Different correlations between spin Hall angle measured by the 2nd harmonic method and by the critical current density due to dimension effect in W/Ta multilayers

We obtain varying spin Hall angle ( θ _{SH, 2nd}) values measured by the 2nd harmonic methods in W/Ta multilayers system with relatively low resistivity by doping Ta into mixed-phase W with both α and β phases ( α-W , β-W). A remarkably increased value of θ _{SH, 2nd} is observed from 0.04 (W) to 0.47 (W ₁/Ta _0.25), which is attributed to the formation of β-W ₃Ta. The influences of θ _{SH, 2nd} on the critical switching current density ( J _c) were investigated by the spin Hall angle ( θ _{SH, J c}). It is found that the θ _{SH, J c} has strong correlations with θ _{SH, 2nd} in large dimension samples, indicating the J _c can be lowered by the enhancement of θ _{SH, 2nd}. This correlation gradually disappears in smaller dimension samples, due to the pinning effect and domain wall (DW) surface tension, which are confirmed by microsimulations.