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We investigate the magnetic behavior and critical exponents of quaternaryCoFeV$_{0.8}$Mn$_{0.2}$Si Heusler alloy to understand the interactions acrossthe Curie temperature ($T_{\rm C}$). The Rietveld refinement of the x-raydiffraction pattern with the space group F$\bar{4}$3m confirms a single-phasecubic Y-type crystal structure. The magnetic susceptibility $\chi (T)$ datashow a ferromagnetic nature with a second-order phase transition fromparamagnetic to ferromagnetic at $446\pm1$~K. The saturation magnetization at5~K is determined to be 2.2~$\mu_B$/f.u., which found to be close to theSlater--Pauling rule and indicates its half-metallic nature. The values ofasymptotic critical exponents ($\beta$, $\gamma$, and $\delta$) and the $T_{\rmC}$ are extracted through detailed analytical analysis including the ModifiedArrott plot, the Kouvel-Fisher (K--F) method, and the Widom scaling relation.Interestingly, the estimated values of $\beta$ = 0.369 and $\gamma$ = 1.445closely approximate the theoretical values of the 3D Heisenberg model andsecond-order thermodynamic phase transition across the $T_{\rm C}$. Theobtained exponents lead to the collapse of renormalized isotherms, representedby the relationship between the magnetization (m) and the applied magneticfield (h), into two distinct branches above and below the $T_{\rm C}$, whichvalidates the reliability of the analysis. Furthermore, these exponents suggestthat 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 3DHeisenberg model.

Complex magnetic interactions and critical behavior analysis in quaternary CoFeV$_{0.8}$Mn$_{0.2}$Si Heusler alloy