We have fabricated an ultrahigh-vacuum-processed, ordered, single-crystalline nanodot array. By mapping the magnetization of the nanodots with spin polarized scanning tunneling microscopy in the same chamber where they were grown, we are able to understand how the short-range order of the nanodot array is determined by the magnetostatic dipole interaction among neighboring nanodots. We also demonstrate tuning the magnetic interaction in the nanodot array by controlling those magnetic energies. Further magnetic simulations support the observed results consistently.

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