L. Petrescu / Journal of Advanced Research in Physics 1(2), 021003 (2010) 1 Abstract — Ossart model is common used in characterization of the major loop of magnetic materials because it is using only few experimental data and the results are satisfying. The equation presented by the authors does not take into account the remanent magnetization and, therefore, the modeled loop is not close to the experimental one in that region. The aim of is paper is to present the advantages and the drawbacks of this model using a modified parameter which is depending of the remanent magnetization. Keywords — Hysteresis modeling, Ossart model. I. INTRODUCTION Magnetic recording media are commonly used in many daily activities. The behavior of this kind of material is very important in a lot of devices [1]. Creating a hysteresis model means to make a good compromise between accuracy and computational efficiency. Using a simple analytical model can be interesting even if it does not show information about the material. Such a model can be compared with the accuracy of the Preisach-derived models, but the computational time and the quantity of the experimental data needed for parameter identification could represent an advantage for such a model. A model like this was proposed by Cortial and Ossart in [2], a simple and fast analytical model used for thin magnetic films with satisfying result for major and minor loops. From now on this model it will be called Ossart model. The model presented by its authors will be named classic Ossart model (COM) and the one proposed here will be named modified Ossart model (MOM). Both models are using the same equations for identification, the differences being the identification of one specific parameter. COM has started from the premise that magnetic recording materials are characterized by a high rectangularity of the major hysteresis loop, a remanent magnetization close to the saturation value. This information is not exact in the case of anisotropic materials characterized by an easy magnetization axis (ea) and a hard magnetization Manuscript received June 8, 2010. * Corresponding author (lucian.petrescu@upb.ro) axis (ha). For the hysteresis loop in ha, the rectangularity is less then 0.5, so the remanent point is an important information in material characterization. II. OSSART MODEL FOR MAJOR LOOP Identification of the model parameters starts from the closure point of the loop. We will consider that point to be the saturation. Beyond the closure point (H f < H < H s ), saturation is reached after reversible rotation of the magnetization. This part of the magnetization curve is modeled by the parabolic function presented in [2], but it is not very important in global characterization of the hysteresis loop. A normalization of the experimental data is made relatively to the closure values of the magnetic field (H f ) and magnetization (M f f r r f c c f f ; ; ; M M m H H h M M m H H h = = = = ). (1) The magnetization m is given by (2) as the sum of a hyperbolic tangent and an arctangent functions: [ ]       ⋅ ⋅ + ⋅ = ) ( 2 tan 1 ) ( tanh 2 1 ) ( h g R a h g R h m π π (2) where the function g(h) used in (2) is calculated as it follows: ) 1 )( 1 ( / ) 1 ( ) ( c h h h h h g + − − = δ (3) δ(1) is “1” for the descending curve and “-1” for the ascending one. The parameter R in (2) is the key difference between the models. In COM, R is defined like in (4): ( ) 2 c f f c 1 h M H h k R − ⋅ ⋅ ⋅ − = (4) where k is the slope of the experimental loop in coercive point, c H H dM dH k = = (figure 1). This is why MOM calculates this parameter using the information of the remanent point. So, the magnetic moment for h = 0, gives the value in this specific point, m r r 2 tan 1 tanh 2 1 ) 0 ( m R a R m =       ⋅ + = π π and for h = 0, g(h) = 1, that leads to the equation (5): (5) Modified Ossart model for magnetic characterization Lucian Petrescu 1 Electrical Engineering Faculty, University POLITEHNICA of Bucharest, Splaiul Independentei, 313, Bucharest, 060042, Romania