Critical behaviors of van der Waals itinerant ferromagnet Fe_3.8GaTe₂

The critical behavior of the van der Waals ferromagnet Fe_3.8GaTe₂was systematically studied through measurements of isothermal magnetization, with the magnetic field applied along thec-axis. Fe_3.8GaTe₂undergoes a non-continuous paramagnetic to ferromagnetic phase transition at the Curie temperatureT_c∼ 355 K. A comprehensive analysis of isotherms aroundT_cutilizing the modified Arrott diagram, the Kouvel-Fisher method, the Widom scaling law, and the critical isotherm analysis yielded the critical exponent ofβ= 0.411,γ= 1.246, andδ= 3.99. These critical exponents are found to be self-consistent and align well with the scaling equation at high magnetic fields, underscoring the reliability and intrinsic nature of these parameters. However, the low-field data deviates from the scaling relation, exhibiting a vertical trend whenT<T_c. This discrepancy suggests the occurrence of a first-order phase transition in the crystal under a low magnetic field whenT<T_c. Mössbauer spectra were employed to provide insights into the critical behaviors of magnetic moments at different sites, including (Fe1)A, (Fe1)B, and Fe2. The results are consistent with the isothermal magnetization analysis. Additionally, the renormalization group theory analysis reveals that the spin coupling within the Fe_3.8GaTe₂crystal follows the three-dimensional Heisenberg ({d:n} = {3:3}) type with long-range magnetic and exchange interaction decays with a distance asJ(r) ≈r^-4.80.