  We argue that \Delta L=2 neutrino spin flavor precession, induced by the
primordial magnetic fields, could have a significant impact on the leptogenesis
process that accounts for the baryon asymmetry of the universe. Although the
extra galactic magnetic fields is extremely weak at present time (about 10^{-9}
Gauss), the primordial magnetic filed at the electroweak scale could be quite
strong (of order 10^{17} Gauss). Therefore, at this scale, the effects of the
spin flavor precession are not negligible. We show that the lepton asymmetry
may be reduced by 50% due to the spin flavor precession. In addition, the
leptogenesis will have different feature from the standard scenario of
leptogenesis, where the lepton asymmetry continues to oscillate even after the
electroweak phase transition.
