Spin-orbit effects on the structural, homotop, and magnetic configurations of small pure and Fe-doped Pt clusters

We report ab initio calculations of the atomic and electronic structures, and related magnetic properties of platinum clusters of seven atoms both pure and substitutionally doped with an iron impurity. A relativistic Hamiltonian including spin-orbit coupling effects is self-consistently solved in the noncollinear framework within the density functional theory as implemented in the VASP code. We show that spin-orbit coupling is crucial for determining the energetic order of structural isomers of small platinum clusters, but not for the low-lying iron-doped platinum clusters. We analyze the influence of Fe doping on the overall improvement of the magnetic efficiency of the nanoparticle, i.e., large total moment and high stability against remagnetization. Results are reported for the spin-orbit energy, the magnetic anisotropy energy corresponding to the remagnetization barrier, and the orbital contribution to the total magnetic moment, which can be experimentally measured in free-standing clusters by means of X-ray magnetic circular dichroism spectroscopy.