Fig. 3: Correlation between SOTs and the relative alignment between the spin polarization and the magneto-crystalline easy axis of AFIs.

a Schematics of Hall bar devices patterned on a single crystalline substrate (MgO or Al₂O₃). The devices are patterned in different directions relative to the substrate’s crystallographic orientations, which affect the direction of current flow I and, consequently, the orientation of spin polarization μ of ISC in FM relative to the magneto-crystalline easy axis n of AFIs. The μ of the ISC in the FM is transverse to the I. b Effective spin Hall angles vs. charge current direction, as obtained from devices patterned on NiO(1.5)/Ni(3)/SiO_x thin films grown on MgO substrates with different crystallographic orientations: (001), (110), and (111). The numbers in the parentheses denote the thickness in nanometers. \(\bar{{{\bf{S}}}\,}\) in the graphs represents the summed values of the component of all preferred \(\hat{{{\bf{n}}}}\) along \(\hat{{{\boldsymbol{\mu }}}}\), as obtained from \(\mathop{\sum }_{i=1}^{N}\left|\widehat{{{\boldsymbol{\mu }}}}\cdot {\widehat{{{\bf{n}}}}}_{i}\right|\). c Effective spin Hall angles vs. charge current direction, as obtained from devices patterned on V₂O₃(3)/Cr₂O₃(20)/Ni(3)/SiO_x thin films grown on two sapphire substrates with different crystallographic orientations: c-plane (0001) and m-plane (\(10\bar{1}0\)). For the devices on the c-plane sapphire substrate, the μ of the ISC is always transverse to the n, irrespective of the device’s pattern orientation. In contrast, for devices on the m-plane sapphire substrate, the μ can be either transverse or parallel to the n, depending on the device’s pattern orientation.