Prediction of topological phases in metastable ferromagnetic MPX3 monolayers

Density functional theory calculations are carried out to study the electronic and topological properties of $M\mathrm{P}{X}_{3}$ $(M=\mathrm{Mn},\mathrm{Fe},\mathrm{Co},\mathrm{Ni}; X=\mathrm{S},\mathrm{Se})$ monolayers in the ferromagnetic (FM) metastable magnetic state. We find that FM ${\mathrm{MnPSe}}_{3}$ monolayers host topological semimetal signatures that are gapped out when spin-orbit coupling 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.