Distribution function of wall-pinning defects in perminvar

Abstract

Defects which impede the motion of magnetic domain walls may be described by a distribution function, n, in range z₀. The range is the distance the mean position of a wall may move past a defect before it snaps free from the pinning action of the defect. The quantity n(z₀) dz₀ gives the number of defects per unit volume having a range between z₀ and z₀+dz₀. The distribution function n(z₀) for a sample of magnetically annealed perminvar has been completely determined. It is given by n(z₀)=(N/z₀)q(z₀). The density parameter N=3.1×10¹⁴ m⁻³. The function q(z₀) is given graphically. This function drops to e⁻¹ of its initial value (unity) at the mean range Z=2.5 μm. The spring constant associated with wall deformation k=9.5×10⁻³ N/m. The average total number of defects with which a wall interacts at any one time is found to be N₀=3×10⁵. Equations are developed to evaluate Z, N, k, and N₀ from measurements made on major and minor hysteresis loops. However, to evaluate the spring constant k and range parameter Z, it is necessary to know the total area of domain wall in the sample, or some other equivalent piece of information. The method may be employed to study the production and annealing of defects in magnetic materials which are sufficiently simple. It has the merit that the defects are sorted out by range rather than all being lumped into a single number, such as resistivity change.