Microstructural analysis, magnetic properties, magnetocaloric effect, and critical behaviors of Ni0.6Cd0.2Cu0.2Fe2O4 ferrites prepared using the sol–gel method under different sintering temperatures

This work focuses on the microstructural analysis, magnetic properties, magnetocaloric effect, and critical exponents of Ni0.6Cd0.2Cu0.2Fe2O4 ferrites. These samples, denoted as S1000 and S1200, were prepared using the sol–gel method and sintered separately at 1000 °C and 1200 °C, respectively. XRD patterns confirmed the formation of cubic spinel structures and the Rietveld method was used to estimate the different structural parameters. The higher sintering temperature led to an increased lattice constant (a), crystallite size (D), magnetization (M), Curie temperature (TC), and magnetic entropy change (−ΔSM) for samples that exhibited second-order ferromagnetic–paramagnetic (FM–PM) phase transitions. The magnetic entropy changed at an applied magnetic field (μ0H) of 5 T, reaching maximum values of about 1.57–2.12 J kg−1 K−1, corresponding to relative cooling powers (RCPs) of 115 and 125 J kg−1 for S1000 and S1200, respectively. Critical exponents (β, γ, and δ) for samples around their TC values were studied by analyzing the M(μ0H, T) isothermal magnetizations using different techniques and checked by analyzing the −ΔSM vs. μ0H curves. The estimated values of β and γ exponents (using the Kouvel–Fisher method) and δ exponent (from M(TC, μ0H) critical isotherms) were β = 0.443 ± 0.003, γ = 1.032 ± 0.001, and δ = 3.311 ± 0.006 for S1000, and β = 0.403 ± 0.008, γ = 1.073 ± 0.016, and δ = 3.650 ± 0.005 for S1200. Obviously, these critical exponents were affected by an increased sintering temperature and their values were different to those predicted by standard theoretical models.