Modeling Dynamic Magnetic Response of Spinel Soft Ferrites with the Steepest-Entropy-Ascent Quantum Thermodynamics Formalism
Selecting soft ferrites for alternating-field applications requires balancing magnetic response, dissipation, nonlinearity, and heating. We use a field-driven steepest-entropy-ascent quantum thermodynamic (SEAQT) model to compare the electron, phonon, and magnon responses of Fe$_3$O$_4$, MnFe$2$O$4$, and (Mn${0.5}$Zn${0.5}$)Fe$_2$O$_4$ within a common first-principles framework. The model treats spatially uniform longitudinal relaxation and neglects domain-wall motion, transverse rotation, resonance, eddy-current effects, and heat removal. We use $τ_e=0.05$ ps and $τ_p=3$ ps for all three materials, with effective longitudinal magnon relaxation times of 500, 200, and 85 ps, respectively; these literature-motivated values are model inputs, not fits to measured losses. Within this framework, the Mn--Zn ferrite gives the largest peak longitudinal magnetization change, retains its response best at high frequency, and shows the largest work per cycle and peak-to-peak magnon temperature change, whereas MnFe$_2$O$_4$ gives the largest normalized $χ''$ peak. Thus, no single ferrite ranks highest across all metrics: the preferred material depends on the property, frequency, field amplitude, and cation configuration of interest. The model therefore provides a spectrum- and kinetics-resolved screening tool for engineering comparison of ferrites rather than a prediction of total core loss.