Mesoscale Dzyaloshinskii-Moriya interaction in curved geometry

A broken chiral symmetry in magnetic systems manifests itself at the appearance of either periodical (e.g. helical or cycloid modulations) or localized magnetization structures (e.g. chiral domain walls and skyrmions) [1,2]. The origin of these magnetic textures is spin-orbit driven Dzyaloshinskii-Moriya interaction (DMI), which is intrinsic to the crystal or layer stack. Recently, it was reported that geometrically broken symmetry in curvilinear systems leads to the appearance of exchange-driven DMI-like chiral term in energy functional [3,4]. This term is determined by the sample geometry (it is linear with respect to curvature and torsion) and is therefore extrinsic to the crystal or layer stack. The magnetic properties of curvilinear magnets with intrinsic DMI will be necessarily determined by the interplay between two types of chiral interactions. Hence, the resulting chiral term in such type of objects is referred to as a vector of mesoscale DMI, which is the vector sum of the intrinsic and extrinsic DMI vectors. The symmetry and strength of this term are determined by the geometrical and material properties of the curvilinear magnet. Here we study the properties of the mesoscale DMI using a one-dimensional helical wire as a case of study. The clear cut comparison with the straight wire with intrinsic DMI reveals: (i) a single vector of magnetochirality, which is referred to as vector of the mesoscale DMI, originates from the vector sum of the intrinsic and extrinsic DMI vectors; (ii) a symmetry and period of the chiral modulated structures are determined by the strength and direction of the mesoscale DMI vector; (iii) a phase transition between homogeneous and chiral modulated states in the case of mesoscale DMI is a complex second-order phase transition with the intermediate conical state.

References

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[2] N. Nagaosa, Y. Tokura, Nature Nanotechnology 8, 899-911 (2013)
[3] Y. Gaididei, V. P. Kravchuk, D. D. Sheka, Phys. Rev. Lett. 112, 257203 (2014)
[4] O. V. Pylypovskyi, V. P. Kravchuk, D. D. Sheka, D. Makarov, O. G. Schmidt, Y. Gaididei, Phys. Rev. Lett. 114, 197204 (2015)