Spin Conductivity in Two-Dimensional Non-Collinear Antiferromagnets

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.