  We investigate the vibrational properties and Raman spectra of
two-dimensional Ga$_2$O$_3$ monolayer, using density functional theory. Two
ferroelectric (FE) phases of Ga$_2$O$_3$ monolayer with wurtzite(WZ) and
zincblende(ZB) structures( FE-WZ and FE-ZB, respectively ) are considered. The
Raman tensor and angle-dependent Raman intensities of two major Raman peak
($A^1_1$ and $A^2_1$) in both FE-WZ (497, and 779 cm$^{-1}$) and FE-ZB (481,
and 772 cm$^{-1}$) Ga$_2$O$_3$ monolayers are calculated for the polarizations
of scattered light parallel and perpendicular to that of the incident light.
The characteristics of angle-dependent Raman intensities are analyzed. The
averaged non-resonant Raman spectra of minor peaks in FE-WZ($E^1$) and
FE-BZ($E^1$ and $E^2$) are compared with that of major peaks $A^1_1$ and
$A^2_1$ . These predictions on Raman spectra of Ga$_2$O$_3$ monolayer may guide
rational design of two-dimensional optical devices.
