The theory of cylindrical magnetic domains

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 σ
w
/πM
²
s
, where σ
w
is the wall energy density and M
s
, is the saturation magnetization. For domains to exist, the effective anisotropy field must be greater than 4πM
s
.