Wall-Pinning Model of Magnetic Hysteresis

Abstract

A simple model for the motion of a domain wall in most magnetic materials is presented. The real flexible wall is represented by an equivalent rigid plane wall. The motion of the plane is impeded by springs which are attached to the wall and to defects in the material in the wake of the plane. A spring breaks when the force it exerts on the wall reaches a value characteristic of the defect, and the energy stored in it is lost to the motion. The model is similar to one developed earlier but is based on a more plausible view of the interaction of a wall with a defect. In common with the earlier model, it describes both reversible and irreversible flux changes; it predicts a small-signal hysteresis loop which is similar to, but significantly different from, the Rayleigh loop; it explains the frictional nature of magnetic hysteresis without invoking any ad hoc energy-loss mechanisms. It is sufficiently simple to be applied to complex problems. It agrees with the results of exact dynamic calculations to good accuracy and is exact when applied to quasistatic problems. The model is derived by considering the motion of an anisotropic flexible wall pinned by a periodic array of defects. The springs of the model represent the distortions of the wall in the vicinity of the defects. It is shown that the force f exerted by the defect on the wall and the energy W per defect stored in wall distortions are related approximately to the average displacement z̄ of the wall from the defect by the equations f(t)=kz̄(t), W(t)=kz̄2(t)/2,where k is a spring constant associated with wall deformation. These relations justify the spring model. Finally, a comparison is made among f, W, and z̄ calculated as functions of time for a step of applied field from both the exact equations and from the spring model. The agreement is, in all cases, better than 10% of the final values. After the wall breaks free from a defect the energy stored in distortion is dissipated in viscous damping. It does not affect the average wall position and is thus lost to the motion in agreement with the model.