Fig. 4: Enhanced SOT efficiency via synergic operation of orbital and spin currents in Pt/Co/Pt and diffusion model.
From: Harnessing synergy of spin and orbital currents in heavy metal/ferromagnet multilayers
a The \({\xi }_{{{\rm{DL}}}}\) of Pt(5)/Co(t) (brown) and Pt(5)/Co(t)/Pt(1) (red) with different \({t}_{{{\rm{Co}}}}\), and anomalous Pt(5)/Co(1)/Al(1)/Pt(1) (black square) and Co(1)/Pt(5) (black star). The spin torque contribution (light violet shading) come from bottom Pt(5) (\({\xi }_{{{\rm{DL}}}}^{{{\rm{SH}}}}\) > 0) and top Pt(1) (\({\xi }_{{{\rm{DL}}}}^{{{\rm{SH}}}2}\) < 0). The orbital torque contribution (light orange shading) \({\xi }_{{{\rm{DL}}}}^{{{\rm{OH}}}}\) is positive and the orbital torque from top Pt(1) is ignored here. The total spin torque \({\xi }_{{{\rm{DL}}}}^{{{\rm{SH}}}}+{\xi }_{{{\rm{DL}}}}^{{{\rm{SH}}}2}\) and \({\xi }_{{{\rm{DL}}}}^{{{\rm{OH}}}}\) have same sign, i.e., orbital torque increases \({\xi }_{{{\rm{DL}}}}\). The error bars represent the standard deviation uncertainties and are smaller than the markers. b Schematic illustration of spin (blue straight arrows) or orbital (red curved arrows) current transport and SOT generation in Pt(5)/Co(t)/Pt(1). Where Pt has positive spin Hall conductivity (\({\sigma }_{{{\rm{SH}}}}^{{{\rm{Pt}}}}\) > 0) and orbital Hall conductivity (\({\sigma }_{{{\rm{OH}}}}^{{{\rm{Pt}}}}\) > 0). Spin current generates spin torque at lower Pt/Co interface, and orbital current passes through Co and is converted into positive orbital torque at upper Co/Pt interface with positive conversion coefficient \({\eta }_{{{\rm{LS}}}}\). And the black arrows denote the magnetic moment and SOT induced deflection. c Current-induced magnetization switching curve, Hall resistance \({R}_{{xy}}\) with respect to \({J}_{{{\rm{HM}}}}\), of Pt(5)/Co(1) (brown) and Pt(5)/Co(1)/Pt(1) (red). Pt(5)/Co(1)/Pt(1) has lower switching current density and higher \({\mu }_{0}{H}_{{{\rm{k}}}}\), meaning higher switching efficiency. d Orbital torque contribution \({\xi }_{{{\rm{DL}}}}^{{{\rm{OH}}}}\) with respect to \({t}_{{{\rm{Co}}}}\) of three series samples, Pt(5)/Co(t)/Pt(1) (red), Ta(5)/Co(t)/CoPt(2) (green) and Pt(5)/Co(t)/CoPt(2) (blue). They can be fitted well by same diffusion length parameter \({\lambda }_{{{\rm{d}}}}^{{{\rm{Co}}}}\).
