  We investigate the effect of a magnetic field on the vacuum of
low-temperature QCD at large-N_c in the presence of a chiral chemical
potential, using the holographic Sakai-Sugimoto model. Above some critical
chemical potential we find an instability, which triggers a decay of the
homogeneous vacuum to a non-homogeneous configuration with a spiral form, which
we construct explicitly. We find that this decay is suppressed for sufficiently
large magnetic field, and determine the critical strength. We find that the new
vacuum does not exhibit the chiral magnetic effect. This is related to the way
the chiral chemical potential is introduced. We discuss an alternative way of
introducing the chiral chemical potential that leads to a nonzero chiral
magnetic effect.
