Scaling Analysis of Paramagnetic-to-Ferromagnetic Phase Transitions in Spinel Ferrites Zn 0.7 Mg 0.3 Fe 2 O 4 Based on Magnetic Entropy Change

We have investigated the critical behavior of Zn 0.7 Mg 0.3 Fe 2 O 4 ferrite near the ferromagnetic-paramagnetic (FM-PM) phase-transition temperature ( T C ). The M(T) curve exhibits that a PM-to-FM phase transition occurs around 198 K, which can be described as a second-order transition based on the positive slope of the Arrott plot. However, the scaling analysis of magnetic entropy change exhibits that Δ S M ( T ) curves do not collapse into a single universal curve, indicating that the observed PM-FM phase transition is not an authentic second-order phase transition. The critical parameters obtained with the Kouvel-Fisher method (and the critical isotherm method) were β = 0.4745, γ = 1.1650, and δ = 2.8659. The critical exponents of the samples are very close to the mean-field model for β = 0.5, γ = 1.0, and δ = 3.0, indicating that the long-range and short-range ferromagnetic orderly interactions coexisted with interaction phases and the long-range ferromagnetic orderly interaction dominates. According to previous studies, the doping of Mg 2+ ions has an effect on ZnFe 2 O 4 . Here, the doping level is 30%, short-range FM coupling appears in the PM region, and the FM-PM phase transition in the temperature range of 203.6 to 398 K becomes a first-order phase transition. The second-order phase transition only occurs at T < 203.6 K. When the magnetic field increases above 10 kOe, the first-order phase transition can be converted into the second-order phase transition. These results suggest that the change in magnetic entropy scaling is useful for elucidating the nature of magnetic phase transitions.