Critical behavior in Ni0.15Cu0.15Zn0.7Fe2O4 spinel ferrite

We report an in-depth investigation of the critical behavior in Ni0.15Cu0.15Zn0.7Fe2O4 (NCZFO) spinet ferrite synthesized via the solid-state reaction method. The structural analysis demonstrates that NCZFO belongs to the Fd (3) over barm space group of the cubic crystal system. The magnetic transformation in NCZFO at approximately T-C = 290 K is of the second order, as per the Banerjee criteria. Employing various models, we have attempted to estimate the CP (critical parameter) values. The self-consistency of the CPs is confirmed by Widom's relation as well as the scaling hypothesis. The values of the CPs manifest that the magnetic ordering in NCZFO belongs to the Heisenberg theory in three dimensions, signifying short-range ferromagnetic interactions. The relationship between the exchange distance (J(r)) and the spatial distance (r) in NCZFO are expected to decline as J(r) similar to r(-4.947).