Critical behavior of the single-crystalline van der Waals bonded ferromagnet Cr2Ge2Te6

Layered ${\mathrm{Cr}}_{2}{\mathrm{Ge}}_{2}{\mathrm{Te}}_{6}$ is a promising two-dimensional (2D) material for van der Waals bonded ferromagnetic devices since its ferromagnetism can be maintained upon exfoliating the bulk down to a few layers. However, the magnetic interaction properties and phase-transition type of this system remain controversial. In this work, we systematically study the magnetic properties and critical behavior of ${\mathrm{Cr}}_{2}{\mathrm{Ge}}_{2}{\mathrm{Te}}_{6}$ single crystal. The angle dependence of magnetization indicates that ${\mathrm{Cr}}_{2}{\mathrm{Ge}}_{2}{\mathrm{Te}}_{6}$ has a weak magnetic anisotropy along the $c$ axis but no magnetic anisotropy in the $ab$ plane. Based on the field-dependent magnetic entropy change $[\mathrm{\ensuremath{\Delta}}{S}_{M}(T,H)]$, the critical exponents of $\ensuremath{\beta}=0.177(9)$, $\ensuremath{\gamma}=1.746(8)$, and $\ensuremath{\delta}=10.869(5)$ are obtained around ${T}_{C}=66.4(3)$ K. With these critical exponents, the $M(T,H)$ and $\mathrm{\ensuremath{\Delta}}{S}_{M}(T,H)$ curves follow the universality scaling laws, implying their high reliability and self consistency. The determined critical exponents are close to the 2D-Ising model with spatial dimensionality $d=2$ and spin dimensionality $n=1$. These results suggest that for 2D-Ising-like ${\mathrm{Cr}}_{2}{\mathrm{Ge}}_{2}{\mathrm{Te}}_{6}$, the weak magnetic anisotropy is crucial for the stabilization of the long-range ferromagnetic ordering, which is also consistent with the prediction of renormalized spin wave theory.