Prediction of topological phases in metastable ferromagnetic MPX$_3$ monolayers

Density functional theory calculations are carried out to study the electronic and topological properties of $M$P$X_3$ ($M$ = Mn, Fe, Co, Ni, and $X$ = S, Se) monolayers in the ferromagnetic (FM) metastable magnetic state. We find that FM MnPSe$_3$ monolayers host topological semimetal signatures that are gapped out when spin-orbit coupling (SOC) is included. These findings are supported by explicit calculations of the Berry curvature and the Chern number. The choice of the Hubbard-$U$ parameter to describe the $d$-electrons is thoroughly discussed, as well as the influence of using a hybrid-functional approach. The presence of band inversions and the associated topological features are found to be formalism-dependent. Nevertheless, routes to achieve the topological phase via the application of external biaxial strain are demonstrated. Within the hybrid-functional picture, topological band structures are recovered under a pressure of 15% (17 GPa). The present work provides a potential avenue for uncovering new topological phases in metastable ferromagnetic phases.