  Two-dimensional crystals of trapped ions are a promising system with which to
implement quantum simulations of challenging problems such as spin frustration.
Here, we present a design for a surface-electrode elliptical ion trap which
produces a 2-D ion crystal and is amenable to microfabrication, which would
enable higher simulated coupling rates, as well as interactions based on
magnetic forces generated by on-chip currents. Working in an 11 K cryogenic
environment, we experimentally verify to within 5% a numerical model of the
structure of ion crystals in the trap. We also explore the possibility of
implementing quantum simulation using magnetic forces, and calculate J-coupling
rates on the order of 10^3 / s for an ion crystal height of 10 microns, using a
current of 1 A.
