Classical Stern-Gerlach profiles ofMn5andMn6clusters

Abstract

${\mathrm{Mn}}_{5}$ and ${\mathrm{Mn}}_{6}$ clusters have recently been found to exhibit Stern-Gerlach profiles marked by a central peak that broadens with the increasing field gradient. The profiles neither exhibit a reminiscence of space quantization as observed through a splitting of beams for the case of free atoms, nor a net deflection characteristic of superparamagnetic relaxations observed in other transition metal clusters. It is proposed that this new behavior results from a weak coupling of localized atomic moments. ab initio electronic structure studies are carried out to show that a ${\mathrm{Mn}}_{5}$ cluster has isomers with spin magnetic moments of $3\phantom{\rule{0.3em}{0ex}}{\ensuremath{\mu}}_{\mathrm{B}}$, $13\phantom{\rule{0.3em}{0ex}}{\ensuremath{\mu}}_{\mathrm{B}}$, and $23\phantom{\rule{0.3em}{0ex}}{\ensuremath{\mu}}_{\mathrm{B}}$ while a ${\mathrm{Mn}}_{6}$ cluster has isomers with moments of $2\phantom{\rule{0.3em}{0ex}}{\ensuremath{\mu}}_{\mathrm{B}}$, $8\phantom{\rule{0.3em}{0ex}}{\ensuremath{\mu}}_{\mathrm{B}}$, $16\phantom{\rule{0.3em}{0ex}}{\ensuremath{\mu}}_{\mathrm{B}}$, and $26\phantom{\rule{0.3em}{0ex}}{\ensuremath{\mu}}_{\mathrm{B}}$, respectively. The isomers can be obtained by sequential turning of the local atomic moments starting from the ferromagnetic state and can be seen in the negative ion photoelectron spectra of the anions. The weak coupling of the atomic moments, however, leads to unconventional spin dynamics that result in classical broadening of the Stern-Gerlach profiles and lower apparent magnetic moments. The theoretical results illustrate how a combination of the negative ion photodetachment spectroscopy and Stern-Gerlach profiles can provide information on the net spin moment, interatomic spin coupling, and spin dynamics.