  We study the behavior of magnetic superconductors which involve a local
attractive interaction between electrons, and a coupling between local moments
and the electrons. We solve this `Hubbard-Kondo' model through a variational
minimization at zero temperature and validate the results via a Monte Carlo
based on static auxiliary field decomposition of the Hubbard interaction. Over
a magnetic coupling window that widens with increasing attractive interaction
the ground state supports simultaneous magnetic and superconducting order. The
pairing amplitude remains s-wave like, without significant spatial modulation,
while the magnetic phase evolves from a ferromagnet, through non-collinear
`spiral' states, to a Neel state with increasing density and magnetic coupling.
We find that at intermediate magnetic coupling the
antiferromagnetic-superconducting state is gapless, except for the regime of
Neel order. We map out the phase diagram in terms of density, magnetic coupling
and attractive interaction, establish the electron dispersion and effective
`Fermi surface' in the ground state, provide an estimate of the magnetic and
superconducting temperature scales via Monte Carlo, and compare our results to
available data on the borocarbides.
