Manipulation of the domain wall propagation in magnetic wires is a keypractical task for a number of devices including racetrack memory and magneticlogic. Recently, curvilinear effects emerged as an efficient mean to impactsubstantially the statics and dynamics of magnetic textures. Here, wedemonstrate that the curvilinear form of the exchange interaction of a magnetichelix results in an effective anisotropy term and Dzyaloshinskii--Moriyainteraction with a complete set of Lifshitz invariants for a one-dimensionalsystem. In contrast to their planar counterparts, the geometrically inducedmodifications of the static magnetic texture of the domain walls in magnetichelices offer unconventional means to control the wall dynamics relying onspin-orbit Rashba torque. The chiral symmetry breaking due to theDzyaloshinskii-Moriya interaction leads to the opposite directions of thedomain wall motion in left- or right-handed helices. Furthermore, for themagnetic helices, the emergent effective anisotropy term andDzyaloshinskii-Moriya interaction can be attributed to the clear geometricalparameters like curvature and torsion offering intuitive understanding of thecomplex curvilinear effects in magnetism.
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