On the interplay between geometrical structure and magnetic anisotropy: a relativistic density-functional study of mixed Pt–Co and Pt–Fe trimers and tetramers in the gas-phase and supported on graphene

The structural and magnetic properties of mixed Pt-Co and Pt-Fe trimers and tetramers in the gas-phase and supported on a free-standing graphene layer have been calculated using density-functional theory. The influence of the strong magnetic moments of the 3d atoms on the Pt atoms and the influence of the strong spin-orbit coupling contributed by the Pt atoms on the 3d atoms have been studied in detail. All mixed trimers form isocele triangles in the gas-phase. On a graphene layer the structure is influenced by the strong binding of the 3d atoms, leading to an asymmetric configuration for Pt-rich and more symmetric structures for 3d-rich clusters. The magnetic anisotropy energy defined as the energy difference for easy and hard magnetization directions varies between 5 and 13 meV/atom for the free trimers, but is strongly reduced to values between 0.7 and 6.6 meV/atom for the graphene-supported clusters. The saddle-point energy representing the barrier against magnetization reversal is on average 3 meV/atom for free trimers, it is reduced to 2 meV/atom for the more symmetric PtCo(Fe)(2) clusters, and to only about 0.3 meV/atom for the asymmetric Pt(2)Co(Fe) cluster on graphene. For the mixed tetramers the strong magnetism stabilizes a flat geometric structure, except for Pt(3)Co which forms a distorted trigonal pyramid. The geometry of the graphene-supported tetramers is very different due to the requirement of a good match to the substrate. Large magnetic anisotropy energies are found for free Pt(3)Co where the change of the magnetization direction also induces a transition from a high- to a low-moment magnetic isomer. For all other free tetramers the magnetic anisotropy energy ranges between 3 to 5 meV/atom only, it is further reduced to 0.4 to 3.8 meV/atom for the graphene-supported tetramers. The reduction is strongest for Pt(3)Fe/graphene because of the asymmetric structure of the adsorption complex. The barriers against magnetization reversal range between only 0.3 meV/atom for Pt(3)Fe/graphene and about 3 meV/atom for PtFe(3) and Pt(3)Co. Altogether our results demonstrate a strong correlation between the geometric and magnetic degrees of freedom and the necessity to base investigations of the magnetic anisotropy of nanostructures on a simultaneous optimization of the total energy with respect to all geometric and magnetic parameters.