Fermi-surface origin of helical single Q-state and skyrmion lattice in centrosymmetric Gd compounds

We show from first principles that cylindrical structures within the Fermi surface are the origin of the single-Q helical state in the GdRu$_2$Si$_2$ and Gd$_2$PdSi$_3$ intermetallic compounds. The geometry of the Fermi surface nesting describes the strength and sign of the underlying pairwise Ruderman-Kittel-Kasuya-Yosida interactions between the Gd moments as the main mechanism. These interactions are quasi-two-dimensional, isotropic within the Gd layers, and provide a transition temperature and helix period in very good agreement with experiment. Using atomistic spin-dynamical simulations, we investigate the effects of magnetic anisotropy and construct a general magnetic phase diagram that explains the stabilization of the 2Q skyrmion lattice observed in experiment with applied magnetic fields.