Magnetic Hysteresis in Simple Materials. I. Theory

Abstract

A wall‐pinning model is applied to the motion of a single domain wall. The model assumes that hysteresis is due to localized pinning of walls at defects and their subsequent snapping free. A distribution function is introduced to describe the differing strengths of defects in a real sample. The general theory is applied to the symmetric minor loop, the virgin curve, and to drifting minor loops. The theory makes two interesting predictions about the relation between symmetric minor loops and the virgin curve. They are both properties of the Rayleigh loop. One of these is that the virgin curve is the locus of apexes of centered minor loops. A method for measuring the distribution function from a minor loop is given. The theory is then specialized to the case of a particular distribution function which has been found to hold experimentally. The theory is applied to the cases described above. Special attention is given to the Rayleigh region. It is found that there is a relation between the Rayleigh constants μ and a and the coercive force H_c similar to that given by Néel, namely, $${\text{μ/a=1.58H}}_c$$ . For a sinusoidal variation of flux, the first three Fourier components of mmf are calculated.