Critical behavior in the Mn$_{5}$Ge$_{3}$ ferromagnet

High-Curie-temperature ferromagnets are promising candidates for designing new spintronic devices. Here we have successfully synthesized a single-crystal sample of the itinerant ferromagnet Mn$_{5}$Ge$_{3}$ used flux method and its critical properties were investigated by means of bulk dc-magnetization at the boundary between the ferromagnetic (FM) and paramagnetic (PM) phase. Critical exponents $\beta=0.336 \pm 0.001$ with a critical temperature $T_{c}=300.29 \pm 0.01$ K and $\gamma=1.193 \pm 0.003$ with $T_{c} = 300.15 \pm 0.05$ K are obtained by the modified Arrott plot, whereas $\delta = 4.61 \pm 0.03$ is deduced by a critical isotherm analysis at $T_{c} = 300$ K. The self-consistency and reliability of these critical exponents are verified by the Widom scaling law and the scaling equations. Further analysis reveals that the spin coupling in Mn$_{5}$Ge$_{3}$ exhibits three-dimensional Ising-like behavior. The magnetic exchange is found to decay as $J(r)\approx r^{-4.855}$ and the spin interactions are extended beyond the nearest neighbors, which may be related to different set of Mn--Mn interactions with unequal magnitude of exchange strengths. Additionally, the existence of noncollinear spin configurations in Mn$_{5}$Ge$_{3}$ results in a small deviation of obtained critical exponents from those for standard 3D-Ising model.