  We propose a method to derive the spin current operator for non-collinear
Heisenberg antiferromagnets. We show that the spin conductivity calculated by
the spectral representation with the spin current satisfies the f-sum rule. We
also study the spin conductivity at T=0 within spin wave theory. We show how
the spin conductivity depends on the external magnetic field with changing
magnon spectrum. We also find that the spin Drude weight vanishes for any
external magnetic field at T=0.
