Electronic and optical properties of $\theta -{\mathrm{Al}}_2{\mathrm{O}}_3$ and comparison to $\alpha -{\mathrm{Al}}_2{\mathrm{O}}_3$

$\theta -{\mathrm{Al}}_2{\mathrm{O}}_3$ is a metastable phase of alumina with local Al coordinations closely related to those in $\gamma -{\mathrm{Al}}_2{\mathrm{O}}_3.$ The electronic structure and the linear optical properties of $\theta -{\mathrm{Al}}_2{\mathrm{O}}_3$ are studied by means of first-principles local density calculations. The results are compared with the stable phase $\alpha -{\mathrm{Al}}_2{\mathrm{O}}_3.$ An indirect band gap of 4.64 eV is obtained, which is about 1.6 eV smaller than that of $\alpha -{\mathrm{Al}}_2{\mathrm{O}}_3.$ The other band structure parameters are found to be quite close, and the calculated density of states (DOS) differ from that of $\alpha -{\mathrm{Al}}_2{\mathrm{O}}_3$ in fine details. Site- and orbital-resolved partial DOS show significant dependence on local coordinations for both Al and O atoms. They are in reasonable agreement with the experimental energy loss near edge spectra of $\gamma -{\mathrm{Al}}_2{\mathrm{O}}_3.$ Effective charge and bond order calculations show $\theta -{\mathrm{Al}}_2{\mathrm{O}}_3$ to be comparable to $\alpha -{\mathrm{Al}}_2{\mathrm{O}}_3.$ For the linear optical properties, a refractive index 1.73 is obtained, which is close to 1.78 for $\alpha -{\mathrm{Al}}_2{\mathrm{O}}_3.$ The bulk plasmon peak in the energy loss function of $\theta -{\mathrm{Al}}_2{\mathrm{O}}_3$ is located at 22.6 eV, which is lower by about 1 eV than that in $\alpha -{\mathrm{Al}}_2{\mathrm{O}}_3.$ The anisotropy in the optical properties of $\alpha -{\mathrm{Al}}_2{\mathrm{O}}_3$ occurs mainly at the low photon energy region of less than 20 eV, and that for the $\theta -{\mathrm{Al}}_2{\mathrm{O}}_3$ is insignificant.