Predictability of magnetic hysteresis and thermoremanent magnetization using Preisach theory

Preisach theory is a phenomenological model of hysteresis that is the basis for FORC analysis in rock magnetism. In FORC analysis, a system is characterized using first-order reversal curves (FORCs), each of which is a magnetization curve after a reversal in the direction of change of the magnetic field. Preisach theory uses the same curves to predict the magnetic response to changes in the magnetic field. In rock magnetism, the Preisach model has been adapted to predict general properties of thermoremanent magnetization (TRM), and even to inferpaleointensity from room-temperature FORCs.

Preisach theory represents hysteresis by a collection of hysteresis units called hysterons; the distribution of hysterons is inferred from FORC measurements. Each hysteron represents a two-state system. This is similar to a single-domain (SD) magnet, but the first-order theory cannot represent the magnetism of a simple system of randomly oriented SD magnets. Such a system can be represented by a second-order Preisach theory, which requires the measurement of magnetization curves after two reversals of the direction of change. One can generalize this process to higher order reversal curves, although each increase in the number of reversals greatly increases the number of measurements that are needed.

The magnetic hysteresis of systems of interacting SD magnets is calculated using numerical homotopy, a method that can find all the solutions of the equilibrium equations for such a system. The hysteresis frequently has features that cannot be represented by any order of Preisach theory. Furthermore, there are stable magnetic states that are not reachable during isothermal hysteresis unless thermal fluctuations are large enough. Such states would not be visible at room temperature but would contribute to TRM.