Separating Intrinsic and Domain-Mediated Anomalous Hall Conductivity in Co$_3$Sn$_2$S$_2$ via Contact Engineering
Decoupling the global Berry-curvature contribution to the anomalous Hall conductivity (AHC) from local domain- and texture-related contributions in bulk ferromagnetic Weyl semimetals is difficult in standard measurements. We address this in a $\sim$670$μ$m-thick Co$_3$Sn$_2$S$_2$ single crystal using a contact architecture that promotes depth-distributed current flow. We find that the AHC depends on the field-enforced domain state: above $\sim$0.3\,T, a single- or few-domain configuration reveals a momentum-space intrinsic Berry-curvature response, with a crossover near $\sim$125\,K driven by rapid magnetization decrease and reduced magnetic anisotropy. In low-field zero-field-cooled (ZFC) multidomain states, the Hall response is modified by domain physics, with possible real-space Berry curvature and moderate extrinsic contributions. These results demonstrate contact engineering as a practical, non-invasive strategy for separating the momentum-space intrinsic AHC from domain-mediated and extrinsic contributions in thick Weyl semimetal crystals.