Fluctuations and instabilities of ferromagnetic domain-wall pairs in an external magnetic field

A classical continuum model of an effectively one-dimensional ferromagnet will exchange and anisotropies of hard and easy-axis type is considered. In the presence of an external magnetic field along the easy axis, the lowest-lying topological excitations are shown to be untwisted or twisted pairs of π-domain walls. The fluctuations around these structures are investigated. It is shown that the fluctuations around the twisted and untwisted domain-wall pair are governed by the same set of operators. The untwisted domain-wall pair has exactly one unstable mode and thus represents a critical nucleus for magnetization reversal in effectively one-dimensional systems. The twisted domain-wall pair is stable for small external fields but becomes unstable for large magnetic fields. The former effect is related to thermally induced coercivity reduction in elongated particles while the latter effect is related to ‘‘chopping’’ of twisted Bloch wall pairs in thin films. In view of a statistical mechanical theory of magnetization reversal which will be presented in a separate article, the scattering phase shifts of spin waves around these structures are calculated. The applicability of the present theory to magnetic thin films is discussed. Finally, it is noted that the static properties of the present model are equivalent to those of a nonlinear σ model with anisotropies and an external field.