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Description
A new differential isotropic model of ferromagnetic hysteresis (DIMFH) [1] has been developed, which has removed the contradictions and ambiguities in the original Jiles-Atherton (J-A) model. This model is simpler, uses only 4 parameters ($M_s$, $a$, $h$, $β$) with clear physical meaning and is based on a new assumption: the existence of so-called magnetic clusters - a coherent regions of ferromagnetic material with size of $10^4$ - $10^6$ of Bohr magnetons. Magnetic clusters form an intermediate stage between atomic magnetic moments and magnetic domains.
In this paper we focus our attention to one of the unsolved problems of the DIMFH: the influence of temperature on the saturation magnetization $M_s$ and on the average magnitude of the cluster magnetic moment $m$. Magnetization curves of an amorphous Fe$_{77.5}$Si$_{7.5}$B$_{15}$ ribbon sample were measured from room temperature up to $400$ °C and successfully fitted by the DIMFH model with high precision. Temperature dependence of $M_s$ parameter is correlated with a simple two-level system model with Weiss approximation. The fitted values of Weiss coefficient $w = 284.56$ and number of Bohr magnetons $N \approx 2$ are in good agreement with literature for systems containing iron [2]. The $w$ coefficient is further compared to the DIMFH parameter $\beta$ describing average mutual interaction between magnetic clusters. Differences in $w$ and $\beta$ values are discussed in detail.
The magnetic moment cluster $m$ is related to the thermodynamic temperature $T$ through the parameter $a$ of the DIMFH model using the relation $a \equiv \frac{k_\mathrm{B}T}{\mu_0 m}$, where $k_\mathrm{B}$ and $\mu_0$ are the Boltzmann constant and vacuum permeability, respectively. By fitting magnetization curves at different temperatures using the DIMFH model, a linear decrease in the parameter $a$ with increasing temperature T was determined. Such conclusion supports an idea that the magnitude of the magnetic cluster $m$ increases during the system heating. For a room temperature, cluster size of $1.25 \cdot 10^5$ Bohr magnetons is calculated, while for $250$ °C, size of $2.86 \cdot 10^5$ Bohr magnetons is obtained. For higher temperatures approaching the Curie temperature, the assumptions of the DIMFH model are not valid.
Acknowledgements
This work was supported by the Ministry of Education, Youth and Sports of the Czech Republic, projects no. CZ.02.1.01/0.0/0.0/17_048/0007399 and SP2025/009.
References
[1] J. Pytlík et al., “Differential isotropic model of ferromagnetic hysteresis,” Physical Review B, vol. 108, no. 10. American Physical Society (APS), Sep. 15, 2023. https://doi.org/10.1103/physrevb.108.104414
[2] D. Jiles, „Introduction to magnetism and magnetic materials. Third edition.” Boca Raton: CRC Press, Taylor & Francis Group, 2016. ISBN 978-1-4822-3887-7
