  Recently, two-dimensional ferromagnetic semiconductors have been an important
class of materials for many potential applications in spintronic devices. Based
on density functional theory, we systematically explore the magnetic and
electronic properties of CrGeS$_3$ with the monolayer structures. The
comparison of total energy between different magnetic states ensures the
ferromagnetic ground state of monolayer CrGeS$_3$. It is also shown that
ferromagnetic and semiconducting properties are exhibited in monolayer
CrGeS$_3$ with the magnetic moment of 3 $\mu_{B}$ for each Cr atom, donated
mainly by the intense $dp$$\sigma$-hybridization of Cr $e_g$-S $p$. There are
the bandgap of 0.70 eV of spin-up state in the monolayer structure when 0.77 eV
in spin-down state. The global gap is 0.34 eV (2.21 eV by using HSE06
functional), which originates from bonding $dp\sigma$ hybridized states of Cr
$e_g$-S $p$ and unoccupied Cr $t_{2g}$-Ge $p$ hybridization. Besides, we
estimate that the monolayer CrGeS$_3$ possesses the Curie temperature of 161 K
by mean-field theory.
