  We investigate the density-shear instability in Hall-MHD via numerical
simulation of the full non-linear problem, in the context of magnetar activity.
We confirm the development of the instability of a plane-parallel magnetic
field with an appropriate intensity and electron density profile, in accordance
with analytic theory. We find that the instability also appears for a
monotonically decreasing electron number density and magnetic field, a
plane-parallel analogue of an azimuthal or meridional magnetic field in the
crust of a magnetar. The growth rate of the instability depends on the Hall
properties of the field (magnetic field intensity, electron number density and
the corresponding scale-heights), while being insensitive to weak resistivity.
Since the Hall effect is the driving process for the evolution of the crustal
magnetic field of magnetars, we argue that this instability is critical for
systems containing strong meridional or azimuthal fields. We find that this
process mediates the formation of localised structures with much stronger
magnetic field than the average, which can lead to magnetar activity and
accelerate the dissipation of the field and consequently the production of
Ohmic heating. Assuming a $5\times10^{14}$G magnetic field at the base of
crust, we anticipate that magnetic field as strong as $10^{15}$G will easily
develop in regions of typical size of a few $10^{2}$ meters, containing
magnetic energy of $10^{43}$erg, sufficient to power magnetar bursts. These
active regions are more likely to appear in the magnetic equator where the
tangential magnetic field is stronger.
