#### Abstract

We have undertaken theoretical studies of spin and orbital magnetic moments as well as magnetic anisotropy energies for ${M}_{13}$ $\left(M=\text{Fe},\text{Co},\text{Ni}\right)$ and ${M}_{13}{\text{Pt}}_{n}$ $\left(n=3,4,5,20\right)$ clusters including the spin-orbit coupling in the framework of density functional theory. For all ${M}_{13}$ clusters considered we find tendencies for small structural distortions which can be characterized by either Jahn-Teller (JT) or Mackay transformations (MT). The magnetic anisotropy energy (MAE) along with the spin and orbital moments are calculated for ${M}_{13}$ icosahedral clusters and the angle-dependent energy differences are modeled using a Néel model with local anisotropies. From our studies, the MAE for JT-distorted ${M}_{13}$ clusters are found to be larger relative to the MT clusters and more than two orders of magnitude larger compared to the corresponding bcc or fcc bulk values. In addition, we demonstrate for one example that Pt capping may further enhance the MAE compared to the uncapped JT- and the Mackay-distorted ${\text{Fe}}_{13}$ cluster.

DOI: http://dx.doi.org/10.1103/PhysRevB.82.054418

5 More- Received 21 May 2010
- Revised 15 July 2010
- Published 13 August 2010

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