OPTOELECTRONICS AND ADVANCED MATERIALS – RAPID COMMUNICATIONS Vol. 4, No. 4, April 2010, p. 505 - 508 Rotational first-order reversal curves (rFORC) diagrams L. STOLERIU * , P. POSTOLACHE, P. ANDREI a , A. STANCU Dept. of Physics, "Alexandru Ioan Cuza" University, Iasi 700506, Romania a Dept. of Electrical and Computer Eng., Florida State University and Florida A&M University, Tallahassee, FL, USA In recent years, there is a strong interest in the development of more efficient vector hysteresis models which can correctly describe the magnetization processes in ferromagnetic materials taking into account the vector nature of both applied field and magnetic moment. The scalar Preisach-type models complemented with the identification based on a set of first-order reversal curves (FORC) are typical examples of scalar hysteresis models which can provide accurate results in a large variety of cases. In the development of vector models the main difficulties are the numerical implementation and the lack of clear and tractable identification techniques. In this paper we are introducing a new type of measurement, a set of FORCs measured on the rotational hysteresis, and we are investigating it as a testing method for the vector hysteresis models performances. (Received September 21, 2009; accepted April 11, 2010) Keywords: Vector hysteresis modelling, FORC diagram, Preisach model 1. Introduction The study of the magnetic processes taking place in real-world applications, like the processes behind the technology of magnetic information recording and storage or the magnetic behaviour of electrical machines, cannot neglect the vector character of both physical quantities involved – the magnetic field H and the magnetic moment M . The great variety of models for magnetic hysteresis can be included in two main classes: - The physical models, from which category the micromagnetic models based on solving the Landau- Lifshitz-Gilbert [1] differential equations are one of the most widely used, are based on physical properties of the studied sample. The main strength of this kind of models is that their results can be easily linked with the physical parameters or causes. - The phenomenological models, from which the Preisach model [2] is one of the most representatives, try to mimic the observed experimental behaviour using mainly mathematical tools, without necessarily using physical hypothesis. In this case the parameters of the model have no direct link with the physical properties of the sample. In recent years, there is a strong interest in the development of more efficient phenomenological vector hysteresis models which can correctly describe the magnetization processes in ferromagnetic materials taking into account the complex vector nature of both applied field and magnetic moment. The intense studies concentrated on scalar hysteresis have provided a number of models with reliable identification techniques which can explain a wide range of typical scalar measurements specific to most measuring devices commonly available in the laboratories. The scalar Preisach-type models complemented with the identification based on a set of First-order reversal curves (FORC) is a typical example of a scalar hysteresis model [3] which can provide accurate results in a wide range of cases. Despite the success of the phenomenological models in the scalar hysteresis modelling, the development of vector models was not as successful, due to the difficult implementation of the different variants (e.g. [4], [5]) or due to the lack of clear and tractable identification techniques. This is one of the reasons why the most successful approach in the modelling of the vector magnetic behaviour is still the full micromagnetic (physical) approach. However, the main disadvantage of applying a micromagnetic model to large systems is that it requires huge computing resources so, in this context, phenomenological vector models represent a possible solution to get the required accuracy with high numerical efficiency The most widely used strategy for designing phenomenological vector models is to enhance a scalar model by adding the angle of the applied field with respect to certain defined directions on the sample as input parameters. In the case of Preisach-type models, the calculus is taking in consideration a distribution of magnetic entities with different coercive and magnetic interaction fields, called Preisach function. The entities are associated with a straightforward geometric representation, the Preisach plane, which can give a clear image of the evolution of a system when the magnetic field changes. The Preisach-type models are usually generalized to vector models by adding an angular dependence to the scalar Preisach function [4]. One of the first tests that a vector generalization of a scalar Preisach-type model should pass is the simulation of major hysteresis loop branches, for any orientation of the