Second-order topological insulators and tunable topological phase transitions in honeycomb ferromagnets

Intrinsic magnetic topological insulators categorized by bulk-boundary correspondence are of significant fundamental and technological importance in topotronics. Yet the topological phase transition with variation of the bulk-boundary correspondence remains elusive. Here, using a tight-binding model and first-principles calculations, we demonstrate that $2H\text{\ensuremath{-}}M{\mathrm{Br}}_{2}$ $(M=\mathrm{Ru} \text{and} \mathrm{Os})$ monolayers are intrinsic ferromagnetic (FM) second-order topological insulators (SOTIs) distinguished by the emergence of well-localized nontrivial corner states. Remarkably, with giant valley polarization, we point out the possibilities of the two-dimensional FM SOTIs for displaying a rich topological phase diagram; that is, topological phase transitions from FM SOTIs to quantum anomalous Hall insulators and then to normal insulators emerge by engineering the valleys. The obtained quantum anomalous Hall effect is characterized by a nonzero Chern number $\mathcal{C}=\ifmmode\pm\else\textpm\fi{}1$ and one chiral edge state. Our results not only uncover a general framework to tune the bulk-boundary correspondence but also motivate a technological avenue to bridge valleytronics and magnetic topology with potential applications in topotronics and valleytronics.