  We carry out the spectral analysis of singular matrix valued perturbations of
3-dimensional Dirac operators with variable magnetic field of constant
direction. Under suitable assumptions on the magnetic field and on the
perturbations, we obtain a limiting absorption principle, we prove the absence
of singular continuous spectrum in certain intervals and state properties of
the point spectrum. Constant, periodic as well as diverging magnetic fields are
covered, and Coulomb potentials up to the physical nuclear charge Z<137 are
allowed. The importance of an internal-type operator (a 2-dimensional Dirac
operator) is also revealed in our study. The proofs rely on commutator methods.
