Extended Data Fig. 4: Anomalous Hall conductivity of the Mn3Sn layer and estimate of the magnetic anisotropy using angular dependence of the anomalous Hall effect.
From: Perpendicular full switching of chiral antiferromagnetic order by current
a, Magnetic field dependence of the Hall conductivity in the Mn3Sn (30 nm) layer of the MgO(110)-substrate /W(7 nm)/Mn3Sn(30 nm)/MgO(5 nm) stack at 300 K (Method). The Hall conductivity of the Mn3Sn layer in the W/Mn3Sn conducting layer is estimated using the experimentally obtained resistivity of the W(7 nm)/Mn3Sn(30 nm) layer and W(7 nm) layer (Methods). b, Angular (θ) dependence of the Hall voltage normalized by the voltage obtained at θ = 0 for the MBE-grown Mn3Sn stack under 1 T (red circles) at 300 K. The blue solid curve corresponds to the angular dependence expected in the sample with the anisotropy field for the 2-fold magnetic anisotropy field K2/Mr = 1.5 ± 0.1 T, 4-fold magnetic anisotropy field K4/Mr = 0.5 ± 0.1 T, and 6-fold magnetic anisotropy field K2/Mr = 0.4 ± 0.1 T, which are obtained by using the equation (K2/2)sin2θM + (K4/4)sin4θM + (K6/6)sin6θM − μ0MrHsin(θ − θM) = 0. Here K2/4/6, μ0H, Mr, θ and θM denote the 2-/4-/6-fold magnetic anisotropic energy, external magnetic field, remnant (spontaneous) magnetization, magnetic field angle, and angle of the magnetic order parameter (the polarized direction of the cluster magnetic octupole) (see Methods). Inset: Schematic illustration of the measurement set-up for the W/Mn3Sn devices. The purple and green arrows represent the directions of the magnetic field H and current I, respectively. θ and θM are the polar angle of the magnetic field and of the polarized direction of the cluster magnetic octupole (orange arrow) in the z–x plane, respectively.
