Magnetic hedgehog lattices in noncentrosymmetric metals*

Recently, three-dimensional topological spin textures called the magnetic hedgehog lattices (HLs) were discovered in the B20-type compounds MnSi_1-xGe_x [1]. The HLs have periodic arrays of magnetic monopoles and anti-monopoles, which induce interesting transport phenomena, such as the topological Hall effect and the topological thermoelectric transport. However, their stabilization mechanism has not been fully understood thus far. Here we investigate the ground state of an effective spin model with long-range interactions arising from the itinerant nature of electrons by variational calculations and simulated annealing. We find that the HLs are stabilized even at zero field by the synergetic effect of symmetric and antisymmetric interactions from the spin-charge and spin-orbit couplings, respectively. We also clarify the full phase diagram in the magnetic field, which includes multiple phase transitions with changes in the number of monopoles and anti-monopoles [2].

[1] Y. Fujishiro et al., Nat. Commun. 10, 1059 (2019).
[2] S. Okumura, S. Hayami, Y. Kato, and Y. Motome, arXiv:1908.05044.