Interplay of Stacking, Structural Relaxation, and Exchange Coupling in the Magnetic Anisotropy of Cr-capped Co5/Pd(111) Ultrathin Films Near a Spin-Reorientation Transition

We present a first-principles study of Cr-capped Co5/Pd(111) ultrathin films in the near-compensated regime where Co stacking, structural relaxation, and Cr–Co exchange coupling compete on comparable energy scales and jointly determine the magnetic anisotropy. Three representative Co growth stackings are considered: pure fcc, hcp-rich, and mixed fcc+hcp. The hcp-rich stacking is found to be the lowest-energy structure and the most favorable configuration for approaching perpendicular magnetic anisotropy (PMA). We find that the magnetocrystalline anisotropy (MCA) of the non-relaxed films remains in-plane, whereas structural relaxation strongly suppresses the in-plane anisotropy and brings the system close to the spin-reorientation transition (SRT). Within PBE and the magnetic-force-theorem approach, antiferromagnetic Cr–Co coupling shifts the anisotropy toward the perpendicular side and yields the largest positive MCA for the relaxed hcp-rich film. The inclusion of moderate on-site Coulomb corrections through the Ueff parameter further shows that the hcp-rich AF configuration remains the structural ground state, but reveals that the Cr–Co exchange-energy scale and the precise balance between magnetocrystalline and shape anisotropy are Ueff-dependent. Within PBE, inclusion of the dipolar shape-anisotropy term keeps all configurations effectively in-plane. More generally, the results identify Cr/Co5/Pd(111) as a correlation-sensitive system close to a spin-reorientation boundary, rather than as either a universally in-plane film or a robust PMA state. Layer- and k-resolved analyses reveal that this near compensation originates from a competition between buried and middle Co layers, which favor in-plane magnetization, and the upper Pd region, the top Co layer beneath Cr, and the Cr cap, which favor the out-of-plane direction. In reciprocal space, the MCA is governed by the cancellation of positive and negative finite-k hot spots rather than by states near the Γ-point. Fully self-consistent spin–orbit calculations show that the relaxed AF configurations are especially fragile: the frozen-potential approximation overestimates the tendency toward perpendicularity and can even reverse the direction of the easy-axis. Our results identify the relaxed hcp-rich AF Cr/Co5/Pd(111) film as the closest precursor to robust PMA and establish stacking, relaxation, and interfacial exchange as key control parameters for tuning Cr/Co/Pd-based films across the SRT.