  The van der Waals ferromagnet Cr$_2$Ge$_2$Te$_6$ (CGT) has a two-dimensional
crystal structure where each layer is stacked through van der Waals force. We
have investigated the nature of the ferromagnetism and the weak perpendicular
magnetic anisotropy (PMA) of CGT by means of X-ray absorption spectroscopy and
X-ray magnetic circular dichroism (XMCD) studies of CGT single crystals. The
XMCD spectra at the Cr $L_{2,3}$ edge for different magnetic field directions
were analyzed on the basis of the cluster-model multiplet calculation. The Cr
valence is confirmed to be 3+ and the orbital magnetic moment is found to be
nearly quenched, as expected for the high-spin $t_{2g}$$^3$ configuration of
the Cr$^{3+}$ ion. A large ($\sim 0.2$ eV) trigonal crystal-field splitting of
the $t_{2g}$ level caused by the distortion of the CrTe$_6$ octahedron has been
revealed, while the single-ion anisotropy (SIA) of the Cr atom is found to have
a sign {\it opposite} to the observed PMA and too weak compared to the reported
anisotropy energy. The present result suggests that anisotropic exchange
coupling between the Cr atoms through the ligand Te $5p$ orbitals having strong
spin-orbit coupling has to be invoked to explain the weak PMA of CGT, as in the
case of the strong PMA of CrI$_3$.
