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A theory of the magnetisation process in ferromagnets, based on existing ideas of domain rotation and domain wall motion is presented. This has been developed via a consideration of the various energy terms into a mathematical description of the process leading to an equation of state for a ferromagnet. The differential equation has been solved and a solution containing terms up to the second order presented, showing the essential features of ferromagnetic hysteresis. The theory has then been used to explain the effects of stress on magnetisation. It has been found that the magnetisation approaches the anhysteretic curve when a ferromagnet is subjected to stress and this is the underlying principle behind such changes in magnetisation. The change of magnetisation with stress can not be predicted solely on the basis of the magnetostriction coefficient except in special cases when the initial (zero stress) conditions of magnetisation lie on the anhysteretic. This condition is also approximately satisfied at higher fields.

A mathematical theory of hysteresis in ferromagnetic materials is presented based on existing ideas of domain wall motion and domain rotation. Hysteresis is shown to occur as a result of impedances to changes of magnetization such as when domain walls are pinned, while the mutual interactions of the magnetic moments are shown to be of secondary importance in this respect. An equation for the anhysteretic or ideal magnetization curve is derived based on a mean field approximation and this is shown to be dependent on the mutual interactions of the moments but independent of impedances such as pinning. The introduction of a term which measures the impedance to changes in magnetization leads to a simple differential equation of state for a ferromagnet which exhibits all the features of hysteresis. Some modifications of the simple model are necessary in order to bring the solution closer to the real situation. Results are presented which show all the features of hysteresis such as initial magnetization curve, major hysteresis loops, and minor hysteresis loops in excellent agreement with experimental results.

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