  We perform systematic first-principles calculations to investigate the
spin-phonon coupling (SPC) of Cr2Ge2Te6 (CGT) monolayer (ML). It is found that
the Eg phonon mode at 211.8 cm^{-1} may have a SPC as large as 3.19 cm^{-1}, as
it directly alters the superexchange interaction along the Cr-Te-Cr pathway.
Furthermore, the strength of SPC of the CGT ML can be further enhanced by an
in-plane compressive strain. These results provide useful insights for the
understanding of SPC in novel two-dimensional magnetic semiconductors and may
guide the design of spintronic and spin Seebeck materials and devices.
