexchange and crystal field simultaneously at play in YVO${}_3$: Resonant inelastic x-ray scattering at the V $L$ edge and the O $K$ edge

We report on the observation of orbital excitations in YVO${}_3$ by means of resonant inelastic x-ray scattering (RIXS) at energies across the vanadium $L$${}_3$ and oxygen $K$ absorption edges. At the V $L$${}_3$ edge, we are able to resolve the full spectrum of orbital excitations up to 5 eV. In order to unravel the effect of superexchange interactions and the crystal field on the orbital excitations, we analyzed the energy and temperature dependence of the intra-$t_{2g}$ excitations at 0.1–0.2 eV in detail. While these results suggest a dominant influence of the crystal field, peak shifts of about 13–20 meV observed as a function of the transferred momentum $q\parallel a$ reflect a finite dispersion of the orbital excitations. This is puzzling since theoretical models based on superexchange interactions predict a dispersion only for $q\parallel c$. Furthermore, we demonstrate that RIXS at the O $K$ edge is very sensitive to intersite excitations. At the O $K$ edge, we observe excitations across the Mott-Hubbard gap and an additional feature at 0.4 eV, which we attribute to two-orbiton scattering, i.e., an exchange of orbitals between adjacent sites. Altogether, our results indicate that both superexchange interactions and the crystal field are important for a quantitative understanding of the orbital excitations in YVO${}_3$.

Figure 1

RIXS overview spectra (lower statistics, accumulated over 30 min each) at $T=300$ K for nine different incident energies across the V $L_3$ edge (512–519 eV) and at the O $K$ edge ($\ge$530 eV). The x-ray absorption spectrum (XAS) measured in total electron yield is shown in the right panel, with color-coded points indicating the excitation energies $E_{\mathrm{in}}$ used for the RIXS spectra. A sketch of the scattering geometry is shown in the inset. All spectra were measured with $E\parallel c$. The RIXS spectra were measured at a scattering angle of $2\theta ={130}^{\circ }$. The inelastic peaks with energy transfers up to 4 eV correspond to orbital excitations. The steep increase of the RIXS signal at 4.5 eV for $E_{\mathrm{in}}=530.1$ eV at the O $K$ edge is in good agreement with the onset of charge-transfer excitations observed in the optical conductivity.[30, 51, 52] However, the large intensity, exceeding the intensity of the elastic peak, points towards x-ray fluorescence emission, possibly superimposed by the charge-transfer excitations mentioned above.

Figure 2

RIXS signal of YVO${}_3$ for $E\parallel c$ at 22, 100, and 300 K for $E_{\mathrm{in}}=517.1$ eV and 2$\theta ={90}^{\circ }$. These data sets have been accumulated over 3 h each. (Inset) Temperature-dependent XAS spectra of YVO${}_3$ for polarization $E\parallel c$ at 22, 100, and 300 K recorded in total fluorescence yield mode.

Figure 3

Comparison of the RIXS signal for $E_{\mathrm{in}}=512.6$ eV (red) and 517.1 eV (green). The thin magenta curve shows the same data for $E_{\mathrm{n}}=512.6$ eV on a larger scale (thick line: smoothed). The strong high-energy RIXS features observed for $E_{\mathrm{in}}=517.1$ eV can also be resolved for $E_{\mathrm{in}}=512.6$ eV but with strongly reduced spectral weight.

Figure 4

Low-energy RIXS spectra of YVO${}_3$ at the V $L_3$ edge. (Top) Temperature dependence of the intra-$t_{2g}$ excitations with $2\theta ={90}^{\circ }$ and $E_{\mathrm{in}}=512.6$ or 517.1 eV at 22, 100, and 300 K. (Middle) Dependence on the scattering angle $2\theta$ with $2\theta ={90}^{\circ }$ and 130${}^{\circ }$ for $T=100$ K and different values of $E_{\mathrm{in}}$. (Bottom) Dependence on $E_{\mathrm{in}}$. Data for $E_{\mathrm{in}}=517.1$ eV are offset for clarity in the top and middle panels. All spectra were accumulated over 3 hours with $E\parallel c$ and $q\parallel a$. To estimate the contribution from the elastic peak with a full width at half maximum of 60 meV, the spectra have been mirrored around zero (dotted lines).

