  The first two-dimensional (2D) polymorphs of antimony dioxide, namely,
$\gamma$-Sb$_2$O$_4$ and $\delta$-Sb$_2$O$_4$, are predicted using the
evolutionary algorithm combined with first-principles density functional theory
(DFT) calculations. Out-of-plane ferroelectricity is found in
$\gamma$-Sb$_2$O$_4$, while in-plane ferroelectricity is found in
$\delta$-Sb$_2$O$_4$. The predicted dipole moments of $\gamma$-Sb$_2$O$_4$ and
$\delta$-Sb$_2$O$_4$ phases are 36.63 and 14.96 e\r{A}, respectively, implying
that they can be good candidates for making ferroelectric devices. The
calculations show that doping with other group V elements or applying strain
can lower the switching energy barriers and thus facilitate switching. Results
from GW calculations show indirect band gaps of 5.51 and 3.39 eV for
$\gamma$-Sb$_2$O$_4$ and $\delta$-Sb$_2$O$_4$ in their monolayers,
respectively. Raman spectra are calculated to facilitate the experimental
investigation of the predicted structures. The existence of both in-plane and
out-of-plane 2D ferroelectricity and the large band gaps make this material
system particularly interesting for potential applications.
