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

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