The Energy and General Translation Force of Cylindrical Magnetic Domains

Magnetic memory and logic devices employing cylindrical domains in uniaxial platelets have recently received considerable attention. 1,2 The theory of the static stability of these domains3 and its application to cylindrical domain devices4'"' have been discussed in previous papers. This paper is concerned with the translational forces acting on the domains and their effect on device performance. * Present address Department of Electrical Engineering, McMaster University, Hamilton, Ontario. 711 712 T H E B E L L SYSTEM TECHNICAL JOURNAL, MARCH 1971 In most device applications, cylindrical domains are propagated by gradients in the applied field.1-2 Cylindrical domains may, however, be propagated by gradients in any of the independent parameters which determine the total domain energy. These parameters are: the applied field, H; the plate thickness, h; the saturation magnetization, M,, ; and the wall energy density, aw . The domain radius, r(>, is not an independent parameter for domains in equilibrium but is determined once the other parameters are specified. The gradients in aw and M,, may be produced by composition gradients, strain gradients or temperature gradients. Composition or thickness gradients may be used to provide forces which are functions of position only, while temperature or strain gradients may be used to provide time variable forces. The translational force is obtained by differentiation of the total domain energy expression with respect to position, under the assumption that the gradients in the domain parameters which produce the translational force are sufficiently small that the domain remains circular and stable; consequently the energy expression remains valid.