Long-range magnetic interactions in Nd${}_2$PdSi${}_3$ and the formation of skyrmion phases in centrosymmetric metals

We present an extensive X-ray and neutron scattering study of the structure and magnetic excitations of Nd${}_2$PdSi${}_3$, a sister compound of Gd${}_2$PdSi${}_3$ which was recently found to host a skyrmion lattice phase despite its centrosymmetric crystal structure. Dispersive magnetic excitations were measured throughout the Brillouin zone and modeled to determine the magnetic interactions between Nd ions. Our analysis reveals that the magnetic interactions in this system extend over large distances and are significantly affected by a crystallographic superstructure formed by ordering of the Pd and Si atoms. The results suggest that the mechanism for the skyrmion phase formation in this family of materials, specifically Gd${}_2$PdSi${}_3$, is through the long-range RKKY interactions rather than short-range triangular-lattice frustration.