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 satis.es 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.eld with changing magnon spectrum. We also.nd that the spin Drude weight vanishes for any external magnetic.eld at T = 0.