  Artificial spin ice systems have opened experimental windows into a range of
model magnetic systems through the control of interactions among nanomagnet
moments. This control has previously been enabled by altering the nanomagnet
size and the geometry of their placement. Here we demonstrate that the
interactions in artificial spin ice can be further controlled by including a
soft ferromagnetic underlayer below the moments. Such a substrate also breaks
the symmetry in the array when magnetized, introducing a directional component
to the correlations. Using spatially resolved magneto-optical Kerr effect
microscopy to image the demagnetized ground states, we show that the
correlation of the demagnetized states depends on the direction of underlayer
magnetization. Further, the relative interaction strength of nearest and
next-nearest neighbors varies significantly with the array geometry. We exploit
this feature to induce frustration in an inherently unfrustrated square lattice
geometry, demonstrating new possibilities for effective geometries in two
dimensional nanomagnetic systems.
