Formation Mechanism of the Helical Q Structure in Gd-Based Skyrmion Materials

Using the ab initio local force method, we investigate the formation mechanism of the helical spin structure in GdRu2Si2 and Gd2PdSi3. We calculate the paramagnetic spin susceptibility and find that the Fermi surface nesting is not the origin of the incommensurate modulation, in contrast to the naive scenario based on the Ruderman-Kittel-Kasuya-Yosida mechanism. We then decompose the exchange interactions between the Gd spins into each orbital component, and show that spin-density-wave type interaction between the Gd-5d orbitals is ferromagnetic, but the interaction between the Gd-4f orbitals is antiferromagnetic. We conclude that the competition of these two interactions, namely, the interorbital frustration, stabilizes the finite-Q structure.