LAUSR

The critical properties of the single-crystalline semiconducting ferromagnet ${\mathrm{Cr}}_{2}{\mathrm{Ge}}_{2}{\mathrm{Te}}_{6}$ were investigated by bulk dc magnetization around the paramagnetic to ferromagnetic phase transition. Critical exponents $\ensuremath{\beta}=0.200\ifmmode\pm\else\textpm\fi{}0.003$ with a critical temperature ${T}_{c}=62.65\ifmmode\pm\else\textpm\fi{}0.07$ K and $\ensuremath{\gamma}=1.28\ifmmode\pm\else\textpm\fi{}0.03$ with ${T}_{c}=62.75\ifmmode\pm\else\textpm\fi{}0.06$ K are obtained by the Kouvel-Fisher method whereas $\ensuremath{\delta}=7.96\ifmmode\pm\else\textpm\fi{}0.01$ is obtained by a critical isotherm analysis at ${T}_{c}=62.7$ K. These critical exponents obey the Widom scaling relation $\ensuremath{\delta}=1+\ensuremath{\gamma}/\ensuremath{\beta}$, indicating self-consistency of the obtained values. With these critical exponents the isotherm $M(H)$ curves below and above the critical temperatures collapse into two independent universal branches, obeying the single scaling equation $m={f}_{\ifmmode\pm\else\textpm\fi{}}(h)$, where $m$ and $h$ are renormalized magnetization and field, respectively. The determined exponents match well with those calculated from the results of the renormalization group approach for a two-dimensional Ising system coupled with a long-range interaction between spins decaying as $J(r)\ensuremath{\approx}{r}^{\ensuremath{-}(d+\ensuremath{\sigma})}$ with $\ensuremath{\sigma}=1.52$.