Phase transition of two-dimensional ferroelectric and paraelectric Ga2O3 monolayers: A density functional theory and machine learning study

${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ is a wide-band-gap semiconductor of great interest for applications in electronics and optoelectronics. Two-dimensional (2D) ${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ synthesized from top-down or bottom-up processes can reveal new heterogeneous structures and promising applications. In this paper, we study phase transitions among three low-energy stable ${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ monolayer configurations using density functional theory and a machine learning Gaussian approximation potential, together with solid-state nudged elastic band calculations. Kinetic minimum energy paths involving direct atomic jump as well as concerted layer motion are investigated. The low phase transition barriers indicate feasible tunability of the phase transition and orientation via strain engineering and external electric fields. Large-scale calculations using the trained machine learning potential on the thermally activated single-atom jumps reveal the clear nucleation and growth processes of different domains. The results provide useful insights into future experimental synthesis and characterization of 2D ${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ monolayers.