  The recently discovered inverse magnetic catalysis around the critical
temperature indicates that some important information is missing in our current
understanding of conventional chiral dynamics of QCD, which is enhanced by the
magnetic field. In this work, we provide a mechanism to explain that the
inverse magnetic catalysis around the critical temperature is induced by
sphalerons. At high temperatures, sphaleron transitions between distinct
classical vacua cause an asymmetry between the number of right- and left-handed
quarks due to the axial anomaly of QCD. In the presence of a strong magnetic
field, the chiral imbalance is enhanced and destroys the right- and left-handed
pairings, which naturally induces a decreasing critical temperature of the
chiral phase transition for increasing magnetic field. The inverse magnetic
catalysis at finite baryon density, and the critical end point in the presence
of a strong magnetic field is also explored in this work.
