  We calculate the production rate of neutral fermions in linear magnetic
fields through the Pauli interaction. It is found that the production rate is
exponentially decreasing function with respect to the inverse of the magnetic
field gradient, which shows the non-perturbative characteristics analogous to
the Schwinger process. It turns out that the production rate density depends on
both the gradient and the strength of magnetic fields in 3+1 dimension. It is
quite different from the result in 2+1 dimension, where the production rate
depends only on the gradient of the magnetic fields, not on the strength of the
magnetic fields. It is also found that the production of neutral fermions
through the Pauli interaction is a magnetic effect whereas the production of
charged particles through minimal coupling is an electric effect.
