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The magnetic anisotropy of the CoPt top layer on a CoPt/AlN multilayer has been studied. The layered structures were sputter deposited on fused quartz substrates and subsequently annealed at 500 C in a vacuum. CoPt layers are of a disordered fcc structure and highly (111) textured. It has been found that the CoPt top layer is perpendicular magnetic anisotropic and shows an enhanced coercivity in comparison with the bottom CoPt/AlN multilayer. A critical (maximum) thickness of 6 nm is found for the perpendicular anisotropy in the CoPt top layer. The structural results indicate that the CoPt top layer has experienced a tensile strain under a certain thickness. However, when the thickness of the CoPt top layer is above 6 nm, the inplane CoPt lattice parameter begins to decrease as the thickness increases, indicating that the CoPt top layer cannot tolerate the elastic energy and shrinks to release this energy. The simultaneous changes of the magnetic anisotropy and the inplane lattice parameter with the thickness strongly suggest that the thickness-dependent magnetic anisotropy of the CoPt top layer is correlated with the elastic strain through the magnetoelastic effect.