  We investigate the QCD magnetic susceptibility chi at the finite
quark-chemical potential (mu>0) and at zero temperature (T=0) to explore the
pattern of the magnetic phase transition of the QCD vacuum. For this purpose,
we employ the nonlocal chiral quark model derived from the instanton vacuum in
the presence of the chemical potential in the chiral limit. Focusing on the
Nambu-Goldstone phase, we find that the magnetic susceptibility remains almost
stable to mu~200 MeV, and falls down drastically until the the quark-chemical
potential reaches the critical point mu_c~320 MeV. Then, the strength of the
chi is reduced to be about a half of that at mu=0, and the first-order magnetic
phase transition takes place, corresponding to the chiral restoration. From
these observations, we conclude that the response of the QCD vacuum becomes
weak and unstable to the external electromagnetic field near the critical
point, in comparison to that for vacuum. It is also shown that the breakdown of
Lorentz invariance for the magnetic susceptibility, caused by the finite
chemical potential, turns out to be small.
