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The effects on the ferromagnetism of a nitrogen defect in Cu-doped AlN with a Cu concentration of 2.77-8.33% have been investigated by first-principles. For AI0.9723Cu0.0277N, a global magnetic moment of 1.46 μB/cell with a localized magnetic moment of 0.75 μB/Cu is found. The formation of Cu-Cu in AlN with the N vacancy (VN) is more energetically favorable than that without the VN. Hence, the Cu + VN state is produced easily. The Cu magnetic moment of Cu-Cu pair becomes very low by the weak 3d-3d spin coupling due to the spin-exchange interaction between Cu-3d and N defect states.