Fig. 1: Co₂MnGa thin lamella devices.

a Top-view false-color SEM micrograph of Sample N2 (12 × 12 × 0.4 μm). The central blue region is the thin Co₂MnGa crystal. Insulating, amorphous carbon (dark brown) is added by FIB to protect the sides of the device. Electrical contacts at all 8 corners are made by depositing platinum strips (gray) via FIB and connecting them to pre-patterned gold electrodes (yellow). b The temperature dependences of the four-point resistances on the upper/lower faces (H = 0 T) in Sample O1 (thickness = 1 μm). The high-conductance-axis (upper = \(\hat{{{{{{{{\bf{y}}}}}}}}}\), lower = \(\hat{{{{{{{{\bf{x}}}}}}}}}\)) resistances have metallic temperature dependences that match those of bulk Co₂MnGa crystals. (The isotropic-equivalent resistance is denoted with a black star at T = 290 K.) The low-conductance-axes (upper = \(\hat{{{{{{{{\bf{x}}}}}}}}}\), lower = \(\hat{{{{{{{{\bf{y}}}}}}}}}\)) resistances have anomalous temperature dependences that decay slowly at high temperatures but sharply below T = 10 K. The inset diagram depicts the corner-contact labeling scheme used throughout to identify each R_ij,kl. c A diagram depicting the 90^∘-twist planar anisotropy in a 3D lamella. The dashed blue lines indicate the high-conductance axes. The anisotropy is such that when current is directed along the z-axis edges, a surface potential arises that is strongly distorted in opposite lateral directions on the upper/lower faces. This effect is reminiscent of how crossed polarizers block light (upper-right inset). d The left inserts are magnetic force micrographs of the remanent magnetic domains observed in thin Co₂MnGa lamellae (5 × 5 × 1.3 μm) (without electrical contacts). These feature Landau flux-closure patterns rotated by 90° between upper and lower faces. Scale bar = 1 μm. The sketch on the right depicts the arrangement of the surface magnetization textures on the 3D lamellae.