  At low temperature, information can be stored in the orientation of the
localized magnetic moment of an adatom. However, scattering of electrons and
phonons with the nanomagnet leads its state to have incoherent classical
dynamics and might cause fast loss of the encoded information. Recently, it has
been understood that such scattering obeys certain selection rules due to the
symmetries of the system. By analyzing the point-group symmetry of the surface,
the time-reversal symmetry and the magnitude of the adatom effective spin, we
identify which nanomagnets configurations are to be avoided and which are
promising to encode a stable bit. A new tool of investigation is introduced and
exploited: the quasi-spin quantum number. By means of this tool, our results
are easily generalized to a broad class of bipartite cluster configurations
where adatoms are coupled through Heisenberg-like interactions. Finally, to
make contact with the experiments, numerical simulations have been performed to
show how such stable configurations respond to typical scanning tunneling
microscopy measurements.
