We measure the spin-orbit torques (SOTs), current-induced switching, and domain wall (DW) motion in synthetic ferrimagnets consisting of $\mathrm{Co}$/$\mathrm{Tb}$ layers with differing stacking order grown on a $\mathrm{Pt}$ underlayer. We find that the SOTs, magnetic anisotropy, compensation temperature, and SOT-induced switching are highly sensitive to the stacking order of $\mathrm{Co}$ and $\mathrm{Tb}$ and to the element in contact with $\mathrm{Pt}$. Our study further shows that $\mathrm{Tb}$ is an efficient SOT generator when in contact with $\mathrm{Co}$, such that its position in the stack can be adjusted to generate torques additive to those generated by $\mathrm{Pt}$. With optimal stacking and layer thickness, the dampinglike SOT efficiency reaches 0.3, which is more than twice that expected from the $\mathrm{Pt}$/$\mathrm{Co}$ bilayer. Moreover, the magnetization can be easily switched by the injection of pulses with current density of about (0.5--$2)\ifmmode\times\else\texttimes\fi{}{10}^{7}\phantom{\rule{0.2em}{0ex}}\mathrm{A}/{\mathrm{cm}}^{2}$ despite the extremely high perpendicular magnetic anisotropy barrier (up to 7.8 T). Efficient switching is due to a combination of large SOTs and low saturation magnetization owing to the ferrimagnetic character of the multilayers. We observe current-driven DW motion in the absence of any external field, which is indicative of homochiral N\'eel-type DWs stabilized by the interfacial Dzyaloshinkii-Moriya interaction. These results show that the stacking order in transition metal/rare-earth synthetic ferrimagnets plays a major role in determining the magnetotransport properties relevant for spintronic applications.
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