  Individual nuclear spin states can have very long lifetimes and could be
useful as qubits. Progress in this direction was achieved on MgO/Ag(001) via
detection of the hyperfine interaction (HFI) of Fe, Ti and Cu adatoms using
scanning tunneling microscopy (STM). Previously, we systematically quantified
from first-principles the HFI for the whole series of 3d transition adatoms
(Sc-Cu) deposited on various ultra-thin insulators, establishing the trends of
the computed HFI with respect to the filling of the magnetic s- and d-orbitals
of the adatoms and on the bonding with the substrate. Here we explore the case
of dimers by investigating the correlation between the HFI and the magnetic
state of free standing Fe dimers, single Fe adatoms and dimers deposited on a
bilayer of MgO(001). We find that the magnitude of the HFI can be controlled by
switching the magnetic state of the dimers. For short Fe- Fe distances, the
antiferromagnetic state enhances the HFI with respect to that of the
ferromagnetic state. By increasing the distance between the magnetic atoms, a
transition towards the opposite behavior is observed. Furthermore, we
demonstrate the ability to substantially modify the HFI by atomic control of
the location of the adatoms on the substrate. Our results establish the limits
of applicability of the usual hyperfine hamiltonian and we propose an extension
based on multiple scattering processes.
