  We analyze the equilibrium and non-equilibrium frequency-dependent spin
current noise and spin conductance through a quantum dot in the local moment
regime. Spin current correlations are shown to behave markedly differently from
charge correlations: Equilibrium spin cross-correlations are suppressed at
frequencies below the Kondo scale, and are characterized by a universal
function that we determine numerically for zero temperature. For asymmetrical
quantum dots dynamical spin accumulation resonance is found for frequencies of
the order of the Kondo energy. At higher temperatures surprising low-frequency
anomalies related to overall spin conservation appear.
