Self-assembled magnetic nanostructures of

$\chem{CoPt_{3}}$(111) nanostructures, prepared by self-assembled growth on $\chem{WSe_{2}}$(0001) substrates, present a 111-oriented fcc structure with a hexagonal island shape and a relatively narrow size distribution. $\chem{L1_{2}}$-type ordering is already observed in nanostructures grown at 150$\un{{}^{\circ}C}$, a temperature considerably lower than that required to order $\chem{CoPt_{3}}$ continuous films. This change is attributed to the nanoscopic island shape, which increases the possibilities of surface atomic arrangements provided by the different growing facets. From the superparamagnetic behavior of the nanostructures, a strong decrease of magnetic anisotropy with the occurrence of $\chem{L1_{2}}$ ordering is deduced