Fig. 1: Orbital–current-induced spin torque in Cr/ferromagnet heterostructures.
From: Efficient conversion of orbital Hall current to spin current for spin-orbit torque switching
a, b Schematic illustrations of the angular momentum transfer by spin current (red arrows) and orbital current (blue arrows) for Co (a) and Ni (b) ferromagnets (FMs). The spin (orbital) angular momentum is represented by S (L). The source of S and L is marked by the subscript of SHE (OHE) for spin Hall effect (orbital Hall effect). \({{{\eta }}}_{{{{L}}} - {{{S}}}}^{{{{{{{{\rm{Co}}}}}}}}({{{{{{{\rm{Ni}}}}}}}})}\) is the orbital-to-spin conversion efficiency of Co (Ni). c The \({{{R}}}_{{{{xy}}}}^{2{{{\omega }}}}({{{\varphi }}})\) measurement geometry for a Hall-bar sample. \(\varphi\) is the azimuthal angle of the external magnetic field (Bext) with respect to the current direction. d, e Azimuthal angle (φ) dependent second harmonic Hall resistance, \({{{R}}}_{{{{xy}}}}^{2{{{\omega }}}}({{{\varphi }}})\), under different Bext of Co (3.0 nm)/Cr (7.5 nm) (d) and Ni (2.0 nm)/Cr (7.5 nm) (e) samples. The solid lines are the fitting curves using Eq. (2). Each \({{{R}}}_{{{{xy}}}}^{2{{{\omega }}}}({{{\varphi }}})\) curve of Co/Cr (d) and Ni/Cr (e) is shifted by a y-axis offset to clearly show the Bext dependence. f \({{{R}}}_{{{{{{{{\rm{COS\varphi }}}}}}}}}^{2{{{\omega }}}}/{{{R}}}_{{{{{{{{\rm{AHE}}}}}}}}}^{1{{{{{{{\mathbf{\omega }}}}}}}}}\) as function of 1/Beff of Ni/Cr (red), Co/Cr (light-green), Ni/Pt (magenta), and Co/Pt (green) samples. Each solid line is the linear fitting line. The error bars in f are due to the standard deviation of the fitting of the \({{{R}}}_{{{{xy}}}}^{2{{{\omega }}}}({{{\varphi }}})\) versus φ curves using Eq. (2), which are smaller than the symbol size. g Cr thickness (tCr) dependent damping-like torque efficiency (ξDLT) of Ni/Cr (red) and Co/Cr (light-green) samples, where tCr ranges from 2 to 12.5 nm. The fitting results of orbital and spin diffusion lengths for Ni/Cr and Co/Cr are given in solid curves. The ξDLT’s of the reference Ni/Pt (magenta) and Co/Pt (green) samples are included for comparison. Lines are guides to eyes. All measurements are conducted at 300 K. The error bars in g are due to the standard deviation of the linear fitting of the cosφ components of Eq. (2) versus 1/Beff.
