Controlling topology through targeted composite symmetry manipulation in magnetic systems

The possibility of selecting magnetic space groups by orienting the magnetization direction or tuning magnetic orders offers a vast playground for engineering symmetry-protected topological phases in magnetic materials. In this work, we study how selective tuning of symmetry and magnetism can influence and control the resulting topology in a two-dimensional magnetic system, and we illustrate such a procedure in the ferromagnetic monolayer ${\mathrm{MnPSe}}_{3}$. Density functional theory calculations reveal a symmetry-protected accidental semimetallic (SM) phase for out-of-plane magnetization, which becomes an insulator when the magnetization is tilted in-plane, reaching band-gap values close to 100 meV. We identify an order-2 composite antiunitary symmetry and threefold rotational symmetry that induce the band crossing, and we classify the possible topological phases using symmetry analysis, which we support with tight-binding and $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ models. Breaking of inversion symmetry opens a gap in the SM phase, giving rise to a Chern insulator. We demonstrate this explicitly in the isostructural Janus compound ${\mathrm{Mn}}_{2}{\mathrm{P}}_{2}{\mathrm{S}}_{3}{\mathrm{Se}}_{3}$, which naturally exhibits Rashba spin-orbit coupling that breaks inversion symmetry. Our results map out the phase space of topological properties of ferromagnetic transition-metal phosphorus trichalcogenides, and they demonstrate the potential of the magnetization-dependent metal-to-insulator transition as a spin switch in integrated two-dimensional electronics.