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The critical properties of the single-crystalline van der Waals bondedferromagnet Fe$_{3-x}$GeTe$_2$ were investigated by bulk dc magnetizationaround the paramagnetic (PM) to ferromagnetic (FM) phase transition. TheFe$_{3-x}$GeTe$_2$ single crystals grown by self-flux method with Fe deficiency$x \approx 0.36$ exhibit bulk FM ordering below $T_c = 152$ K. TheM\"{o}ssbauer spectroscopy was used to provide information on defects and localatomic environment in such crystals. Critical exponents $\beta = 0.372(4)$ witha critical temperature $T_c = 151.25(5)$ K and $\gamma = 1.265(15)$ with $T_c =151.17(12)$ K are obtained by the Kouvel-Fisher method whereas $\delta =4.50(1)$ is obtained by a critical isotherm analysis at $T_c = 151$ K. Thesecritical exponents obey the Widom scaling relation $\delta = 1+\gamma/\beta$,indicating self-consistency of the obtained values. With these criticalexponents the isotherm $M(H)$ curves below and above the critical temperaturescollapse into two independent universal branches, obeying the single scalingequation $m = f_\pm(h)$, where $m$ and $h$ are renormalized magnetization andfield, respectively. The exponents determined in this study are close to thosecalculated from the results of the renormalization group approach for aheuristic model of three-dimensional Heisenberg ($d = 3, n = 3$) spins coupledwith the attractive long-range interactions between spins that decay as$J(r)\approx r^{-(3+\sigma)}$ with $\sigma=1.89$.

Critical behavior of the van der Waals bonded ferromagnet Fe$_{3-x}$GeTe$_2$