Optical properties of ${\mathrm{V}}_2{\mathrm{O}}_3$ in its whole phase diagram

Vanadium sesquioxide ${\mathrm{V}}_2{\mathrm{O}}_3$ is considered a textbook example of Mott-Hubbard physics. In this paper, we present an extended optical study of its whole temperature/doping phase diagram as obtained by doping the pure material with $M=\text{Cr}$ or Ti atoms $\left({\mathrm{V}}_{1-x}{M}_x\right){}_2{\mathrm{O}}_3$. We reveal that its thermodynamically stable metallic and insulating phases, although macroscopically equivalent, show very different low-energy electrodynamics. The Cr and Ti doping drastically change both the antiferromagnetic gap and the paramagnetic metallic properties. A slight chromium content induces a mesoscopic electronic phase separation, while the pure compound is characterized by short-lived quasiparticles at high temperature. This study thus provides a new comprehensive scenario of the Mott-Hubbard physics in the prototype compound ${\mathrm{V}}_2{\mathrm{O}}_3$.

Figure 1

Temperature vs doping phase diagram of ${\mathrm{V}}_2{\mathrm{O}}_3$ according to Ref. [14]. In the paramagnetic metallic (PM) and paramagnetic insulating (PI) phases, the compound has a corundum crystal structure, whereas the low-temperature antiferromagnetic insulating (AFI) phase shows a monoclinic symmetry (crystal structures have been adapted from Ref. [16]). Empty diamonds stand for temperature and doping values investigated in the present work.

Figure 2

The near-normal incidence reflectance of four differently doped samples of ${\mathrm{V}}_2{\mathrm{O}}_3$ is reported on the left column at selected temperatures from far-infrared to visible frequencies. Right column shows the corresponding optical conductivities as obtained by Kramers-Kronig transformations on the same frequency scale and at the same temperatures of $R(\omega )$. Solid diamonds stand for ${\sigma }_{\mathrm{dc}}$ values in the PM phase.

Figure 3

(Top) The real part of the optical conductivity in the PM phase at 300 K (red line) and 200 K (green line) is shown for ${\mathrm{V}}_2{\mathrm{O}}_3$ and $\left({\mathrm{V}}_{0.955}{\mathrm{Ti}}_{0.045}\right){}_2{\mathrm{O}}_3$, respectively. A Drude-Lorentz fit (empty circles) is also shown for $T=200$ K along with the different spectral components (dashed lines): a Drude term, a MIR band, and the high-frequency Hubbard transitions. (Bottom) Comparison of the optical conductivities of pure ${\mathrm{V}}_2{\mathrm{O}}_3$ and of the 1.1% chromium doped sample in their PM metallic phase at $T=220$ K. The poor metallic behavior of the Cr-doped system is due to an electronic phase separation in a large temperature range across the Mott-Hubbard transition [38], which can be described in terms of an effective medium approximation EMA (see text). Solid diamonds stand for ${\sigma }_{\mathrm{dc}}$ values.

Figure 4

(a) and (b) Scanning photoemission microscopy images and photoemission spectra on $\left({\mathrm{V}}_{0.989}{\mathrm{Cr}}_{0.011}\right){}_2{\mathrm{O}}_3$, collected at 27 eV photon energy and at different temperatures on a 50 $\mu \text{m}$ by 50 $\mu \text{m}$ sample area. The pictorial contrast between metallic (yellow) and insulating (blue) zones is obtained from the photoemission intensity at the Fermi level [42], normalized by the intensity on the V $3d$ band (binding energy $-1.2$ eV). Inhomogeneous properties are found within the PM phase at $T=220$ K, while at 320 K in the PI phase a homogeneous insulating state is obtained. (c) and (d) Histogram of the intensity distribution of the PM (PI) photoemission map (open symbols) as extracted from the map at 220 (320) K.

Figure 5

(a) Spectral weight of pure ${\mathrm{V}}_2{\mathrm{O}}_3$ integrated up to 8000 ${\mathrm{cm}}^{-1}$ and plotted as a function of $T^2$, showing a linear behavior. The optical conductivity from 100 to 550 K is shown in the inset. (b) Correlation diagram between two different ways of estimating the strenght of electron-electron interactions in various materials.

Figure 6

(Top) Optical conductivity of ${\mathrm{V}}_2{\mathrm{O}}_3$ in its antiferromagnetic insulating phase for various dopings. The dashed curve corresponds to a oxygen-vacant crystal (Ref. [22]). (Bottom) A strong reduction of the AFI optical gap can be observed in both Cr and Ti dopings as highlighted by subtracting the pure sample curve from the Cr and Ti data.