Microscopic theory of flexo Dzyaloshinskii-Moriya-type interaction

We study interaction between two magnetic impurities mediated by itinerant electrons on the surface of curved magnets based on perturbation theory. We show that Dzyaloshinskii-Moriya type interaction can arise from inhomogeneous spin texture by bending, without any spin-orbit coupling. Analytical expressions of the Dzyaloshinskii-Moriya type interaction are obtained. We demonstrate this effect in a one-dimensional ring model.