  Inspired by recent experiments on fully spin polarized Na clusters, we
perform a systematic survey of neutral Na clusters at all conceivable spin
polarizations. We study the impact of spin state on ionic configuration, on
global shape, and on optical response. For small clusters, the magic electronic
shell at 4 spin-up electrons is a dominating feature leading to preferred
binding for all clusters having four spin-up electrons (combined with 1 to 4
spin-down electrons). Such a preference fades away for larger systems where the
unpolarized state is generally preferred.
