# An Alternative Formulation of the Harrison Model
## 3 Results  
Exemplary modeling was carried out for a Pr\({}_{8}\)Dy\({}_{1}\)Fe\({}_{60}\)Co\({}_{77}\)Ni\({}_{6}\)B\({}_{14}\)Zr\({}_{1}\)Ti\({}_{3}\) ribbon (a hard magnet, examined previously in [9]). The details on sample preparation are provided in [42]. Figure 7 depicts the decomposition of the measured hysteresis loop into the irreversible hysteresis loop related to the bistability phenomenon and the anhysteretic curve in accordance with the approach outlined in the previous section. In modeling, we considered just two hysterons without weighting to make the structure really simple; the dependence \(h=h(m)\) generating bistability for the first hysteron was \(h_{51}=m^{5}-0.5m\). The other unit was of type (5), where the value of the \(a\) parameter was taken as \(a=-3.3\). The results of modeling are presented in Figure 8. It can be stated  
Figure 6: The affine transformation based on angle \(\Theta\); (**a**)—measured hysteresis loop, (**b**) irreversible hysteresis loop. Solid lines—hysteresis loop, dashed line—anhysteretic curve (approximate shapes). The figure may be compared to Figure 5 in [10] or Figure 10 in [39]. that, despite its simplicity, the model is able to capture the shape of the measured hysteresis curves quite well, which may be inferred from a visual comparison with previous modeling results [9] (drawn with red dotted lines). It is noticeable that the shape of the measured hysteresis curve is better reproduced with the new approach. The \(J\)-\(H\) dependencies modeled with the original model from [9] generally overestimated the values which may be considered \"figures of merit\", i.e., coercivity and remanence polarization, and the shapes of modeled hysteresis curves remained in qualitative agreement with the experiment. In terms of quantitative assessment, the discrepancy between coercive field strength modeled with the present model and its experimental counterpart is merely 1.05%; this value should be compared to 11.4% discrepancy for the model from [9] and the experimental value for this specific point. For remanence polarization, the respective discrepancy values are 11.4% (the present model) and 17.2% (model from [9]). Figure 8: The measured (dots) and the modeled (solid lines) hysteresis curves. Additionally, the modeling results for the same sample from Ref. [9] ([PERSON] et al., 2022) are shown as red dotted lines. Figure 7: The decomposition of measured hysteresis loop into irreversible and reversible components. The present model works much better, particularly for lower values of magnetic flux density, and the value of coercive field strength is very well reproduced. The departures of modeled hysteresis curves from the experimental data points around the \"knee\" and in the region approaching saturation may be due to the arbitrary choice of hysterons with specified characteristics and considering just two of them. We believe that much better accuracy may be achieved if more units are taken into account. It is evident that use of many hysterons in the analysis results in better capability of reproducing experimental results (due to increased number of degrees of freedom of the description--this explains the successful story of the Preisach formalism); on the other hand, we wanted to keep the model structure as simple as possible in our preliminary tests. As a second attempt to apply the developed description in practice, we carried out modeling for a cylinder core wound of Co-based amorphous alloy AMMET212. As pointed out by [PERSON], his approach should be valid both for soft and hard magnetic materials. The considered material is extremely soft since the measured value of coercive field strength is 5.1 A/m (this is a value five order of magnitude lower than for the praseodymium-dysprosium sample shown in Figure 8). Again, we considered a combination of just two hysterons.