  We give a further step in the quantum mechanical description of engineered
atomic spin structures by deriving a master equation of the Redfield type that
governs the dynamics of the atomic spin density matrix. By generalizing this
approach to charge-specific density matrices, we are able to describe magnetic
transport quantities, such as the average inelastic current and the shot noise,
accessible by tunneling spectroscopy. Our method suitably describes moderate
lead-atom coupling regimes where quantum coherence effects cannot be
disregarded. We contrast our approach with the existing descriptions in terms
of rate equations and show examples where coherence effects are crucial to
understand the physics of spin-polarized tunnel current through spin
structures.
