DFT investigation of magnetocrystalline anisotropy in Fe, Co, \(\hbox {Pd}_{0.97}\hbox {Co}_{0.03}\) and \(\hbox {Pd}_{0.97}\hbox {Fe}_{0.03}\) systems: from bulk to thin-films

Abstract

The nature of low-impurity ferromagnetism remains a challenging problem in the solid-state community because of the strong dependence of magnetic properties on composition, concentration, and structural geometry of diluted alloys. To shed light on this complexity, we conducted a comprehensive density functional theory investigation of magnetocrystalline anisotropy in Fe, Co, \(\hbox {Pd}_{0.97}\hbox {Co}_{0.03}\) systems across bulk, monolayer, and thin-film geometries. By employing advanced noncollinear spin–orbit coupling calculations, we accurately evaluated the magnetocrystalline anisotropy energies, complemented by detailed atomic-, spin-, and orbital-resolved density of states analyses. Our findings reveal that Fe and Co exhibit contrasting easy-axis orientations that strongly depend on the system geometry. Remarkably, even a low Co doping level of 3 at.% in Pd is sufficient to drive anisotropy trends closely mirroring those of pure Co. In contrast, Pd–Fe systems at the same concentration do not reproduce the anisotropy of pure Fe, showing isotropic behavior in bulk. These insights offer valuable perspectives on tuning magnetic anisotropy through minimal doping in diluted alloys.