Intra-unit-cell resolved intertwining of multi-$Q$ charge and spin textures in an itinerant skyrmion magnet

Abstract

The mechanisms stabilizing non-collinear magnetism in centrosymmetric crystals remain unclear, but likely involve spin-spin interactions mediated by itinerant electrons, such as the RKKY interaction. Finite-$Q$ magnetic order may then be accompanied by electronic modulations that are observable using a scanning tunneling microscope. In five successive magnetic phases of GdRu$_{2}$Ge$_{2}$, including two nano-scale skyrmion crystal phases, we show that multi-$Q$ magnetism among Gd 4$f$ spins entails a corresponding multi-$Q$ texture among the Ru 4$d$ orbitals that contribute itinerant electron bands. With atomically-resolved images of each electronic texture's motif, and a simple numerical modeling scheme drawing on the underlying spin structures, we infer their key relationship: The alignment between nearest-neighbor Gd spins tightly correlates with the local density-of-states of the Ru 4$d$ orbitals on the two bond-centered sublattices of the Gd square net. These analyses offer a microscopic view of the atomic-scale intertwining of charge and spin degrees-of-freedom in non-collinear itinerant magnets.