Magnetic properties of small Pt-capped Fe, Co and Ni clusters: A density functional theory study

Theoretical studies on M$_{13}$ (M = Fe, Co, Ni) and M$_{13}$Pt$_n$ (for $n$ = 3, 4, 5, 20) clusters including the spin-orbit coupling are done using density functional theory. The magnetic anisotropy energy (MAE) along with the spin and orbital moments are calculated for M$_{13}$ icosahedral clusters. The angle-dependent energy differences are modelled using an extended classical Heisenberg model with local anisotropies. From our studies, the MAE for Jahn-Teller distorted Fe$_{13}$, Mackay distorted Fe$_{13}$ and nearly undistorted Co$_{13}$ clusters are found to be 322, 60 and 5 $\mu$eV/atom, respectively, and are large relative to the corresponding bulk values, (which are 1.4 and 1.3 $\mu$eV/atom for bcc Fe and fcc Co, respectively.) However, for Ni$_{13}$ (which practically does not show relaxation tendencies), the calculated value of MAE is found to be 0.64 $\mu$eV/atom, which is approximately four times smaller compared to the bulk fcc Ni (2.7 $\mu$eV/atom). In addition, MAE of the capped cluster (Fe$_{13}$Pt$_4$) is enhanced compared to the uncapped Jahn-Teller distorted Fe$_{13}$ cluster.