  We investigate a simple tight-binding Hamiltonian to understand the stability
of spin-polarized transport of states with an arbitrary spin content in the
presence of disorder. The general spin state is made to pass through a linear
chain of magnetic atoms, and the localization lengths are computed. Depending
on the value of spin, the chain of magnetic atoms unravels a hidden transverse
dimensionality that can be exploited to engineer energy regimes where only a
selected spin state is allowed to retain large localization lengths. An
analysis is carried out to understand the roles played by the spin projections
in different energy regimes of the range of states. We introduce a new measure,
viz, a spin-resolved localization length for this purpose. We study
uncorrelated disorder in the potential profile offered by the magnetic
substrate or in the orientations of the magnetic moments concerning a given
direction in space. Our results show that the spin filtering effect is robust
against weak disorder and hence the proposed systems should be good candidates
for experimental realizations of spin-selective transport.
