Current driven second harmonic domain wall resonance in ferromagnetic metal/ nonmagnetic metal bilayer: a field-free method for spin Hall angle measurements

Abstract: We study the ac current-driven domain wall motion in bilayer ferromagnetic metal (FM)/nonmagnetic metal (NM) nanowire. The solution of the modified Landau-Lifshitz-Gilbert equation including all the spin transfer torques is used to describe motion of the domain wall in presence of the spin Hall effect. We show that the domain wall center has second harmonic frequency response in addition to the known first harmonic excitation. In contrast to the experimentally observed second harmonic response in harmonic Hall measurements of spin-orbit torque in magnetic thin films, this second harmonic response directly originates from spin-orbit torque driven domain wall dynamics. Based on the spin current generated by domain wall dynamics, the longitudinal spin motive force generated voltage across the length of the nanowire is determined. The second harmonic response introduces additionally a new practical field-free and all-electrical method to probe the effective spin Hall angle for FM/NM bilayer structures that could be applied in experiments. Our results also demonstrate the capability of utilizing FM/NM bilayer structure in domain wall based spin torque signal generators and resonators.