Estimating spin Hall angle in heavy metal/ferromagnet heterostructures

We developed equations to estimate the spin Hall angle and anisotropy field of ferromagnets in heavy metal/ferromagnet heterostructures using a macrospin model. In this model, critical switching spin current density linearly changes with the applied in-plane magnetic field. Thus the spin Hall angles can be estimated by measuring the critical switching current density under in-plane magnetic field. The obtained spin Hall angle using this method is not only consistent with that obtained by harmonic measurements. Spin Hall angles of PtMn, β-W, Pt and (Bi_0.5Sb_0.5)₂Te₃ estimated by our method are also closed to that obtained using other different methods. Therefore, estimating spin Hall angle by macrospin model can be considered a simple, feasible and widely-applicable approach to obtain the spin Hall angle.