  We examine the proposal that the subset of neutron-star and black-hole X-ray
binaries that form with Ap or Bp star companions will experience systemic
angular-momentum losses due to magnetic braking, not otherwise operative with
intermediate-mass companion stars. We suggest that for donor stars possessing
the anomalously high magnetic fields associated with Ap and Bp stars, a
magnetically coupled, irradiation-driven stellar wind can lead to substantial
systemic loss of angular-momentum. In this paper we apply this mechanism to a
specific astrophysics problem involving the formation of compact black-hole
binaries with low-mass donor stars. At present, it is not understood how these
systems form, given that low-mass companion stars are not likely to provide
sufficient gravitational potential to unbind the envelope of the massive
progenitor of the black hole during a prior `common-envelope' phase. However,
in the absence of magnetic braking, such systems tend to evolve to long orbital
periods. We show that, with the proposed magnetic braking properties afforded
by Ap and Bp companions, such a scenario can lead to the formation of compact
black-hole binaries with orbital periods, donor masses, lifetimes, and
production rates that are in accord with the observations. In spite of these
successes, our models reveal a significant discrepancy between the calculated
effective temperatures and the observed spectral types of the donor stars.
Finally, we show that this temperature discrepancy would still exist for other
scenarios invoking initially intermediate-mass donor stars, and this presents a
substantial unresolved mystery.
