Fig. 1. Dy₂Ti₂O₇/Bi₂Rh₂O₇ pyrochlore heterostructure.

(A) A schematic of the heterostructure composed of nonmagnetic metal Bi₂Rh₂O₇ (BRO) and magnetic insulator Dy₂Ti₂O₇ (DTO) with spin ice configuration. (B) A schematic of the BRO/DTO interface. The charge carrier (purple) on the BRO side flows through the proximitized emergent field b_em (green) penetrating from DTO with 3-in/1-out (3/1) configuration of local spins J_Dy (red), resulting in the transverse Hall current (curved purple arrow). The net b_em and magnetization M in a pair of tetrahedra consisting of Dy spins with (C) 2-in/2-out (2/2) and (D) 3/1 configurations under magnetic field along [001] and [111] directions. When the magnetic field is rotated from [001] to [111] directions, the spins surrounded by the dotted ellipses in (C) are flopped to those in (D), resulting in a transition from 2/2 to 3/1 configurations. (E) High-resolution high-angle annular dark-field scanning transmission electron microscopy (STEM) image of the film. The corresponding energy dispersive x-ray spectrometry maps for (F) Bi L, (G) Rh L, (H) Dy L, and (I) Ti K edges.