  We construct back-reacted asymptotically AdS_4 backgrounds with both electric
and magnetic charge, at finite temperature and chemical potential. The system
consists of a condensed bulk Dirac field hovering over a charged black brane.
We give a detailed microscopic treatment of the bulk fermions, from which we
derive the usual fluid approximations describing the condensate. In the context
of holography, such a gravitational solution is dual to a (2+1)-dimensional CFT
with a U(1) current, at finite density and strong coupling, subjected to a
transverse magnetic field.
