Magnetic Möbius stripe without frustration: Noncollinear metastable states

The recently introduced area of topological magnetism searches for equilibrium structures stabilized by a combination of interactions and specific boundary conditions. Until now, the internal energy of open magnetic chains has been explored. Here, we study the energy landscape of closed magnetic chains with on-site anisotropy coupled with antiferromagnetic exchange and dipolar interactions analytically and numerically. We show that there are many stable stationary states in closed geometries. These states correspond to the noncollinear spin spirals for vanishing anisotropy or to kink solitons for high magnetic anisotropy. Particularly, the noncollinear M\"obius magnetic state can be stabilized at finite temperatures in nonfrustrated rings or other closed shapes with an even number of sites without the Dzyaloshinskii-Moriya interaction. We identify the described configurations with the stable stationary states, which appear due to the finite length of a ring.