  We calculate the effective potential of a strong magnetic field induced by
fermions with anomalous magnetic moments which couple to the electromagnetic
field in the form of the Pauli interaction. For a uniform magnetic field, we
find the explicit form of the effective potential. It is found that the
non-vanishing imaginary part develops for a magnetic field stronger than a
critical field and has a quartic form which is quite different from the
exponential form of the Schwinger process. We also consider a linear magnetic
field configuration as an example of inhomogeneous magnetic fields. We find
that the imaginary part of the effective potential is nonzero even below the
critical field and shows an exponentially decreasing behavior with respect to
the inverse of the magnetic field gradient, which is the non-perturbative
characteristics analogous to the Schwinger process. These results imply the
instability of the strong magnetic field to produce fermion pairs as a purely
magnetic effect. The possible applications to the astrophysical phenomena with
strong magnetic field are also discussed.
