Thickness-dependent topological phases in topological magnet Fe₂S₂

Magnetic topological insulators showcase intricate interplay between nontrivial topology and magnetism, providing a fertile ground for exploring various topological quantum phenomena. A recent study reported a ferromagnetic quantum anomalous Hall (QAH) insulator Fe2S2 with huge nontrivial bandgap, but its layer-number-correlated magnetic coupling and topological phases remain unclear. Here, we identify the magnetic coupling and thickness-dependent band topology in Fe2S2 based on first-principles. The results indicate a preferential interlayer antiferromagnetic coupling in the multilayer Fe2S2, giving rise to evident alternating QAH and quantum spin Hall states for odd and even layers, respectively. Moreover, the spin Hall conductivity in even-layer Fe2S2 could be enlarged by increasing the thickness, due to the formation of multiple dissipationless spin transport channels. These findings not only promote the topological magnet Fe2S2 as a potential candidate for diverse topological phase investigations and applications but also provide an avenue to manipulate the quantum states in van der Waals QAH insulators by thickness control.