  The QCD phase diagram is studied, at finite magnetic field. Our calculations
are based on the QCD effective model, the SU($3$) Polyakov linear sigma model
(PLSM), in which the chiral symmetry is integrated in the hadron phase and in
the parton phase, the up-, down- and strange-quark degrees of freedom are
incorporated besides the inclusion of Polyakov loop potentials in the pure
gauge limit, which are motivated by various underlying QCD symmetries. The
Landau quantization and the magnetic catalysis are implemented. The response of
the QCD matter to an external magnetic field such as magnetization, magnetic
susceptibility and permeability has been estimated. We conclude that the parton
phase has higher values of magnetization, magnetic susceptibility, and
permeability relative to the hadron phase. Depending on the contributions to
the Landau levels, we conclude that the chiral magnetic field enhances the
chiral quark condensates and hence the chiral QCD phase diagram, i.e. the
hadron-parton phase transition likely takes place, at lower critical
temperatures and chemical potentials.
