  In this follow-up paper of 1105.2217 we further discuss the occurrence of a
magnetically induced tachyonic instability of the rho meson in the two-flavour
Sakai-Sugimoto model, uplifting two remaining approximations in the previous
paper. That is, firstly, the magnetically induced splitting of the branes is
now taken into account, evaluating without approximations the symmetrized trace
which enters in the non-Abelian Dirac-Born-Infeld (DBI) action. This leads to
an extra mass generating effect for the charged heavy-light rho meson through a
holographic Higgs mechanism. Secondly, we compare the results in the
approximation to second order in the field strength to the results using the
full DBI-action. Both improvements cause an increase of the critical magnetic
field for the onset of rho meson condensation. In addition, the stability in
the scalar sector in the presence of the magnetic field is discussed.
