Magnetic topological textures in nonorientable surfaces

Abstract

Topological magnetic textures confined to two-dimensional (2D) non-orientable manifolds exhibit behaviors absent in planar systems. We investigate bimerons on Möbius surfaces and show that the lack of global orientation alters conservation laws, yielding geometry-dependent topology and dynamics. Micromagnetic simulations reveal that the helical twist and non-orientable geometry reshape the effective topological charge and stabilize chiral configurations imposed by the surface. Under spin-polarized currents, bimerons display unconventional transport: the transverse response is locally reversed or globally suppressed due to charge inversion along the manifold. Moreover, we establish an Aharonov-Bohm effect associated with the magnonic modes of the texture; in particular, the translational Goldstone mode implies that a bimeron on a Möbius strip should exhibit path-dependent quantum interference. These results identify a geometry-driven regime of magnetization dynamics and provide a route to curvature-engineered spintronic functionalities.

Figures (2)

• Figure 1: Magnetization components of a topological bimeron texture (left panels) stabilized on a Möbius surface. The corresponding emergent magnetic field ${B}^{e}_n$, locally perpendicular to the surface, is shown in the right panels at successive times during its evolution.
• Figure 2: Snapshots of the bimeron motion along a Möbius ring (a) and a straight strip with a torsion (b) under a spin-polarized current with $j = -2 \times 10^{12}$ A/m$^2$, and $\alpha = \xi = 0.1$. Panels (I)–(IV) show the magnetization profile at increasing times. Due to the non-orientable topology of the Möbius strip, the bimeron undergoes a continuous reorientation, resulting in a flipped internal structure after one full traversal. (c) Time evolution of the distance between the bimeron’s center of mass and the (initially) outer edge of the Möbius strip under an applied electric current density $j = 2\times 10^{12}$ A/m$^2$, considering that $\xi=0.1$, $P=0.5$, and different values of damping. We observe that, when the skyrmion Hall effect is present ($\alpha\neq \xi$). Depending on whether $\alpha > \xi$ or $\alpha <\xi$, the effective Magnus force initially bends motion towards the inner or the outer edge of the strip, respectively.