  Organometallic clusters based on transition metal atoms are interesting
because possible applications in spintronics and quantum information. In
addition to the enhanced magnetism at the nanoscale, the organic ligands may
provide a natural shield again unwanted magnetic interactions with the matrices
required for applications. Here we show that the organic ligands may lead to
non-collinear magnetic order as well as the expected quenching of the magnetic
moments. We use different density functional theory (DFT) methods to study the
experimentally relevant three cobalt atoms surrounded by benzene rings
(Co$_3$Bz$_3$). We found that the benzene rings induce a ground state with
non-collinear magnetization, with the magnetic moments localized on the cobalt
centers and lying on the plane formed by the three cobalt atoms. We further
analyze the magnetism of such a cluster using an anisotropic Heisenberg model
where the involved parameters are obtained by a comparison with the DFT
results. These results may also explain the recent observation of null magnetic
moment of Co$_3$Bz$_3^+$. Moreover, we propose an additional experimental
verification based on electron paramagnetic resonance.
