  We have calculated the explicit form of the real and imaginary parts of the
effective potential for uniform magnetic fields which interact with spin-1/2
fermions through the Pauli interaction. It is found that the non-vanishing
imaginary part develops for a magnetic field stronger than a critical field,
whose strength is the ratio of the fermion mass to its magnetic moment. This
implies the instability of the uniform magnetic field beyond the critical field
strength to produce fermion pairs with the production rate density
$w(x)=\frac{m^{4}}{24\pi}(\frac{|\mu B|}{m}-1)^{3}(\frac{|\mu B|}{m}+3)$ in the
presence of Pauli interaction.