Figure 5

RIXS spectra of the intra-$t_{2g}$ excitations for different temperatures (top: 22 K; middle: 100 K; bottom: 300 K) and different scattering angles (left: $2\theta ={90}^{\circ }$; right: 130${}^{\circ }$) for $E_{\mathrm{in}}=512.6$ eV. The elastic line has been subtracted by mirroring it around zero (see Fig. 4). In order to account for the two-peak structure, we fitted two Gaussians to the data (solid lines). The peak positions of both peaks show shifts of less than 40 meV as a function of temperature. Most of the observed changes of the line shape can be explained by the variation of spectral weight, i.e., of the peak areas. At 100 K, both Gaussian peaks show a shift of about 20 meV as a function of the scattering angle $2\theta$.

Figure 6

RIXS spectra of YVO${}_3$ for an incident energy of $E_{\text{in}}=517.1$ eV at $T=100$ and 300 K for $2\theta ={90}^{\circ }$ and 130${}^{\circ }$. Black solid lines depict fits of the spin-flip intra-$t_{2g}$ excitations using two oscillators with Gaussian line shape.

Figure 7

Comparison of RIXS data measured at the O $K$ edge (bottom panel) and of the optical conductivity ${\sigma }_1^c\left(\omega \right)$ of YVO${}_3$ as determined by ellipsometry (top panel, from Ref. 30). The dashed line in the bottom panel shows data for the V $L_3$ edge from Fig. 2.

Figure 8

Sketch of the ground state, intermediate states, and different final states for RIXS at the O $K$ edge of YVO${}_3$. Each diamond corresponds to a VO${}_6$ octahedron with three nondegenerate $t_{2g}$ levels indicated by the horizontal bars. For a single octahedron, the ground state is a superposition of $3d^2$ and $3d^3\underline{L}$, where $\underline{L}$ denotes a ligand O $2p$ hole. See main text for a discussion of intermediate and final states.

Figure 9

Top panel/left axis: RIXS spectra of YVO${}_3$ at $T=100$ K and $2\theta ={90}^{\circ }$ for $E_{\text{in}}=530.1$ eV (O $K$ edge, blue) and 512.6 eV (V $L_3$ edge, yellow) as well as the difference between the two spectra (red). Top/right axis: optical conductivity ${\sigma }_1^c$ of YVO${}_3$ at $T=100$ K for $E\parallel c$ (dashed green) and $\Delta \sigma ={\sigma }_1^c\left(100\text{K}\right)-{\sigma }_1^c\left(4\text{K}\right)$ (solid green line). The strong increase of ${\sigma }_1^c$ at low and high energies reflects absorption by (multi) phonons and the onset of interband excitations, respectively (for details see Ref. 21). The two-orbiton excitation is forbidden in optics below $T=77$ K. Thus the 4-K data can be used as an estimate for the background of phonons and single orbital excitations. The difference ${\sigma }_1^c\left(100\text{K}\right)-{\sigma }_1^c\left(4\text{K}\right)$ shows an estimate of the two-orbiton contribution at 100 K with a peak at 0.4 eV, similar to the RIXS difference spectrum. Middle and bottom panel: RIXS spectra for $E_{\text{in}}=530.1$ eV and two different $q$ values obtained by changing the scattering angle, i.e., 2$\theta ={90}^{\circ }$ (middle) and 130${}^{\circ }$ (bottom). For an estimate of the peak shape and position of the two-orbiton peak at 0.4 eV in RIXS, two Gaussians at 0.12 and 0.22 eV have been fitted (width and area) after subtracting the mirrored elastic line.

Figure 10

Optical absorption of DyScO${}_3$ and DySc${}_{0.9}$V${}_{0.1}$O${}_3$ for $E\parallel b$ at 300 K. The additional absorption peaks observed in DySc${}_{0.9}$V${}_{0.1}$O${}_3$ are due to orbital excitations of the substituted V${}^{3+}$ ions.