$c$-Axis Dimer and Its Electronic Breakup: The Insulator-to-Metal Transition in ${\mathrm{Ti}}_2{\mathrm{O}}_3$

We report on our investigation of the electronic structure of ${\mathrm{Ti}}_2{\mathrm{O}}_3$ using (hard) x-ray photoelectron and soft x-ray absorption spectroscopy. From the distinct satellite structures in the spectra, we have been able to establish unambiguously that the Ti-Ti $c$-axis dimer in the corundum crystal structure is electronically present and forms an $a_{1g}{a}_{1g}$ molecular singlet in the low-temperature insulating phase. Upon heating, we observe a considerable spectral weight transfer to lower energies with orbital reconstruction. The insulator-metal transition may be viewed as a transition from a solid of isolated Ti-Ti molecules into a solid of electronically partially broken dimers, where the Ti ions acquire additional hopping in the $a\text{−}b$ plane via the $e_g^{\pi }$ channel, the opening of which requires consideration of the multiplet structure of the on-site Coulomb interaction.

Popular Summary

As a transition metal oxide heats up, it can suddenly change from an insulator to a conductor. This fascinating phenomenon is accompanied by changes in the crystal structure and, often, also in the magnetic structure. Band-structure calculations, the standard theory for describing the electronic structure of solid-state materials, fail to describe this behavior. In particular, band theory has great difficulties explaining how these materials become insulators at low temperature. It is clear that interactions among electrons must be taken into account; however, these types of problems that involve many interacting particles can quickly become unsolvable. It is therefore important in these calculations to have good starting points and smart approximations. We have experimentally identified the key elements of the electronic structure of such a system so that a valid and accurate theoretical model can be constructed.

We used x-ray spectroscopies to study the electronic structure of the transition metal oxide ${\mathrm{Ti}}_2{\mathrm{O}}_3$. From distinct features in our spectra, we found that the insulating phase can be viewed as a solid consisting of electronically isolated Ti-Ti diatomic molecules (dimers)—contradicting results from band-structure calculations. We also see that as temperature increases, dimers partially break up, which causes the transition toward a metallic state. This is associated with a reconstruction of the electron orbitals that opens up an extra channel for transferring electrons, along with a dramatic decrease in the effective Coulomb interaction.

These experiments reveal an amazing amount of detail about all of the relevant ingredients in a metal-insulator transition. These findings may therefore serve as an important benchmark for future theoretical studies.

Figure 1

Experimental valence-band (VB) XPS spectrum of ${\mathrm{Ti}}_2{\mathrm{O}}_3$ taken at 300 K (black line), together with the Au Fermi cutoff (thin black line) as reference for $E_F$. Also shown is the Ti $3d$ one-electron removal spectrum from the ${\mathrm{TiO}}_6$ (blue line) and the ${\mathrm{Ti}}_2{\mathrm{O}}_9$ (red line) clusters, as described in the text. Inset: Corundum structure of ${\mathrm{Ti}}_2{\mathrm{O}}_3$, with the $c$-axis Ti-Ti dimers marked in red.

Figure 2

Experimental Ti $2p$ core-level photoemission spectra of ${\mathrm{Ti}}_2{\mathrm{O}}_3$ taken at 300 K with $h\nu =1486.6\mathrm{eV}$ (black line, XPS), $h\nu =5931\mathrm{eV}$ (red circle, HAXPES ESRF), and $h\nu \simeq 6500\mathrm{eV}$ (dark-green triangle symbol, HAXPES SPring-8), and experimental Ti $2p$ core-level photoemission spectra of ${\mathrm{YTiO}}_3$ taken at 300 K (navy circle) and of ${\mathrm{LaTiO}}_3$ taken at 200 K (green line) with $h\nu \simeq 6500\mathrm{eV}$ (HAXPES SPring-8). Also shown are the theoretical configuration-interaction calculations using the ${\mathrm{TiO}}_6$ (blue line) and the ${\mathrm{Ti}}_2{\mathrm{O}}_9$ (red line) clusters; see text.

Figure 3

Panel (a): Experimental polarization-dependent Ti-$L_{2,3}$ XAS spectra of ${\mathrm{Ti}}_2{\mathrm{O}}_3$ taken at 150 K, 300 K, 458 K, 500 K, and 575 K. Panel (b): Calculated polarization-dependent Ti-$L_{2,3}$ XAS spectra for the corresponding temperatures using the ${\mathrm{Ti}}_2{\mathrm{O}}_9$ cluster. In the bottom of panels (a) and (b) are the corresponding linear dichroic (LD) spectra. Panel (c): Close-up of the experimental LD spectrum in the low-temperature phase (blue and black circles) and the simulation using the ${\mathrm{TiO}}_6$ (green line: $a_{1g}$) and the ${\mathrm{Ti}}_2{\mathrm{O}}_9$ (red line: $a_{1g}{a}_{1g}$) clusters. Panel (d): Temperature dependence of the Ti $2p$ core-level spectrum and the simulations using the ${\mathrm{Ti}}_2{\mathrm{O}}_9$ cluster.

Figure 4

Left panel: Close-up of the temperature dependence of the valence-band spectra of ${\mathrm{Ti}}_2{\mathrm{O}}_3$ taken with $h\nu \simeq 6.5\mathrm{keV}$ (HAXPES SPring-8), together with the Au Fermi cutoff as $E_F$ reference. Right panel: Close-up of the temperature dependence of the O $K$-edge XAS spectra of ${\mathrm{Ti}}_2{\mathrm{O}}_3$.

Figure 5

Temperature-dependent resistivity of ${\mathrm{Ti}}_2{\mathrm{O}}_3$ from 10 K to 575 K, showing the insulator-to-metal transition.

Figure 6

Total-energy-level diagram for the photoemission process in a hydrogen molecule model. The two accessible final states $|{\mathrm{FS}}^{+}⟩$ and $|{\mathrm{FS}}^{-}⟩$ yield two lines in the spectrum of intensities $I^{+}$ and $I^{-}$, respectively, according to the initial-state coefficients $\alpha$ and $\beta$. The corresponding spectrum is indicated on the right.

Figure 7

Calculated valence-band photoemission spectra of ${\mathrm{Ti}}_2{\mathrm{O}}_3$ using the ${\mathrm{Ti}}_2{\mathrm{O}}_9$ cluster for several values of the inter-Ti hopping $dd\sigma$.