Evaluating the nonadiabatic spin-transfer torque using coupled oscillation of magnetic vortices

In this paper, we detect the coupled oscillation of magnetic vortices in Ni-81 Fe-19 gourd-shaped thin films electrically to evaluate the nonadiabatic spin-transfer torque (STT) coefficient beta, which is important for understanding a variety of STT-related phenomena. We excite a translational mode in coupled magnetic vortices by applying an alternating electrical current that causes both STT and Oersted field torque. Since the coupled oscillation modes due to the STT and Oersted field torque have totally different eigenfrequencies, the coupled oscillation spectrum can be used to evaluate beta, which is generally difficult to distinguish from the Oersted field contributions. Based on the ratio between the amplitudes of the spectrum's Lorentzian and anti-Lorentzian components, the value of beta is found to be 0.085 +/- 0.016, which is 4.3 times larger than the Gilbert damping constant alpha.