Phonon, infrared, and Raman spectra of LiGa5O8 from density functional perturbation theory

${\mathrm{LiGa}}_{5}{\mathrm{O}}_{8}$ with a cubic spinel-type structure was recently reported to be an ultrawide-band-gap semiconductor with unintentional $p$-type conduction. While the origin of $p$-type doping is still unclear, the fundamental properties of this material are of interest. Here, we present a first-principles study of the phonons using density functional perturbation theory. The phonon band structures show no unstable modes, verifying the stability of the structure. We focus mainly on the phonons at the Brillouin zone center for which a full symmetry analysis is presented. We present the dielectric function contributions from the infrared active modes as well as the Raman spectra and their polarization dependence. The phonon density of states integrated over the Brillouin zone is also presented as this may be related to disordered Raman spectra.