Nanoscale Penetration Depth of Emergent Magnetic Field at an Oxide Spin-Ice/Metal Interface.

The geometrically frustrated spin-ice pyrochlore Dy2Ti2O7 (DTO) provides a platform for exploring topological physics arising from emergent magnetic fields (bem). While proximity-coupled interfaces have enabled the detection of bem in insulating magnets via the topological Hall effect (THE), harnessing these phenomena for practical applications requires quantification of their spatial extent. Here, we investigate bem propagation across (Pb0.9Sr0.1)2Ru2O6.5 (PSRO)/DTO heterostructures. By systematically varying the conducting PSRO layer thickness (t), we demonstrate that the THE amplitude deviates from the 1/t dependence characteristic of purely interfacial scattering. Instead, the signal exhibits an exponential decay with a penetration length of ∼2.3 nm, reflecting the characteristic length scale of the conduction electron wave function overlap with the frustrated spin texture. This finding provides evidence for the spatial penetration of Berry curvature into an adjacent metal, establishing a fundamental design parameter for integrating spin-ice physics into topological oxide electronics.