Fermi-Surface Origin of Skyrmion Lattices in Centrosymmetric Rare-Earth Intermetallics

We show from first principles that barrel-shaped structures within the Fermi surface of the centrosymmetric intermetallic compounds GdRu_{2}Si_{2} and Gd_{2}PdSi_{3} give rise to Fermi surface nesting, which determines the strength and sign of quasi-two-dimensional Ruderman-Kittel-Kasuya-Yosida pairwise exchange interactions between the Gd moments. This is the principal mechanism leading to their helical single-q spin-spiral ground states, providing transition temperatures and magnetic periods in good agreement with experiment. Using atomistic spin-dynamic simulations, we draw a direct line between the subtleties of the three-dimensional Fermi surface topology and the stabilization of a square skyrmion lattice in GdRu_{2}Si_{2} at applied magnetic fields as observed in experiment.