  The amplification of magnetic fields plays an important role in explaining
numerous astrophysical phenomena associated with binary neutron-star mergers,
such as mass ejection and the powering of short gamma-ray bursts. Magnetic
fields in isolated neutron stars are often assumed to be confined to a small
region near the stellar surface, while they are normally taken to fill the
whole stars in the numerical modelling. By performing high-resolution, global,
and high-order general-relativistic magnetohydrodynamic simulations we
investigate the impact of a purely crustal magnetic field and contrast it with
the standard configuration consisting of a dipolar magnetic field with the same
magnetic energy but filling the whole star. While the crust-configurations are
very effective in generating strong magnetic fields during the
Kelvin-Helmholtz-instability stage, they fail to achieve the same level of
magnetic-field amplification of the full-star configurations. This is due to
the lack of magnetized material in the neutron-star interiors to be used for
further turbulent amplification and to the surface losses of highly magnetized
matter in the crust-configurations. Hence, the final magnetic energies in the
two configurations differ by more than one order of magnitude. We briefly
discuss the impact of these results on astrophysical observables and how they
can be employed to deduce the magnetic topology in merging binaries.
