Generalized auto-oscillator model for arbitrary artificial spin ices

Artificial spin ices (ASIs) are ensembles of geometrically structured, interacting magnetic nano-elements that exhibit frustration as a result of their design [1] and can be considered magnonic crystals [2]. While the magnon band structures in ASIs is rich, it is time consuming to compute numerically [3] and only a few analytical approaches have been presented [4]. Here, we present a generalized semi-analytical model based on a Holstein-Primakoff transformation [5] to compute the band structure of arbitrary ASIs. The numerical model accounts for arbitrary positioning and rotation of nanoislands and returns the full non-local dipole coupling between elements. While the model currently assumes a two-dimensional dispersion, it can be easily extended to three-dimensional ASIs and their full band structure.



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

[2] S. Gliga, E. Iacocca, and O. G. Heinonen, APL Materials 8, 040911 (2020)

[3] E. Iacocca, S. Gliga, and O. G. Heinonen, Phys. Rev. Appl. 13, 044047 (2020)

[4] E. Iacocca et al., Phys. Rev. B 93, 134420 (2016); T. D. Lasnier and G. M. Wysin, Phys. Rev. B 101, 224428 (2020)

[5] A. Slavin and V. Tiberkevich, IEEE Trans. Magn. 45, 1875 – 1918 (2008)