Virtual magnetic hills to unlock the inner phases of hexagonal colloidal ice

Abstract

We study the low energy states in a hexagonal colloidal ice realized by using repulsive paramagnetic colloids conned by gravity within a honeycomb lattice of traps. In contrast to similar systems featuring optical or topographic double wells, here we introduce eld tunable "virtual" magnetic hills. These hills are created by placing pairs of xed paramagnetic particles close to the semicylindrical traps that contain the interacting, mobile colloids. With this strategy, a single magnetic eld can be used to simultaneously tune the particle pair-interactions and the hill elevation, without losing the trap bistability at any eld strength. We use numerical simulations to explore the rich low energy states of the system. By varying both the relative distance and magnetic content of the xed particles, not only the eects of the rst but also of the second nearest neighbors can be accessed, allowing to reach the inner charge-ordered ice-II phase. Our strategy of controlling the vertex energetics via xed, eld tunable interstitial units may be extended to other geometrically frustrated systems on dierent length scales, including nanoscale spin ice and macroscopic magnetic metamaterials.