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.
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