  In the chiral symmetric phase, the polarized instanton--anti-instanton
molecule pairing induces a nontrivial repulsive interaction in the iso-scalar
axial-vector channel. As a consequence, one unusual property is observed that
in the chiral restoration phase, there is a first order phase transition for
the spontaneous generation of local CP violation and chiral imbalance.
Furthermore, it is found that external magnetic fields will lower the critical
temperature for the local CP-odd phase transition and catalyze the chiral
imbalance, which destroys the chiral condensate with pairing quarks between
different chiralities. A reasonable strength of the repulsive interaction in
the iso-scalar axial-vector channel can naturally explain the inverse magnetic
catalysis around the critical temperature under external magnetic fields.
