Fig. 1: Bi₂Ir₂O₇/Dy₂Ti₂O₇ heterostructure.

a Schematic diagram of the Dy₂Ti₂O₇/Bi₂Ir₂O₇ heterostructure and the measurement configuration. b A schematic drawing showing a zoomed region across the interface. The local spins (gray) are shown on the DTO sides with a few of them (red) flipped to break the ice rule and form the ‘3-in-1-out/1-in-3-out’ configuration. A wavy surface curve (pink) is shown on the BIO side to denote charge carrier. c A typical AFM image of DTO substrate surface with atomically flat terraces. d Transmission electron microscopy image with [1-10] being the lamella surface normal shows the sharp BIO/DTO interface of the heterostructure. The white patches are from focus iron beam milling (see Materials and Methods). A thicker film sample with thickness ~10.5 nm was used in the TEM study to protect the interface. e An X-ray diffraction scan covering the DTO [222] to [444] peaks of a BIO/DTO heterostructure.