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Electronic correlation can strongly influence the electronic properties oftwo-dimensional (2D) materials with open d- or f-orbitals. Herein, by takingsingle-layer (SL) H-FeBr$_2$ as a representative of the SL H-FeX$_2$ (X=Cl, Br,I) family, we investigated the electronic correlation effects in the magneticanisotropy and electronic topology of such a system based on first-principlescalculations with DFT+\textit{U} approach. Our result is that the magneticanisotropy energy (MAE) of SL H-FeBr$_2$ shows a non-monotonic evolutionbehaviour with increasing electronic correlation strength, which is mainly dueto the competition between different element-resolved MAEs of Fe and Br.Further investigations show that the evolution of element-resolved MAE arisesfrom the variation of the spin-orbital coupling (SOC) interaction betweendifferent orbitals in each atom. Moreover, tuning the strength of theelectronic correlation can drive the occurrence of band inversions, causing thesystem to undergoes multiple topological phase transitions, resulting in aquantum anomalous valley Hall (QAVH) effect. These exotic properties areuniversal for the SL H-FeX$_2$ (X = Cl, Br, I) family. Our work sheds light onthe role of electronic correlation effects in tuning magnetic and electronicstructures in the SL H-FeX$_2$ (X = Cl, Br, I) family, which could guideadvances in the development of new spintronics and valleytronics devices basedon these materials.

Tuning the magnetic anisotropy and topological phase with electronic correlation in single-layer H-FeBr$_2$