  Study of observed spin evolution of long-period X-ray pulsars challenges
quasi-spherical and Keplerian disk accretion scenarios. It suggests that the
magnetospheric radius of the neutron stars is substantially smaller than Alfven
radius and the spin-down torque applied to the star from accreting material
significantly exceeds the value predicted by the theory. We show that these
problems can be avoided if the fossil magnetic field of the accretion flow
itself is incorporated into the accretion model. The initially spherical flow
in this case decelerates by its own magnetic field and converts into a
non-Keplerian disk (magnetic slab) in which the material is confined by its
intrinsic magnetic field ("levitates") and slowly moves towards the star on a
diffusion timescale. Parameters of pulsars expected within this
magneto-levitation accretion scenario are evaluated.
