Curvature effects on phase transitions in chiral magnets

Periodical ground states of magnetization exist in chiral ferromagnetic films, if the constant of Dzyaloshinsii-Moriya interaction (DMI) exceeds some critical value $d_0$. Here, we demonstrate that $d_0$ can be significantly modified in curved film. As a case study, we consider tubular geometry of films with an easy axis anisotropy oriented normally to the film. For two different types of DMI we build phase diagrams of ground states for a wide region of the curvatures and DMI strengths. The periodical state of the tube can be considered as a sequence of domain walls (DW), similarly to the case of a planar film. However, in the presence of the curvature, the competition between DMI and exchange can lead to a new type of DW which is inclined with respect to the cylinder axis and possesses a structure which is intermediate between Bloch and Neel DW structures. The exact analytical solution for the new DW is obtained. All analytical calculations are confirmed by numerical simulations.