Critical behavior in the van der Waals itinerant ferromagnet Fe 4 GeTe 2

The critical phenomenon of the magnetic phase transition in the van der Waals itinerant ferromagnet ${\mathrm{Fe}}_{4}{\mathrm{GeTe}}_{2}$ has been investigated by measuring the dc magnetization. The compound undergoes a continuous paramagnetic to ferromagnetic phase transition at the Curie temperature ${T}_{C}=270.0\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. A detailed analysis of magnetization isotherms measured in the vicinity of ${T}_{C}$ with magnetic field $H$ applied parallel to the $ab$ plane yields the asymptotic critical exponents $\ensuremath{\beta}=0.37, \ensuremath{\gamma}=1.20$, and $\ensuremath{\delta}=4.21$, whereas the magnetization isotherms for $H\ensuremath{\parallel}c$ yield $\ensuremath{\beta}=0.34, \ensuremath{\gamma}=1.20$, and $\ensuremath{\delta}=4.52$. Both sets of the critical exponents obey the scaling relation and scaling equation of the magnetic state predicted by the scaling theory. The renormalization group theory analysis for the critical exponents and the analysis based on the self-consistent renormalization theory of spin fluctuations manifest a quasi-two-dimensional itinerant magnetism in the ${\mathrm{Fe}}_{4}{\mathrm{GeTe}}_{2}$ single crystal where the magnetic exchange coupling $J(r)$ is the long-range type that decreases spatially slower than ${r}^{\ensuremath{-}4.76}$. Moreover, a small reduction in the value of $\ensuremath{\beta}$ for $H\ensuremath{\parallel}c$ attests to the observed weak effective uniaxial magnetic anisotropy of ${\mathrm{Fe}}_{4}{\mathrm{GeTe}}_{2}$.