Critical behavior of Zn0.6−xNixCu0.4Fe2O4 ferrite nanoparticles

We have investigated the critical behavior of Zn0.6−xNixCu0.4Fe2O4 (x = 0, 0.2 and 0.4) ferrite nanoparticles near the ferromagnetic-paramagnetic (FM-PM) phase-transition temperature (TC). Experimental results reveal that all samples undergo a second-order phase transition. Through various techniques such as modified Arrott plot, Kouvel-Fisher method and critical isotherm analysis, the estimated critical exponents are close to those expected for three-dimensional Heisenberg class for x = 0 (β = 0.386 ± 0.002, γ = 1.271 ± 0.012 and δ = 4.387 at TC = 305 K). Whereas for a high amount of Ni, these exponents belong to a different universality class (β = 0.716 ± 0.063, γ = 0.807 ± 0.008 and δ = 2.010 at TC = 565 K for x = 0.2 sample) and (β = 0.785 ± 0.004, γ = 0.797 ± 0.002 and δ = 2.061 at TC = 705 K for x = 0.4 sample). This is due to the fact that the substitution of Zn2+ (non-magnetic ions) by Ni2+ (magnetic ions) increases the A-B interaction sites of AB2O4 spinel ferrite which in turn increases the magnetic disorder when increasing Ni content. Using the magnetic entropy change equation: |ΔSMmax|=a(H)n, we have studied the relationship between the exponent n and the critical exponents of our samples. The obtained n value are 0.641, 0.843 and 0.873 for x = 0, 0.2 and 0.4, respectively. These values are in good agreement with those deducted from the critical exponents using the KF method.