Ferromagnetic hysteresis and the effective field

The Jiles-Atherton model of the behavior of ferromagnetic materials determines the irreversible magnetization from the effective field by using a differential equation. This paper presents an exact, analytical solution to the equation, one displaying hysteresis. The inclusion of magnetomechanical couplings for various forms of the magnetostriction does not modify this solution. Consequently, the approach followed here is also very useful to study the effects of stress on the hysteretic magnetization.