Strain-tunable perpendicular magnetic anisotropy in equiatomic Co–Pt: Orbital-resolved design rules from first-principles

Co-Pt alloys are key perpendicular-anisotropy materials for spintronic devices. Using density-functional theory with spin-orbit coupling, we systematically map how the Co:Pt ratio and biaxial strain applied along [001] (fct) and [111] (hcp) govern the magnetic anisotropy energy (MAE). The most robust perpendicular magnetic anisotropy emerges at the equiatomic 1:1 composition, where L1₀ CoPt shows E_MAE≈0.5 meV/atom at zero strain. Under biaxial strain, fct phases display an inverted-parabolic MAE response with a sign change near +2% tensile strain, whereas hcp CoPt maintains positive MAE over the explored strain window with a direct-parabolic trend. Orbital-resolved analysis reveals a competition between Co-driven spin-conserving channels (L_z; Bruno-type behavior) and Pt-dominated spin-flip channels (L_x), accounting for both the composition dependence and the contrasting strain responses. These insights yield practical design rules—keep the equiatomic composition and apply moderate biaxial strain—to maximize PMA and thermal stability, providing guidance for engineering high-density magnetic storage and spin-torque device platforms.