Effect of alloying on spin-orbit torque in Fe_0.75Co_0.25|Pt_xX_1−x bilayers

Optimization of materials for efficient spin current generation and magnetization switching in ferromagnet(FM)/heavy-metal(HM) bilayers is of interest for SOT-MRAM and other applications. Experimentally, alloys of Pt with other elements have been studied as the HM source of spin current, some of which were found to increase the effective spin-Hall angle ξ^j_DL and/or the dampinglike (DL) torque efficiency ξ^E_DL in FM|Pt_xX_1−x bilayers. Here we use the tight-binding LMTO implementation of the nonequilibrium Green’s function (NEGF) technique to calculate the DL SOT efficiencies for Fe_0.75Co_0.25|Pt_xX_1−x bilayers with different alloying elements X, as a function of their concentration. The bcc Fe_0.75Co_0.25 alloy is chosen for the FM layer due to its good lattice matching with fcc Pt and low Gilbert damping. The atomic potentials are obtained using the coherent potential approximation, and the torquances are then evaluated via supercell averaging over substitutional disorder configurations. We find that the largest SOT efficiency ξ^E_DL is achieved by alloying Pt with 10-20% of Au or Rh. Using the calculated residual resistivities of the Pt_xX_1−x alloys, we estimate the lower bounds for the effective spin-Hall angles. The results are compared with available experimental data.