Generic Approach to Intrinsic Magnetic Second-order Topological Insulators via Inverted $p-d$ Orbitals

The integration of intrinsically magnetic and topologically nontrivial two-dimensional materials holds tantalizing prospects for the exotic quantum anomalous Hall insulators and magnetic second-order topological insulators (SOTIs). Compared with the well-studied nonmagnetic counterparts, the pursuit of intrinsic magnetic SOTIs remains limited. In this work, we address this gap by focusing on $p-d$ orbitals inversion, a fundamental but often overlooked phenomena in the construction of topological materials. We begin by developing a theoretical framework to elucidate $p-d$ orbitals inversion through a combined density-functional theory calculation and Wannier downfolding. Subsequently we showcase the generality of this concept in realizing ferromagnetism SOTIs by identifying two real materials with distinct lattices: 1$T$-VS$_2$ in a hexagonal lattice, and CrAs monolayer in a square lattice. We further compare it with other mechanisms requiring spin-orbit coupling and explore the similarities to topological Kondo insulators. Our findings establish a generic pathway towards intrinsic magnetic SOTIs.