Fig. 2: Spin-torque FMR measurements in a Mn₃Sn/Ni-Fe bilayer.

a Measurement setup for spin-torque FMR measurement (ST-FMR). The red and blue arrows on the respective top and bottom surface of the Mn₃Sn stack indicates spin accumulation. b ST-FMR spectrum. c (Upper) Magnetization of Ni-Fe (green arrows) and detected in-plane torque τ^φ (blue arrows) and out-of-plane torque τ^Z (red) in Mn₃Sn/Ni-Fe bilayer system; (Lower) Spin structure of Mn₃Sn and cluster magnetic octupole (orange arrows). d, e In-plane magnetic field angle dependence of symmetric voltage V_S and Anti-symmetric voltages V_A. f, g In-plane torque τ^φ and out-of-plane torque τ^Z. h, i odd- and even-component of τ^φ under reversal of the ferromagnetic magnetization m. Green (Black) dashed line corresponds to τ^φ due to conventional SHE (MSHE). j, k Odd- and even-component of τ^z. Black dashed line corresponds to τ^z due to Oersted field.