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The theory of cylindrical magnetic domains provides conditions governing the size and stability of circular cylindrical magnetic domains in plates of uniaxial magnetic materials together with an estimate of the range of applicability of these conditions. The results of the theory are directly applicable to the design of cylindrical domain devices. Computation to first and second order of the energy variation resulting from general small deviation in the domain shape from an initially circular shape yields the conditions governing domain size and stability. The physical origin of the various terms in the energy expansion is examined in detail. A graph from which many domain size and stability properties may be obtained summarizes the results of the energy variation calculation. The minimum theoretically attainable domain diameter is approximately σw/πMs2, where σw is the wall energy density and Ms is the saturation magnetization. For domains to exist, the effective anisotropy field must be greater than 4πMs.

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.

This paper extends the theory of magnetic domains with emphasis on recent developments in ``hard bubbles''. A spin configuration of a planar Bloch wall containing periodic Bloch lines is presented which minimizes the magnetostatic energy to first order in the parameter 2πMs2/Ku for arbitrary period. The form of this solution is found to suggest the form of the dynamic breakdown of this spin configuration. The remainder of the paper consists of applications of the gyrocoupling force and vector, fg = g × v and g = − (Ms/|γ|)sinθ(▿θ) × (▿φ), respectively, and the dissipation force and dyadic, fa = d · v and d = − α(Ms/|γ|)[(▿θ)(▿θ) + sin2θ(▿φ)(▿φ)]. The use of fg and fa produces results with fewer assumptions and with less calculation than with previous methods. The magnitude of g is found to be an invariant local measure of the ``hardness'' of the domains. Integrating fg and fα produces a general planar wall response function from which the hard bubble dynamic equation is obtained. It is found that the difference between the hard bubble and normal bubble damping parameters can be accounted for by examination of the hard bubble spin-wave spectrum. An estimate of the velocity required for the production of horizontal Bloch lines is made using fg. This velocity is a substantial fraction of the Walker velocity. The vector g is used as an aid in the visualization of the mechanism by which ion implantation suppresses hard bubbles. From the point of view of both mobility and hard bubble suppression, materials having a large in-plane anisotropy are found to be desirable.

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