  Millisecond pulsars are old, fast spinning neutron stars thought to have
evolved from classical pulsars in binary systems, where the rapid rotation is
caused by the accretion of matter and angular momentum from their companion.
During this transition between classical and millisecond pulsars, there is a
magnetic field reduction of around 4 orders of magnitude, which is not well
understood. According to the standard scenario, the magnetic field is reduced
as a consequence of accretion, either through ohmic dissipation or through
screening by the accreted matter. We explored an alternative hypothesis in
which the magnetic field is reduced through ambipolar diffusion before the
accretion. This is particularly effective during the long epoch in which the
pulsar has cooled, but has not yet started accreting. This makes the final
magnetic field dependent on the evolution time of the companion star and thus
its initial mass. We use observed binary systems to constrain the time
available for the magnetic field decay based on the current pulsar companion: a
helium white dwarf, a carbon-oxygen white dwarf, or another neutron star. Based
on a simplified model without baryon pairing, we show that the proposed process
agrees with the general distribution of observed magnetic field strengths in
binaries, but is not able to explain some mildly recycled pulsars where no
significant decay appears to have occurred. We discuss the possibility of other
formation channels for these systems and the conditions under which the
magnetic field evolution would be set by the neutron star crust rather than the
core.
