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<p>Curved and topologically nontrivial magnetic structures offer new pathways to control spin-wave behavior beyond planar geometries. Here, we study spin-wave dynamics in Möbius-shaped soft-magnetic nanostrips using micromagnetic simulations. By comparing single-, double-, and triple-twisted Möbius strips to a topologically trivial bent ring, we isolate the roles of helical twist and non-orientable topology. Möbius geometries exhibit non-degenerate mode doublets associated with counterpropagating spin waves, in contrast to the standing-wave doublets in the trivial case. This splitting arises from a twist-induced geometric (Berry) phase that breaks propagation symmetry, producing non-reciprocal dispersion relations. The Möbius topology further imposes antisymmetric boundary conditions, resulting in half-integer wavelength quantization. Local RF excitation allows for the selective generation of spin waves with defined frequency and propagation direction. An analytical model reproduces the dispersion behavior with excellent agreement. These results highlight how geometric and topological design can be leveraged to engineer spin-wave transport in three-dimensional magnonic systems.</p>

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Rotating spin wave modes in nanoscale Möbius strips

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月27日

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  • Ashfaque Thonikkadavan,
  • Massimiliano d’Aquino,
  • Riccardo Hertel

摘要

Curved and topologically nontrivial magnetic structures offer new pathways to control spin-wave behavior beyond planar geometries. Here, we study spin-wave dynamics in Möbius-shaped soft-magnetic nanostrips using micromagnetic simulations. By comparing single-, double-, and triple-twisted Möbius strips to a topologically trivial bent ring, we isolate the roles of helical twist and non-orientable topology. Möbius geometries exhibit non-degenerate mode doublets associated with counterpropagating spin waves, in contrast to the standing-wave doublets in the trivial case. This splitting arises from a twist-induced geometric (Berry) phase that breaks propagation symmetry, producing non-reciprocal dispersion relations. The Möbius topology further imposes antisymmetric boundary conditions, resulting in half-integer wavelength quantization. Local RF excitation allows for the selective generation of spin waves with defined frequency and propagation direction. An analytical model reproduces the dispersion behavior with excellent agreement. These results highlight how geometric and topological design can be leveraged to engineer spin-wave transport in three-dimensional magnonic systems.