Special Seminar: Fermi surface properties and topology of selected rare-earth intermetallics 

Centrosymmetric rare-earth intermetallic (REI) constitute a playground for the realization of topological spin textures in the magnetization space (e.g. skyrmion lattices) 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 in momentum space. The Weyl fermions mediate highly anisotropic RKKY interactions leading to the emergence of Kitaev (KT) and Dzyaloshinksii-Moriya interactions (DMI). I address 2 questions: (i) What is the origin of the skyrmions lattices with symmetry- forbitten DMI. (2) Are the Weyl nodes responsible for the incommensurate magnetic order in non-centrosysmmetric REI. We perform a systematic first-principles analysis in the framework of the DFT+U and relate the Fermi-surface and electronic properties to magnetic interaction parameters of spin models. The local crystal field coefficients are computed from first-principles as well [3], and are used to evaluate the magneto-crystalline anisotropy. We employ atomistic spin-dynamics simulations and identify the magnetic phases that are stabilized in the 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.