  Electronic and transport properties of a short Ni nanowire suspended between
two semi-infinite ferromagnetic Ni leads are explored in the framework of
density-functional theory. The spin-dependent ballistic conductance of the
nanowire is calculated using a scattering-based approach and the
Landauer-Buttiker formula. The total calculated conductance in units of $G_0 =
2e^2/h$ is around 1.6, in fairly good agreement with the broad peak observed
around 1.5 for the last conductance step in break junctions. Separating
contributions from different spins, we find nearly 0.5 $G_0$ from the majority
spin $s$-like channel, whereas the remaining minority spin conductance of 1.1
$G_0$ contains significant contributions from several $d$ states, but much less
than 0.5 $G_0$ from $s$ states. The influence of the structural relaxation on
the magnetic properties and the ballistic conductance of the nanowire is also
studied.
