Equilibrium shapes of twisted magnetic filaments

It is shown that ferromagnetic filaments with free and unclamped ends undergo buckling instabilities under the action of twist. Solutions of nonlinear equations describing the buckled shapes are found, and it is shown that the transition to the buckled shape is subcritical if the magnetization is parallel to the field and supercritical when the magnetization of the straight filament is opposite to the external field. Solutions with the localized curvature distribution are found in the case of long filaments. The class of solutions corresponding to helices is described, and the behavior of coiled ferromagnetic and superparamagnetic filaments is compared.