  We investigate the magnetic behavior and critical exponents of quaternary
CoFeV$_{0.8}$Mn$_{0.2}$Si Heusler alloy to understand the interactions across
the Curie temperature ($T_{\rm C}$). The Rietveld refinement of the x-ray
diffraction pattern with the space group F$\bar{4}$3m confirms a single-phase
cubic Y-type crystal structure. The magnetic susceptibility $\chi (T)$ data
show a ferromagnetic nature with a second-order phase transition from
paramagnetic to ferromagnetic at $446\pm1$~K. The saturation magnetization at
5~K is determined to be 2.2~$\mu_B$/f.u., which found to be close to the
Slater--Pauling rule and indicates its half-metallic nature. The values of
asymptotic critical exponents ($\beta$, $\gamma$, and $\delta$) and the $T_{\rm
C}$ are extracted through detailed analytical analysis including the Modified
Arrott plot, the Kouvel-Fisher (K--F) method, and the Widom scaling relation.
Interestingly, the estimated values of $\beta$ = 0.369 and $\gamma$ = 1.445
closely approximate the theoretical values of the 3D Heisenberg model and
second-order thermodynamic phase transition across the $T_{\rm C}$. The
obtained exponents lead to the collapse of renormalized isotherms, represented
by the relationship between the magnetization (m) and the applied magnetic
field (h), into two distinct branches above and below the $T_{\rm C}$, which
validates the reliability of the analysis. Furthermore, these exponents suggest
that the spin interaction follows a decay pattern of $J(r) \sim r^{-4.99}$,
indicating a short-range magnetic ordering, akin to the itinerant-electron 3D
Heisenberg model.

Materials Science;Mesoscale and Nanoscale Physics