  The experimental realization of magnetic skyrmions in centrosymmetric
materials has been driven by theoretical understanding of how a delicate
balance of anisotropy and frustration can stabilize topological spin structures
in applied magnetic fields. Recently, the centrosymmetric material
Gd$_{2}$PdSi$_{3}$ was shown to host a field-induced skyrmion phase, but the
skyrmion stabilization mechanism remains unclear. Here, we employ
neutron-scattering measurements on an isotopically-enriched polycrystalline
Gd$_{2}$PdSi$_{3}$ sample to quantify the interactions that drive skyrmion
formation. Our analysis reveals spatially-extended interactions in triangular
planes that are consistent with an RKKY mechanism, and large ferromagnetic
inter-planar magnetic interactions that are modulated by the Pd/Si
superstructure. The skyrmion phase emerges from a zero-field helical magnetic
order with magnetic moments perpendicular to the magnetic propagation vector,
indicating that the magnetic dipolar interaction plays a significant role. Our
experimental results establish an interaction space that can promote skyrmion
formation, facilitating identification and design of centrosymmetric skyrmion
materials.
