Abstract
By density functional theory calculations, we predict a stable two-dimensional (2D) ferromagnetic semiconductor Cr$_2$Ge$_2$Se$_6$, where the Curie temperature $T$$_c$ can be dramatically enhanced beyond room temperature by applying a few percent strain. In addition, the anomalous Hall conductivity in 2D Cr$_2$Ge$_2$Se$_6$ and Cr$_2$Ge$_2$Te$_6$ is predicted to be comparable to that in ferromagnetic metals of Fe and Ni, and is an order of magnitude larger than that in diluted magnetic semiconductor Ga(Mn,As). Based on superexchange interactions, the enhanced $T$$_c$ in 2D Cr$_2$Ge$_2$Se$_6$ by strain can be understood by the decreased energy difference between 3$d$ orbitals of Cr and 4$p$ orbitals of Se. Our finding highlights the microscopic mechanism to obtain the room temperature ferromagnetic semiconductors by strain.
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