The spin ice structures with height offsets were fabricated in two separate electron beam lithography exposure steps (fig. S2) for the plateau definition and then for the nanomagnets. First, gold marks were fabricated on a silicon substrate to align both electron beam exposure steps to the same set of marks. PMMA (polymethyl methacrylate) 950k C2 was spun at 2000 rpm to give a thickness of 170 nm. The pattern for the raised plateau was then exposed with a Vistec VB300 electron beam lithography tool at 100 kV in four separate quadrants of the silicon wafer to allow four different etch depths on the same substrate. The PMMA was then developed using a high-contrast cold development process consisting of 7:3 isopropyl alcohol (IPA):water solution ultrasonicated for 100 s. Cr (10 nm) was evaporated and lifted off to create the etch mask for the raised plateau. The silicon was etched in an Oxford Instruments reactive ion etcher with gas flow of 40-SCCM (standard cubic centimeter per minute) CHF3 and 8-SCCM SF6 at a pressure of 20 mtorr and a power of 50 W. Varying etch times gave the desired variation in etch depth. After stripping the Cr, PMMA was spun again on the substrate at 1000 rpm for the electron beam lithography exposure defining the nanomagnets. After exposure and cold development, a layer of 2.5-nm (TB = 160 K) and 3-nm (TB = 330 K) permalloy (Ni80Fe20) and a capping layer of 3 nm Al were evaporated and lifted off in dichloromethane. The exact values of the etched height offsets were determined using atomic force microscopy (AFM).

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