Weak spin-orbit interactions induce exponentially flat mini-bands in magnetic metals without inversion symmetry

In metallic magnets like MnSi the interplay of two very weak spin-orbit coupling effects can strongly modify the Fermi surface. In the absence of inversion symmetry even a very small Dzyaloshinsky-Moriya interaction of strength delta much less than I distorts a ferromagnetic state into a chiral helix with a long pitch of order 1/delta. We show that additional small spin-orbit coupling terms of order delta in the band structure lead to the formation of exponentially flat mini-bands with a bandwidth of order e(-1/rootdelta) parallel to the direction of the helix. These flat mini-bands cover a rather broad belt of width rootdelta on the Fermi surface where electron motion parallel to the helix practically stops. We argue that these peculiar band structure effects lead to pronounced features in the anomalous skin effect.