  We consider the different structures that a magnetic nanowire adsorbed on a
surface may adopt under the influence of external magnetic or electric fields.
First, we propose a theoretical framework based on an Ising-like extension of
the 1D Frenkel-Kontorova model, which is analysed in detail using the transfer
matrix formalism, determining a rich phase diagram displaying structural
reconstructions at finite fields and an antiferromagnetic-paramagnetic phase
transition of second order. Our conclusions are validated using ab initio
calculations with density functional theory, paving the way for the search of
actual materials where this complex phenomenon can be observed in the
laboratory.
