Artificial spin (and Potts) ice of skyrmions in liquid crystals

Artificial spin ices [1] are engineered arrays of mutually interacting, frustrated, single domain magnetic nano-islands that can be characterized at the degree of freedom level and designed in different arrangements for different emergent behaviors [2]. Beyond magnets, similar ideas have been exported to trapped colloids [3] and vortices in pinned superconductors [4]. In this work, we present a proposal to realize them in a new platform: Liquid crystals. Liquid Crystals possess various advantages as a spin ice platform. Skyrmions in liquid crystals [5], can be confined in traps made of light or field gradients where their preferential position in the trap can mimic a binary Ising spin or a Potts variable. By solving partial differential equations for chiral nematic liquid crystals in the presence of constraints, we demonstrate that skyrmions can reproduce the ice-state of square ice and honeycomb ice. We then extend these simulations to Potts systems.

[1] C. Nisoli et al., Rev. Mod. Phys. 85, 1473 (2013)
[2] Muir J Morrison et al., New Journal of Physics, 15(4):045009 (2013)
[3] A. Libal, C. Reichhardt et al., Phys. Rev. Lett., 97(22):228302, (2006)
[4] A. Libal, C. Reichhardt et al., Phys. Rev. Lett., 102(23):237004 (2009)
[5] Paul J. Ackerman et al., Phys. Rev. E 90, 012505 (2014)