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The Co$_2$Ge$_2$Te$_6$ shows intrinsic ferromagnetic (FM) order, whichorigins from superexchange interaction between Co and Te atoms, with higherCurie temperature ($T_c$) of 161 K. Co$_2$Ge$_2$Te$_6$ monolayer (ML) ishalf-metal (HM), and spin-$\beta$ electron is a semiconductor with gap of 1.311eV. Co$_2$Ge$_2$Te$_6$ ML tends in-plane anisotropy (IPA), with magneticanisotropy energy (MAE) of -10.2 meV/f.u.. Co$_2$Ge$_2$Te$_6$ ML shows gooddynamical and thermal stability. Most interestingly, bilayers presentferromagnetic half-metallicity independent of the stacking orders. Notley, themultilayers ($N\ge 6$) present ferromagnetic HM, while the magnetoelectronicproperties are related with the stacking patterns in thinner multilayers.Moreover, the magnetoelectronic properties are dependent on the stacking ordersof bulk. The magnetic order with multilayers is determined by the super-superexchange and weak van der Waals (vdW) interaction. Co$_2$Ge$_2$Te$_6$ withintrinsic ferromagnetism, good stability of ferromagnetism and half-metallicitycould help researchers to investigate its wide application in the spintronics.

Prediction of High Curie Temperature, Large Magnetic Crystal Anisotropy in 2D Ferromagnetic Co$_2$Ge$_2$Te$_6$ Monolayer and Multilayer