HR: 0830h
AN: GP31B-0748    [PDF]
TI: FORCs, SORCs and Stoner-Wohlfarth Theory
AU: * Newell, A J
EM: newell@geol.ucsb.edu
AF: Dept. of Geological Sciences, Mail code 9630, UCSB, Santa Barbara, CA 93106-9630 United States
AB: The Preisach model is an abstract model of hysteresis, applicable to many kinds of physical phenomena. The Stoner-Wohlfarth model is a physical model of magnetic hysteresis in single-domain ferromagnets. If the Preisach model can be applied to magnets, it can predict the magnetization for an arbitrary sequence of fields. In the ``classical'' Preisach model the hysteresis is determined by the Preisach density $\mu(H_a,H_b)$, where $H_a$ and $H_b$ are extrema in the field. This density can be estimated by measuring the magnetization $M(H_a,H_b)$ in a series of first-order reversal curves (FORCs). However, Mayergoyz and Friedman [IEEE Trans. Magn. \textbf{24}, 212, 1988] showed that the classical Preisach model cannot represent the hysteresis predicted by the Stoner-Wohlfarth theory. To fill the gap, they developed a ``nonlinear'' Preisach model with a three-parameter density $\mu(H_a,H_b,H)$. To determine the density, one must measure second-order reversal curves (SORCs) - an enormous task. Now many researchers use FORCs to parametrize hysteresis without attempting to make predictions, allowing them to relax the restrictions on the classical Preisach model. They use a modified density $\rho(H_c,H_u)=2\mu(H_a,H_b)$, where $H_c = \left(H_b-H_a \right)/2$ and $H_u = \left(H_b+H_a \right)/2$. Classical and nonlinear Preisach densities are calculated for a Stoner-Wohlfarth system of randomly oriented particles with uniaxial anisotropy. High precision is achieved by closed-form integration of single-curve densities. In classical Preisach theory, the density $\rho(H_c,H_u)$ would be an even function of $H_u$, but here it is only nonzero for negative $H_u$. It is concentrated near portions of the $H_c$ and $H_u$ axes, approaching positive infinity as $H_u$ goes to zero and negative infinity as $H_c$ goes to zero. The asymptotes exist because, in a single particle, the slope of the magnetization curve approaches a limit of infinity at the switching field. In addition, there is a delta function along part of the $H_u$ axis associated with the jump at the switching field. This distribution is very difficult to model using numerical simulations. The switching fields range from $0.5H_K$ to $H_K$, where $H_K$ is determined by the anisotropy, but half of the remanence is lost between $0.5H_K$ and $0.524H_K$ (the coercivity of remanence). Thus, at a typical modeling resolution much of the density is concentrated within two or three grid points. The delta function can only be obtained by modifying the procedure for calculating the density to take jumps into account. Adaptive quadrature is used to calculate magnetization curves for Stoner-Wohlfarth theory given an arbitrary sequence of input fields. In particular, FORCs and SORCs can be calculated to several digits of precision. This algorithm is used to demonstrate nonlinear features of Stoner-Wohlfarth hysteresis such as nonlocality.
DE: 1500 GEOMAGNETISM AND PALEOMAGNETISM
DE: 1512 Environmental magnetism
DE: 1540 Rock and mineral magnetism
DE: 3200 MATHEMATICAL GEOPHYSICS (New field)
SC: Geomagnetism and Paleomagnetism [GP]
MN: 2003 Fall Meeting