First-principles studies of spin-phonon coupling in monolayer Cr2Ge2Te6

We perform systematic first-principles calculations to investigate the spin-phonon coupling (SPC) of $\mathrm{C}{\mathrm{r}}_{2}\mathrm{G}{\mathrm{e}}_{2}\mathrm{T}{\mathrm{e}}_{6}$ (CGT) monolayer (ML). It is found that the ${E}_{\mathrm{g}}$ phonon mode at $211.8\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}1}$ may have a SPC as large as $3.19\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}1}$, as it alters the direct exchange interaction across Cr-Cr pairs. The strength of SPC of the CGT ML can be decreased by an in-plane lattice stretch. These results provide useful insights for the understanding of SPC in two-dimensional magnetic semiconductors and may guide the design of spintronic and spin Seebeck materials and devices.