Skyrmion and Meron Crystals in Intermetallic Gd$_3$Ru$_4$Al$_{12}$: Microscopic Model Insights into Chiral Phases

Abstract: Topological spin textures in frustrated intermetallics hold great promise for spintronics applications. However, understanding their origin and properties remains a significant challenge due to competing and often long-range interactions mediated by conduction electrons. Here, by combining neutron scattering experiments with theoretical modeling via unprecedented multi-target fits that further incorporate the ferromagnentic resonance data and magnetization curve, we construct a realistic microscopic model for the prototypical intermetallic skyrmion host \text{Gd}$3$\text{Ru}$_4$\text{Al}${12}$. Beyond magnetic frustration, we identify the competition between dipolar interactions and easy-plane single-ion anisotropy as a key ingredient for stabilizing the rich chiral magnetic phases observed in this compound -- including a hexagonal skyrmion crystal and two distinct meron crystals. Remarkably, the meron crystal in lower field is revealed to be commensurate with the underlying lattice, and its unique three-meron-one-antimeron spin texture is verified by the polarized x-ray diffraction data. At elevated temperatures, the short-range spin correlations in \text{Gd}$3$\text{Ru}$_4$\text{Al}${12}$ are well described by a codimension-two spiral spin-liquid. Perturbations from staggered Dzyaloshinskii-Moriya interactions give rise to chiral fluctuations that account for the temperature and field dependence of the anomalous Hall response. Our results highlight the unique power of neutron scattering, especially when combined with complementary experimental techniques, to unravel complex magnetic phase transitions and provide new insights into the rich variety of topological spin textures in frustrated systems.