Theory of the Static Stability of Cylindrical Domains in Uniaxial Platelets

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Abstract
A theory of the static stability of circular cylindrical domains in uniaxial magnetic platelets has been developed. The predictions of the theory agree well with experiments and provide requirements which link material properties to domain geometry. The theory is developed by assuming a model in which the domains have cylindrical walls of zero width and by then calculating the size and stability of the domains, using a straightforward although somewhat lengthy energy method. It is found that in order for domains to exist Ku⪞2πMs2, where Ku is the uniaxial anisotropy constant and Ms is the saturation magnetization. However, the model is most accurate when Ku≫2πMs2, although in this case the domains tend to have a low mobility. A formula relating domain size to the material parameters, the plate thickness and the applied bias field is obtained. More important, static stability considerations indicate that when all parameters except the bias field are held constant the domains are stable only over a 3:1 diameter range and at best a 1.6:1 bias field range. Cylindrical domains are found to be most stable for device applications when the domain radius is equal to the plate thickness which is in turn approximately equal to σw/πMs2, where σw is the wall energy density.

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