A first-principles calculation of the magnetic anisotropy energies of X/Co (X-Pt, Cu, Ag and Au) metallic multilayers has been performed to investigate the effect of strain on the magnetic anisotropy. It is successfully predicted that Pt/Co and Au/Co multilayers exhibit perpendicular magnetic anisotropies in accordance with experiments. The strength of the hybridization of electronic states at the interface determines the relative position of the Fermi energy to the local density of states (LDOS) of |m| = 2 character of Co d electrons of minority spin. If the LDOS of |m| = 2 character is large at the Fermi energy, a system shows a perpendicular anisotropy. The anisotropy energies of all the systems increase as a function of interatomic distance in the in-plane direction. The magneto-elastic constants are more than twice the value of pure Co. The origin of this large value is explained in terms of the change of relative position of the Fermi level to that of the LDOS of |m| = 2 character as the value of strain increases.
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