Fractional derivatives: from magnetic spectroscopy to high amplitude dynamic hysteresis in soft ferromagnetism

Benjamin Ducharne (1, 2) , B Zhang (3) , Y.A. Tene Deffo (4) , G. Sebald (5)

1 LGEF - Laboratoire de Génie Electrique et Ferroélectricité
2 Purdue University [West Lafayette]
3 Shandong University
4 University of Buéa
5 ELyTMaX

Considering harmonic evolution of the magnetic induction field, we establish a link between a time domain, high amplitude, fractional hysteresis model and the frequency domain, weak amplitude, fractional, ferromagnetic Cole-Cole model. A relation between α (the fractional order), τ (the relaxing time) and ρ (the dynamic constant) can be set. Experimental results performed on a typical soft ferromagnetic (Fe-Si) validate the theory. Correct comparison simulations/measures are observed for both situations (weak and high amplitude excitation) conserving the same set of parameters (α, τ, ρ). The dynamic behavior of a ferromagnetic sample can be set under weak amplitude excitation using simple impedance LCR meter characterization and conserved for the simulation of high amplitude dynamic hysteresis cycles.

Mots clés: Hysteresis; frequency dependence; fractional derivatives; Cole-Cole model

Domaines: Sciences de l'ingénieur [physics]; Matériaux

Benjamin Ducharne, B Zhang, Y.A. Tene Deffo, G. Sebald. Fractional derivatives: from magnetic spectroscopy to high amplitude dynamic hysteresis in soft ferromagnetism. COMPUMAG 2019, Jul 2019, Paris, France. ⟨hal-02154172⟩