Magnetic properties of3dtransition-metal nanostructures: Cr and V clusters embedded in bulk Fe

Abstract

The magnetic and electronic properties of ${\mathrm{Cr}}_{N}$ and ${\mathrm{V}}_{N}$ clusters embedded in Fe are determined by using a realistic $\mathrm{spd}$-band Hubbard-like model Hamiltonian. The spin-density distribution is calculated self-consistently in the unrestricted Hartree-Fock approximation. The local magnetic moments $\ensuremath{\mu}(i)$ and the densities of electronic states ${\ensuremath{\rho}}_{i}(\ensuremath{\varepsilon})$ are obtained at different atoms $i$ of the cluster and of the surrounding Fe matrix. For all the studied clusters $(N<~51\mathrm{atoms})$ the interface magnetic coupling between cluster and matrix moments is antiparallel. The $\ensuremath{\mu}(i)$ of Cr or V atoms at the interface are enhanced by the presence of Fe atoms in their first-nearest-neighbor shell. In most cases the Fe moments close to the cluster are slightly reduced. In ${\mathrm{Cr}}_{N}$ the interface $\ensuremath{\mu}(i)$ are often much larger than the Cr bulk moments [e.g., $\ensuremath{\mu}(i)=\ensuremath{-}1.30{\ensuremath{\mu}}_{B}$ for ${\mathrm{Cr}}_{4}$ in Fe]. In ${\mathrm{V}}_{N}$ large $\ensuremath{\mu}(i)$ are induced which decrease as $N$ increases or as we move from the interface to the interior of the cluster [e.g., $\ensuremath{\mu}(i)=\ensuremath{-}1.29{\ensuremath{\mu}}_{B}$ for ${\mathrm{V}}_{4}$ in Fe]. A remarkable interplay between the antiferromagnetism of Cr, the paramagnetism of V, and the ferromagnetism of Fe is obtained. The magnetic order within ${\mathrm{Cr}}_{N}$ $({\mathrm{V}}_{N})$ changes from ferromagnetic to antiferromagnetic for $N>~9$ $(N>~6).$ This results in an interesting size dependence of the cluster electronic density of states.