  We have studied the moment correlations within triangular lattice arrays of
single-domain co-aligned nanoscale ferromagnetic islands. Independent variation
of lattice spacing along and perpendicular to the island axis tunes the
magnetostatic interactions between islands through a broad range of relative
strengths. For certain lattice parameters, the sign of the correlations between
near-neighbor island moments is opposite to that favored by the pair-wise
interaction. This finding, supported by analysis of the total correlation in
terms of direct and convoluted indirect contributions across multiple pairwise
interactions, indicates that indirect interactions and/or those mediated by
further neighbors can be tuned to be dominant, with implications for the wide
range of systems composed of interacting nanomagnets.
