Simultaneous determination of effective spin-orbit torque fields in magnetic structures with in-plane anisotropy

The strength of spin-orbit torque in ferromagnetic structures is characterized by fieldlike and dampinglike effective fields. Conventionally, two distinct measurement approaches are employed to quantify the magnitude of the respective effective fields in structures with in-plane magnetic anisotropy. Here, we propose and demonstrate a self-validating method, which enables simultaneous quantification of both the fieldlike and dampinglike terms in structures with in-plane magnetic anisotropy. An analytical expression is derived and validated by harmonic Hall resistance measurement. Both the fieldlike and dampinglike effective fields are extracted from a single measurement using the derived fitting functions for the second harmonic Hall resistance. The first harmonic Hall resistance acts as a reference to confirm that the experimental parameters are consistent with the derived equations.