Topological spin textures stabilised by Weyl fermions

Rare-earth intermetallic (REI) constitute a playground for the realization of topological spin textures

relying on Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions between the localized 4f-moments [1].

In non-centrosymmetric REI, namely REAlGe (Si), the breaking of inversion symmetry generates Weyl

nodes which display interesting topological properties. The Weyl fermions mediate highly anisotropic

RKKY interactions leading to the emergence of Kitaev (KT) and Dzyloshinksii-Moriya (DM) interactions.

In presence of an external magnetic field non-trivial textures such as merons are observed [2]. We perform

a systematic first-principles analysis in the framework of the DFT+U for REAlGe (RE=Ce-Gd) and investigate

the contributions of the different exchange interactions (isotropic, DM, and KT) to the incommensurate order.

The local crystal field coefficients are computed from first-principles as well [3], and are used to evaluate the

magneto-crystalline anisotropy. Finally, we employ atomistic spin-dynamic simulations and identify the magnetic

phases that are stabilized in presence of an external magnetic field. Our analysis aims at drawing a direct

connection between the topology of the electronic band structure and the topology of the spin structures in

real space.

[1] J. Bouaziz et al. PRL 128, 157206 (2022); [2] P. Puphal et al. PRL 124, 017202 (2020); [3] C.E. Patrick et al. JPCM 31, 305901 (2019)

*This work was supported by from the European Research Council (ERC Grant No. 856538, project ``3D MAGiC'’).