Exact asymptotic behavior of magnetic stripe domain arrays

The classical problem of magnetic stripe domain behavior in films and plates with uniaxial magnetic anisotropy is treated. Exact analytical results are derived for the stripe domain widths as function of applied perpendicular field, $H$, in the regime where the domain period becomes large. The stripe period diverges as $(H_c-H)^{-1/2}$, where $H_c$ is the critical (infinite period) field, an exact result confirming a previous conjecture. The magnetization approaches saturation as $(H_c-H)^{1/2}$, a behavior which compares excellently with experimental data obtained for a $4 μ$m thick ferrite garnet film. The exact analytical solution provides a new basis for precise characterization of uniaxial magnetic films and plates, illustrated by a simple way to measure the domain wall energy. The mathematical approach is applicable for similar analysis of a wide class of systems with competing interactions where a stripe domain phase is formed.

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