Viscoelastic magnetic loss modeling in soft ferromagnetic materials using fractional derivatives

Magnetization dynamics in soft ferromagnetic materials arise from the combined action of domain-wall motion and dissipative mechanisms linked to microscopic eddy currents and magnetic diffusion, leading to a viscoelastic-like behavior of the core losses. This work introduces a unified modeling framework based on fractional-derivative operators to capture these elastic and viscous contributions within a single constitutive law. Analytical expressions for dynamic losses under sinusoidal excitation are derived and validated using both literature data for classical ferromagnetic materials and new measurements on nanocrystalline 1K107A and 1K107B ribbons. The model achieves excellent accuracy, with NRMSE(%) values below 4%. A strong correlation (Pearson coefficient 0.93) is found between the dissipative parameter �� and ����2, suggesting a potentially universal relation. The results demonstrate that fractional viscoelastic modeling effectively describes magnetic losses and provides a powerful predictive tool for the design of high-efficiency magnetic components.