Spin-transfer-torque resonant switching and injection locking in presence of a weak external microwave field for spin valves with perpendicular materials

摘要

The effects of a weak microwave field in the magnetization dynamics driven byspin-transfer-torque in spin-valves with perpendicular materials have beensystematically studied by means of full micromagnetic simulations. In thesystem we studied, depending on the working point (bias field and current) inthe dynamical stability diagram, we observe either resonant switching andinjection locking. The resonant switching, observed in the switching region,occurs when the field frequency is approaching the frequency of the mainpre-switching mode giving rise to an asymmetric power distribution of that modein the sectional area of the free layer. At the resonant frequency, theswitching time is weakly dependent on the relative phase between the instantwhen the current pulse is applied and the microwave field. The injectionlocking, observed in the dynamical region, is characterized by the followingproperties: (i) a locking bandwidth which is linearly dependent on the forcelocking, and (ii) a locking for integer harmonics of the self-oscillationfrequency. We compare our numerical results with analytical theory fornon-autonomous non-linear system obtaining a good agreement in the currentregion where the oscillation frequency and output power are characterized froma linear relationship.