Dzyaloshinskii-Moriya Interaction as a Consequence of a Doppler Shift due to Spin-Orbit-Induced Intrinsic Spin Current.

We present a physical picture for the emergence of the Dzyaloshinskii-Moriya (DM) interaction based on the idea of the Doppler shift by an intrinsic spin current induced by spin-orbit interaction under broken inversion symmetry. The picture is confirmed by a rigorous effective Hamiltonian theory, which reveals that the DM coefficient is given by the magnitude of the intrinsic spin current. Our approach is directly applicable to first principles calculations and clarifies the relation between the interaction and the electronic band structures. Quantitative agreement with experimental results is obtained for the skyrmion compounds Mn_{1-x}Fe_{x}Ge and Fe_{1-x}Co_{x}Ge.