  Millisecond x-ray pulsars have weak magnetic dipole moments of $\sim
10^{16}$\,T\,m$^3$ compared to ordinary X-ray pulsars with dipole moments of
$10^{20}$\,T\,m$^3$. For this reason a surrounding accretion disc can extend
closer to the neutron star, and thus reach a higher temperature, at which the
opacity is dominated by electron scattering and radiation pressure is strong.
We compute the self-similar structure of such a geometrically thin axisymmetric
accretion disc with an internal dynamo. Such models produce significantly
stronger torques on the neutron star than models without dynamos, and can
explain the strong spin variations in some millisecond X-ray pulsars.
