Orbital anisotropy and low-energy excitations of the quasi-one-dimensional conductor $\beta$-Sr${}_{0.17}$V${}_2$O${}_5$

The electronic structure of the quasi-one-dimensional vanadium beta-bronze β-Sr${}_{0.17}$V${}_2$O${}_5$ has been measured in detail using soft x-ray absorption spectroscopy, x-ray emission spectroscopy, and resonant inelastic soft x-ray scattering. Together, these measurements have been used to derive the experimental site-resolved ($k$-integrated) band structure of a material whose electronic structure is difficult to obtain from first principles. The occupied states, probed by x-ray emission measurements, demonstrate the O 2$p$–V 3$d$ bonding hybridization at the bottom of the O 2$p$ band, with the V 3$d_{xy}$ “magnetic orbitals” well separated in energy. These results are consistent with the carriers being small polarons. The strong anisotropy in the absorption spectrum is used to identify the energy and character of the unoccupied states. Additionally, absorption measurements at the V $L$-edge are compared with atomic multiplet calculations, clarifying the interpretation of the experimental multiplet structure and consistent with the presence of both V${}^{5+}$ and V${}^{4+}$ species. Site-specific electronic excitations, probed by resonant inelastic x-ray scattering at the V $L$-edge, are observed at an energy of 1.1 eV, and are suggested to correspond to transitions from the partially filled $d_{xy}$ magnetic orbital into the unoccupied $d_{xy,yz}$ orbitals.

Figure 1

The crystal structure of β-Sr${}_{0.17}$V${}_2$O${}_5$ projected along the $b$ crystallographic axis, showing the orientation of the VO${}_5$ square pyramids. At the bottom, the orientation of each of the V1O${}_5$, V2O${}_5$, and V3O${}_5$ pyramids are shown with the vanadyl bond (V-O${}_{\mathrm{ap}}$) aligned with the paper vertical, representing their local quantification axes ($x$, y, and $z$). The Sr positions are partially occupied.

Figure 2

(a) V $L_{3,2}$-edge XAS spectra of β-Sr${}_{0.17}$V${}_2$O${}_5$ recorded in TEY (solid lines) and TFY (open symbols) modes. To illustrate the isotropy at this edge, the TFY data is shown for light incident parallel to both the $a$- and $b$-axes. The first derivative of the TEY data is shown at the bottom of the figure for $E$∥$a$; the arrows indicate features associated with local minima. (b) V $L_{3,2}$-edge atomic multiplet calculations for V${}^{5+}$ and V${}^{4+}$ in a tetragonal ($D_{4h}$) distortion to octahedral symmetry (the parameters of the calculation are 10$\mathrm{Dq}$ $=$ 2.1 eV, $D_t$ $=$ $D_s$ $=$ 0.1 eV) using the CTM4XAS program.[33] These spectra have been shifted by −1.4 eV to align with the measured $L_3$-edge. The dashed (green) line in (b) shows the linear superposition of the V${}^{5+}$ and V${}^{4+}$ spectra at a ratio of 0.83:0.17 according to the stoichiometry.

Figure 3

V $L_{3,2}$-edge atomic multiplet calculations of V${}^{5+}$ and V${}^{4+}$ in octahedral ($O_h$) and tetragonal ($D_{4h}$) symmetry. (a) The dependence of the calculated spectra of V${}^{5+}$ on the crystal field splitting, 10$\mathrm{Dq}$, in $O_h$ symmetry. Spectra are shown vertically offset for clarity. (b) Dependence of the V${}^{4+}$ spectra on 10$\mathrm{Dq}$. Also shown in thick red is the V${}^{4+}$ spectrum in $D_{4h}$ symmetry for $D_t$ $=$ $D_s$ $=$ 0.1 eV. (c) The dependence of V${}^{5+}$ spectra on $D_s$ and $D_t$ ($D_{4h}$ symmetry). (d) The effect of reducing the magnitude of the Slater integral in $O_h$ symmetry for V${}^{5+}$.

Figure 4

Polarization dependence of O $K$-edge XAS spectra, recorded in both TEY (solid lines) and TFY (circles) modes.

Figure 5

Polarization-dependent above-threshold O $K$-edge XES spectra of β-Sr${}_{0.17}$V${}_2$O${}_5$ recorded with the sample at room temperature, alongside RXES spectra recorded with a photon energy of 529.7 eV (the arrow indicates the location of elastically scattered x-rays). The solid line is a guide to the eye and represents a binomial smoothing of the raw XES data. Also shown are the O $K$-edge TEY XAS spectra from Fig. 3. For comparison, the leading edge of the TFY data is also displayed by the empty circles. Note that the XAS spectra have been offset by +1 eV with respect to Fig. 3 to account for the core-hole shift (see text).

Figure 6

V $L_3$-edge RIXS spectra for (a), and (b) $E$∥$a$, and (c) $E$∥$b$ recorded at the incident photon energies shown on the V $L_3$-edge XAS spectrum in the inset to (a). The data are shown on an absolute energy scale in (a), and on a loss energy scale in (b) and (c). The regions marked A and B represent the occupied V 3$d$ states and their hybridization with the O 2$p$ states, respectively. The gray regions in (b) and (c) show the elastically scattered light, and the dotted line at −1.1 eV demonstrates the $dd$${}^{*}$ excitation feature. In (b) the dotted lines correspond to the data with the elastic peak and V 3$d$ fluorescent contribution removed (see text), demonstrating the presence of the −1.1 eV RIXS peak at other photon energies.

Figure 7

Schematic energy level diagram for β-Sr${}_{0.17}$V${}_2$O${}_5$ based on the experimental results. The locations of the occupied states are estimated from the onset of the XES and RIXS spectra. Similarly, the unoccupied states are derived from the O $K$-edge XAS spectra; the black solid lines represent the peak positions within the approximate bandwidth of the state. Also shown is the $dd$${}^{*}$ excitation revealed by RIXS measurements.