Non-local symmetry breaking effects, induced by magnetostatics in curvilinear ferromagnetic shells

We present a micromagnetic theory of curvilinear ferromagnetic shells. We show the appearance of new chiral effects, originating from the magnetostatic interaction. They manifest themselves even in statics and are essentially nonlocal. This is in contrast to conventional Dzyaloshinskii--Moriya interaction (material intrinsic or curvature-induced, stemming from the exchange). The physical origin is in a non-zero mean curvature of a shell and non-equivalence between the top and bottom surfaces of the shell. To describe the new effects, we split a conventional volume magnetostatic charge into two terms: (i) magnetostatic charge, governed by the tangent to the sample's surface, and (ii) geometrical charge, given by the normal component of magnetization and the mean curvature. We classify the interplay between the symmetry of the shell, its local curvature and magnetic textures and apply the proposed formalism to analyse magnetic textures in corrugated shells with perpendicular anisotropy.