Magnetocrystalline anisotropy energy of Fe$(001)$, Fe$(110)$ slabs and nanoclusters: a detailed local analysis within a tight-binding model

We report tight-binding (TB) calculations of magnetocrystalline anisotropy energy (MAE) of Iron slabs and nanoclusters with a particuler focus on local analysis. After clarifying various concepts and formulations for the determination of MAE, we apply our realistic TB model to the analysis of the magnetic anisotropy of Fe$(001)$, Fe$(110)$ slabs and of two large Fe clusters with $(001)$ and $(110)$ facets only: a truncated pyramid and a truncated bipyramid containg 620 and 1096 atoms, respectively. It is shown that the MAE of slabs originates mainly from outer layers, a small contribution from the bulk gives rise, however, to an oscillatory behavior for large thicknesses. Interestingly, the MAE of the nanoclusters considered is almost solely due to $(001)$ facets and the base perimeter of the pyramid. We believe that this fact could be used to efficiently control the anisotropy of Iron nanoparticles and could also have consequences on their spin dynamics