Symmetry-Broken Magneto-toroidal Artificial Spin Ice

Artificial Spin Ices (ASIs) are periodic arrangements of magnetostatically interacting nanomagnets that exhibit geometric frustration by design [1]. We investigate magneto-toroidal ASIs (MT-ASIs) where plaquettes of two adjacent nanomagnets are arranged in a square geometry. The possible revolving magnetization within each sub-lattice can define a toroidal moment so that the long-range order can exhibit ferrotoroidicity [2]. However, the magnetization states are degenerate. Here, we induce symmetry-breaking that considering a smaller nanoisland in the plaquette. From micromagnetic simulations, we find magnetic field protocols to access the four available magnetization states. We also use Gænice, a computational tool for arbitrary ASIs [3], to investigate the band structures in MT-ASIs. We find relatively flat bands due to the reduced dipolar coupling and the development of small band gaps. Despite the possible ferrotoroidicity, a topological analysis of the band structure indicates that the bands have zero Chern number. Our results show that MT-ASIs can be reconfigured in four different states with characteristic frequencies differing on the order of GHz.

References:

[1] S. H. Skjærvø et al., Nat. Rev. Phys. 2, 13 – 28 (2020)

[2] J. Lehmann, C. Donnelly, and P.M. Derlet, Nature Nanotech 14, 141144 (2019)

[3] G. Alatteili, V. Martinez, A. Roxburgh, J. C. Gartside, O. G. Heinonen, Sebastian Gliga, E. Iacocca, Journal of Magnetism and Magnetic Materials 589, 171603 (2024)