Magnetic high-order topological insulator in 2D layered CrOCl

High-order topological insulators (HOTIs) have garnered significant interest in recent years due to their unique properties, but their material realization has thus far been limited to those protected by Cn (n = 3,4,6) rotation symmetry and to nonmagnetic crystals. In this study, we propose a HOTI in a recently synthesized two-dimensional (2D) magnetic material, CrOCl. Our findings reveal that the material's ground state, which has ferromagnetic ordering, features corner states carrying a quantized fractional charge. These states are enabled by a twofold rotation symmetry (C2z) and are robust against spin-orbital coupling (SOC). The corner states in CrOCl are distinct from those in nonmagnetic examples and even in magnetic examples, as they can achieve 100% spin polarization in the presence or absence of SOC. Remarkably, the corner states in CrOCl are also robust against layer stacking, symmetry breaking, and even magnetization. Furthermore, under a vertical electric field, the material undergoes a phase transition from HOTI to "hidden high-order topological insulator" phase, with the corner states submerged into edge or bulk states. Our study not only highlights the HOTI properties of 2D CrOCl, but also promotes it as a concrete material platform for exploring the intriguing physics of magnetic HOTIs. We also discuss possible experimental detections and applications of this material, which may pave the way for new advancements in materials sciences and condensed-matter physics.