Spin-fluctuation energies in transition-metal clusters

Abstract

A functional-integral theory of itinerant magnetism is applied to $3d$ transition-metal clusters. The low temperature limit of the local spin-fluctuation energies $\ensuremath{\Delta}{F}_{l}(\ensuremath{\xi})$ at different atoms $l$ is determined as a function of the exchange field $\ensuremath{\xi}$ by using a real-space recursive expansion of the local Green's functions. The size, structural, and local-environment dependence of $\ensuremath{\Delta}{F}_{l}(\ensuremath{\xi})$ is calculated for representative examples of ${\mathrm{Fe}}_{N}$ and ${\mathrm{Ni}}_{N}$ clusters with $N\ensuremath{\leqslant}51$ atoms. The interplay between fluctuations of the module and of the relative orientation of the local magnetic moments is analyzed. Module fluctuations generally dominate in the case of ${\mathrm{Ni}}_{N}$, while $\mathrm{Fe}$ clusters show a stronger tendency to local moment reversals. A remarkable dependence of the spin-excitation spectrum on the local atomic environment and on interatomic bond-length relaxations is revealed. The transition from simple spin flips to module fluctuations of the local exchange fields is discussed as a function of cluster size.