Critical behavior of quasi-two-dimensional semiconducting ferromagnet Cr2Ge2Te6

The critical properties of the single-crystalline semiconducting ferromagnet Cr2Ge2Te6 were investigated by bulk dc magnetization around the paramagnetic to ferromagnetic phase transition. Critical exponents beta = 0.200 +/- 0.003 with a critical temperature T-c = 62.65 +/- 0.07 K and gamma=1.28 +/- 0.03 with T-c = 62.75 +/- 0.06 K are obtained by the Kouvel-Fisher method whereas delta = 7.96 +/- 0.01 is obtained by a critical isotherm analysis at T-c = 62.7 K. These critical exponents obey theWidom scaling relation delta = 1 +gamma/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 +/-(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) approximate to r(-(d+sigma)) with sigma = 1.52.