Fig. 3: Electric control of the MSHT via switching Mn₃Sn.

a–c \({R}_{{{\rm{H}}}}-I\) measurements performed in various conditions. Shared conditions of neighboring figures are shown in a legend between the figures. Current range dependence of R_H, where the absolute value of the maximum current at positive side, I₊ is smaller (larger) than that of the minimum current at negative side, I_- in (a, b). CoFeB initialization dependence of R_H, where CoFeB is initialized along –z (+z) in (b, c). d In-plane magnetic field \({\mu }_{0}{H}_{x}^{{{\rm{meas}}}}\) dependence of \({I}_{-}\)-biased (left) and \({I}_{+}\)-biased (right) loops. \({\mu }_{0}{H}_{x}^{{{\rm{meas}}}}\) varies from −10 to +10 mT with a step of 2 mT. The switching magnitude \(\Delta {R}_{{{\rm{H}}}}\) is qualitatively described by a scaling arrow with a colored gradient. e Switching ratio of the loops shown in (d) and the difference δ between \({I}_{-}\)-biased and \({I}_{+}\)-biased loops. f t_Mo dependence of δ at zero magnetic field. The error bars in (e, f) indicate the standard deviation errors in five continuous rounds of measurements. g Key factors of the Mn₃Sn switching, where \({H}_{y}^{{{\rm{Oe}}}}\) is an Oersted field along y direction. h Schematic for the switching process of Mn₃Sn. Red arrows indicate the net magnetization representing the overall magnetic order of Mn₃Sn. Orange arrows denote the effective rotation direction of the net magnetization of Mn₃Sn under spin injection. Green arrows denote the rotation of the net magnetization of Mn₃Sn driven by the Oersted field.