The saturated magnetic field of the neutron stars

Considering the ferromagnetic screening for the decay of the X-ray neutron star magnetic field in the binary accretion phase, the phase transition of ferromagnetic materials in the crust of neutron star induces the ferromagne tic screening saturation of the accreted crust, which results in the minimu m surface magnetic field of the accreting neutron star, about 10(8) G, if t he accreted matter has completely replaced the crust mass of the neutron st ar. The magnetic field evolution versus accreted mass is given as B-s propo rtional to Delta M-0.9, and the obtained magnetic field versus spin period relation is consistent with the distribution of the binary X-ray sources an d recycled pulsars. The further thermal effect on the magnetic evolution is also studied.