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We investigate the spin-orbit torque exerted on the magnetic moments of thetransition-metal impurities Cr, Mn, Fe and Co, embedded in the surface of thetopological insulator Bi$_{2}$Te$ _{3} $, in response to an electric field anda consequent electrical current flow in the surface. The multiple scatteringproblem of electrons off impurity atoms is solved by first-principlescalculations within the full-potential relativistic Korringa-Kohn-Rostoker(KKR) Green function method, while the spin-orbit torque calculations arecarried out by combining the KKR method with the semiclassical Boltzmanntransport equation. We analyze the correlation of the spin-orbit torque to thespin accumulation and spin flux in the defects. We compare the torque ondifferent magnetic impurities and unveil the effect of resonant scattering. Inaddition, we calculate the resistivity and the Joule heat as a function of thetorque in these systems. We predict that the Mn/Bi$_{2}$Te$_{3}$ is optimalamong the studied systems.

Strong Spin-Orbit Torque effect on magnetic defects due to topological surface state electrons in Bi$_{2}$Te$_{3}$