Different studies carried out in the last three decades on the magnetic susceptibility of the spinel ZnFe₂O₄ ferrite have revealed the positive character of its Curie–Weiss temperature, contradicting its observed antiferromagnetic behavior which is characterized by a well-defined susceptibility peak centered around the Neel temperature (10 K). Some approaches based on ab initio calculations and mixture of interactions have been attempted to explain this anomaly. This work shows how for very low values of the inversion parameter, the small percentage of Fe atoms located in tetrahedral sites gives rise to the appearance of ferrimagnetic clusters around them. Superparamagnetism of these clusters is the main cause of the anomalous Curie–Weiss behavior. This finding is supported experimentally from the thermal dependence of the inverse susceptibility and its evolution with the degree of inversion.

The antiferromagnetic (AFM) transition of the normal ZnFe₂O₄ has been intensively investigated with results showing a lack of long-range order, spin frustrations, and a “hidden” entropy in the calorimetric properties for inversion degrees δ ≈ 0 or δ = 0. As δ drastically impacts the magnetic properties, it is logical to question how a δ value slightly different from zero can affect the magnetic properties. In this work, (Zn_1-δFe_δ)[Zn_δFe_2-δ]O₄ with δ = 0.05 and δ = 0.27 have been investigated with calorimetry at different applied fields. It is shown that a δ value as small as 0.05 may affect 40% of the unit cells, which become locally ferrimagnetic (FiM) and coexists with AFM and spin disordered regions. The spin disorder disappears under an applied field of 1 T. Mossbauer spectroscopy confirms the presence of a volume fraction with a low hyperfine field that can be ascribed to these spin disordered regions. The volume fractions of the three magnetic phases estimated from entropy and hyperfine measurements are roughly coincident and correspond to approximately 1/3 for each of them. The “hidden” entropy is the zero point entropy different from 0. Consequently, the so-called “hidden” entropy can be ascribed to the frustrations of the spins at the interphase between the AFM-FiM phases due to having δ ≈ 0 instead of ideal δ = 0.

The morphological, magnetic, transport and corrosion inhibitory property of La_0.5Ca_0.5MnO₃-AuNPs prepared by sol gel method was determined. The structural property determined by XRD indicated that the unusual broadening of the Bragg's reflection despite the elevated sintering temperature was as a result of the inhibition of the grain growth by the gold nanoparticles (Au-NPs). The morphological property of the sample as determined by SEM and TEM show heterogeneously sized and shaped nanoparticles of an average particle size of 40 nm. The magnetic measurements of La_0.5Ca_0.5MnO₃-AuNPs showed that the sample undergoes a paramagnetic - ferromagnetic phase transition with T_c = 250K and T_b = 150K. Two metal-insulator transitions were observed at T₁ and T₂. The resistivity of the sample was observed to reduce as temperature increased to 300 K. The gravimetric method was used to determine the corrosion inhibitory properties with 1.0 M HCl using different concentration of La05Ca0.5MnO3-AuNPs. The anti-corrosion study was carried out for 21 days and was observed to reduce as concentration of La_0.5Ca_0.5MnO₃-AuNPs increased, but corrosion rate increased as the exposure time increased. The inhibitory property of the sample increased as the concentration of the sample increased. The reaction best fitted the Langmuir isotherm, indicating a monolayer of La_0.5Ca_0.5MnO₃-AuNPs inhibiting the corrosion of the mild steel.