18th Czech and Slovak Conference on Magnetism

Modeling the Effect of Stress on the Magnetization Curves as a Simple Magnetic Field Scaling

2O-02

Jul 8, 2025, 5:15 PM

15m

ORAL Topic 2 - Amorphous, nanocrystalline and other soft magnetic materials Section S2

Speaker

Alexej Perevertov (FZU - Institute of Physics of the Czech Academy of Sciences, Department of Magnetic Measurements and Materials)

Description

The mechanical stress strongly influences the magnetic properties of ferromagnetic materials - the magnetic hysteresis loops measured under constant stress.

In 1930 Kersten analyzed the total energy of a stressed ferromagnet and derived the analytical expression for the relative initial susceptibility that is inversely proportional to the stress for the initial part of the magnetization curve [1]:
$$ \chi = M/H = JS^2/(3\mu_0\gamma_S\sigma).(1)$$ There are many hundreds works on the modeling the effect of stress on the magnetic susceptibility and hysteresis loops [2]. The most popular is the Jiles-Atherton-Sablik model, which is based on the the Jiles-Atherton model with the effective field by stress, which is the function of the stress and the magnetization [3]. Recently we have found that the Kersten relation for a relative susceptibility is also valid for the differential susceptibility of nonlinear $M(H)$ curves of stressed polycrystalline iron-based ferromagnets for any magnetization (not the field) value [4]. The effect of stress is introduced by scaling the magnetic field of the $M(H)$ curve proportionally to stress. This simple relation together with the $M(H)$ curve in the form of the arctangent function gives a very good agreement with experimental curves, reproducing all stress-induced features usually observed on the magnetization curves including the common crossover point. Also it validates the effective field by stress concept used in the Jiles-Atherton-Sablik and its variations. We propose to plot the field and differential susceptibility as a function of magnetization, $H(M)$ and $\chi(M)$ in contrast to convenient $M(H)$ and $\chi(M)$ curves. Then, $\chi(M)$ peaks have the same positions and widths with only difference in the vertical scaling.

Acknowledgements

This work was supported by the Ferroic Multifunctionalities project, supported by the Ministry of Education, Youth, and Sports of the Czech Republic. Project No. CZ.02.01.01/00/22_008/0004591.

References

[1] R.M. Bozorth, Ferromagnetism. Van Nostrand, New York (1951).
[2] A. Kumar and A. Arockiarajan, “Evolution of nonlinear magneto-elastic constitutive laws in ferromagnetic materials: A comprehensive review,” Journal of Magnetism and Magnetic Materials, vol. 546. Elsevier BV, p. 168821, Mar. 2022. https://doi.org/10.1016/j.jmmm.2021.168821
[3] M. J. Sablik and D. C. Jiles, “A model for hysteresis in magnetostriction,” Journal of Applied Physics, vol. 64, no. 10. AIP Publishing, pp. 5402–5404, Nov. 15, 1988. https://doi.org/10.1063/1.342383
[4] A. Perevertov, “A phenomenological magnetomechanical model for hysteresis loops,” 2024, arXiv. https://doi.org/10.48550/ARXIV.2412.08323