Critical behavior of quasi-two-dimensional semiconducting ferromagnet CrGeTe${}_3$

Abstract

The critical properties of the single-crystalline semiconducting ferromagnet CrGeTe${}_3$ were investigated by bulk dc magnetization around the paramagnetic to ferromagnetic phase transition. Critical exponents $\beta =0.200\pm 0.003$ with critical temperature $T_c=62.65\pm 0.07$ K and $\gamma =1.28\pm 0.03$ with $T_c=62.75\pm 0.06$ K are obtained by the Kouvel-Fisher method whereas $\delta =7.96\pm 0.01$ is obtained by the critical isotherm analysis at $T_c=62.7$ K. These critical exponents obey the Widom 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 $m=f_{\pm }(h)$, where $m$ and $h$ are renormalized magnetization and field, respectively. The determined exponents match well with those calculated from the results of renormalization group approach for a two-dimensional Ising system coupled with long-range interaction between spins decaying as $J(r)\approx r^{-(d+\sigma )}$ with $\sigma =1.52$.

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