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

Abstract

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 Pt2Co(Fe) cluster on graphene. For the mixed tetramers the strong magnetism stabilizes a flat geometric structure, except for Pt3Co 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 Pt3Co 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 Pt3Fe/graphene because of the asymmetric structure of the adsorption complex. The barriers against magnetization reversal range between only 0.3 meV/atom for Pt3Fe/graphene and about 3 meV/atom for PtFe3 and Pt3Co. 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.