Composition dependence of the orbital torque in CoxFe1−x and NixFe1−x alloys: Spin-orbit correlation analysis

The spin-orbit correlation in ferromagnet (FM) is an important factor that affects the orbital torque efficiency in the FM. We investigate the spin-orbit correlation in FM alloys, ${\text{Co}}_x{\text{Fe}}_{1-x}$ and ${\text{Ni}}_x{\text{Fe}}_{1-x}$, with varying their composition. We find spots where the spin-orbit correlation is significantly strong near the Fermi surface in ${\text{Co}}_{0.125}{\text{Fe}}_{0.875}$, ${\text{Co}}_{0.25}{\text{Fe}}_{0.75}$, ${\text{Co}}_{0.875}{\text{Fe}}_{0.125}$, and ${\text{Ni}}_{0.5}{\text{Fe}}_{0.5}$, while no such spot appears in ${\text{Co}}_{0.5}{\text{Fe}}_{0.5}$, and ${\text{Ni}}_{0.75}{\text{Fe}}_{0.25}$. These results imply that in the former structures, the orbital polarized current injected into these spots can provide a strong torque to the magnetization of the FM through the orbital torque mechanism. These results also show that even in the same alloy system, the difference in alloy composition can lead to different orbital torque efficiency.