Insight into the electronic structure of the centrosymmetric skyrmion magnet GdRu$_2$Si$_2$

The discovery of a square magnetic-skyrmion lattice in GdRu$_2$Si$_2$, with the smallest so far found skyrmion diameter and without a geometrically frustrated lattice, has attracted significant attention, particularly for potential applications in memory devices and quantum computing. In this work, we present a comprehensive study of surface and bulk electronic structures of GdRu$_2$Si$_2$ by utilizing momentum-resolved photoemission (ARPES) measurements and first-principles calculations. We show how the electronic structure evolves during the antiferromagnetic transition when a peculiar helical order of 4$f$ magnetic moments within the Gd layers sets in. A nice agreement of the ARPES-derived electronic structure with the calculated one has allowed us to characterize the features of the Fermi surface (FS), unveil the nested region along the $k_z$ at the corner of the 3D FS, and reveal their orbital compositions. Our findings suggest that the Ruderman-Kittel-Kasuya-Yosida interaction plays a decisive role in stabilizing the spiral-like order of Gd 4$f$ moments responsible for the skyrmion physics in GdRu$_2$Si$_2$. Our results provide a deeper understanding of electronic and magnetic properties of this material, which is crucial for predicting and developing novel skyrmion-based devices.