IEEE TRANSACTIONS ON MAGNETICS, VOL. 42, NO. 10, OCTOBER 2006 3159 Using Experimental FORC Distribution as Input for a Preisach-Type Model Laurentiu Stoleriu and Alexandru Stancu Department of Solid State and Theoretical Physics, Alexandru Ioan Cuza University, 700506 Iasi, Romania In this paper, we present a method of using the experimental first-order reversal curves (FORC) distribution as input for Preisach-type models. In order to be able to calculate in the model the integral over the FORC distribution we designed an interpolation algorithm of the three-dimensional (3-D) distribution. The algorithm is validated for a simple case—the output of a classical Preisach model—and then is used for realistic, asymmetrical FORC distributions. Several Preisach-type models are tested for the same FORC distribution and it is shown that the PM2 model gives the best results in simulating magnetization curves starting from the FORC diagram. Index Terms—Magnetic hysteresis, magnetic materials, magnetization processes, modeling. I. INTRODUCTION P HENOMENOLOGICAL approach to magnetic modeling is able to give good results in a much shorter time and de- manding lesser computing performance than the physical (mi- cromagnetic) approach. The first-order reversal curves (FORC) method was intro- duced by Mayergoyz [1] as a method to identify the Preisach distribution [2] of a system which can be fully described by the classical Preisach model (CPM). In CPM, a particulate magnetic system is characterized by two independent statistical distribu- tion of coercive and interaction fields. Mayergoyz proved that, in order to be correctly described by a CPM, the system should obey to the wiping out and congruency properties [1]. While most of the real systems meet the terms of the wiping-out prop- erty, the congruency property was hardly ever verified on real systems. The lack of experimental systems which can be correctly de- scribed by CPM determined the evolution of many more re- alistic Preisach-type models—one of the most widely used is the generalized moving Preisach model which adds to the CPM hypotheses the reversible component of the magnetization pro- cesses and a mean field interaction term. In the same time, the interest in the FORC method diminished, especially because of the numerical errors introduced by the second-order derivative of the experimental data requested by this method of identifica- tion. Recently, Pike et al. [3] introduced a versatile numerical method of evaluation of the FORC diagram starting from measured data. They also have separated the method from its origin—the CPM—and suggested to use it only as an ex- perimental tool which can give information about magnetic systems. Since then, a considerable work has been undertaken in the field of the experimental FORC diagram interpretation. The aim of parameter identification in Preisach modeling is to find algebraic functions which, when used as input for the model, fit the experimental observations and are able to predict Digital Object Identifier 10.1109/TMAG.2006.880112 sample’s magnetic behavior. The main point in measuring FORCs and in the calculation from these experimental data FORC diagrams is especially related to the evaluation of in- teraction and coercive fields of the magnetic entities contained in a sample and to the evaluation of the ratio between the re- versible and the irreversible magnetization processes. However, it was recognized by all those who are currently using this experimental method that the FORC diagram, even it is closely related to the well known Preisach distribution [2] (of coercive and interaction fields as well as the reversible distribution) is not identical to this distribution. It has been shown [4] that for real systems the interaction field distribution is changing as a function of the magnetic state so the FORC diagram should be seen like an averaged photography of a moving distribution. It is important to emphasize that ideally, if an experimental FORC is used as the Preisach distribution in a CPM, the set of first-order reversal curves should be properly simulated. How- ever we have shown in [5] that if we measure a set of second- order reversal curves we obtain a different diagram while the CPM will give a diagram identical with the FORC diagram. As in many cases we have observed that the differences are not too important, this gave us the idea to implement a Preisach- type model which uses the experimental FORC distribution as Preisach distribution and to analyze the quality of the predic- tions made by this model. II. THE MODEL To obtain a point on the FORC starting on the descending branch of the major hysteresis loop (MHL), the following field sequence is applied to the sample: , where is a field sufficient to saturate the sample, , named reversal field, is a field in the domain and is the ac- tual field at which the sample magnetic moment—noted with —is measured; the sign minus is indicating that the FORC is measured on the descending branch of MHL. The FORC distribution is given by the second-order mixed deriva- tive (1) 0018-9464/$20.00 © 2006 IEEE