Measurement of collective excitations in ${\text{VO}}_2$ by resonant inelastic x-ray scattering

Vanadium dioxide is of broad interest as a spin-$\frac{1}{2}$ electron system that realizes a metal-insulator transition near room temperature, due to a combination of strongly correlated and itinerant electron physics. Here, resonant inelastic x-ray scattering is used to measure the excitation spectrum of charge and spin degrees of freedom at the vanadium $L$ edge under different polarization and temperature conditions, revealing excitations that differ greatly from those seen in optical measurements. These spectra encode the evolution of short-range energetics across the metal-insulator transition, including the low-temperature appearance of a strong candidate for the singlet-triplet excitation of a vanadium dimer.

Figure 1

Orbital symmetries of ${\mathrm{VO}}_2$ electronic states: (a) Orbital symmetries of electronic states are labeled for (left) the high-temperature metallic state and (right) the low-temperature insulating state, with the Fermi level indicated by a dashed line. The labels $d_{\parallel }^{b*}$ and $d_{\parallel }^a$ indicate gapped $d_{\parallel }$-symmetry states expected in the $M1$ phase. (b) Schematics show anticipated RIXS excitations that could be achieved by changing the symmetry of a $d_{\parallel }$ electron. Scenarios are presented for (left) the rutile metal and for hypothetical $M1$ insulating states based on (middle) strongly correlated singlets and (right) itinerant Peierls band physics.

Figure 2

XAS and RIXS across the metal-insulator transition: (a) Experimental (top) and theoretical (bottom) XAS spectra of $M1$ phase ${\mathrm{VO}}_2$ are shown for two incident photon polarization conditions. (b) The $M1$ phase $\mathbf{E}\parallel {\mathbf{c}}_R$ incident energy dependence of highlighted energy loss windows in (c) (top) is compared with simulations for the $d_{\parallel }^t, {\pi }^{*}$, and ${\sigma }^{*}$ excitations (bottom). Statistical error bars are slightly smaller than the plotted circles, and simulation curves are weighted to match the integration windows, as described in the SM [20]. (c) RIXS spectra in the insulating and metallic states at temperatures $T=260$ and 320 K, respectively. The two $\mathbf{E}\parallel {\mathbf{c}}_R$ curves are upward offset by 100 counts.

Figure 3

Simulated RIXS spectra of a vanadium dimer: The RIXS scattering profile is simulated for $\mathbf{E}\parallel {\mathbf{c}}_R$ polarized incident photons in the high-symmetry (a) $Q=0$ and (b) $Q=\pi$ sectors, and (c) for a superposition given by the experimental value of $Q=0.26\pi$. (d)–(f) show corresponding spectra obtained with $\mathbf{E}\perp {\mathbf{c}}_R$ polarization. Features are plotted with an artificially narrow ${\mathrm{\Gamma }}_f=0.1\mathrm{eV}$ width for visual clarity.

Figure 4

Polarization dependence and feature attribution: Four-Lorentzian fits of the experimental data measured with incident polarization (a) parallel and (b) perpendicular to the $c_R$ axis. The band gap of bulk ${\mathrm{VO}}_2$ is shaded in to highlight likely in-gap states. Three low-energy features nominally represent the singlet-triplet mode ($d_{\parallel }^t$ at $E_t=0.46\mathrm{eV}$, width $\mathrm{\Gamma }=0.43\mathrm{eV}$), and $dd$ excitations into nonbonding ${\pi }^{*}$ ($t_{2g}$) orbitals ($E=0.72$ eV, $\mathrm{\Gamma }=1.5\mathrm{eV}$) and ${\sigma }^{*}$ ($e_g$) orbitals ($E=2.33$ eV, $\mathrm{\Gamma }=1.5\mathrm{eV}$). The broad feature at $E=7.2$ eV is attributed to metal-ligand charge transfer excitations ($E=7.2$ eV, $\mathrm{\Gamma }=5.25\mathrm{eV}$). The singlet-triplet excitation constitutes 23% weight of the combined $d_{\parallel }^t/{\pi }^{*}$ feature when polarization is parallel to the $c_R$ axis, and just 8% under orthogonal polarization.