  We analyse the infinite class of d=3 CFTs dual to skew-whiffed AdS_4 X SE_7
solutions of D=11 supergravity at finite temperature and charge density and in
the presence of a magnetic field. We construct black hole solutions
corresponding to the unbroken phase, and at zero temperature some of these
become dyonic domain walls of an Einstein-Maxwell-pseudo-scalar theory
interpolating between AdS_4 in the UV and new families of dyonic AdS_2 X R^2
solutions in the IR. The black holes exhibit both diamagnetic and paramagnetic
behaviour. We analyse superfluid and striped instabilities and show that for
large enough values of the magnetic field the superfluid instability disappears
while the striped instability remains. For larger values of the magnetic field
there is also a first-order metamagnetic phase transition and at zero
temperature these black hole solutions exhibit hyperscaling violation in the IR
with dynamical exponent z=3/2 and \theta=-2.
