Abstract
Current-induced vortex oscillations in an extended thin-film with point-contact geometry are considered. The synchronization of these oscillations with a microwave external magnetic field is investigated by a reduced order model that takes into account the dynamical effects associated with the significant deformation of the vortex structure produced by the current, which cannot be taken care of by using the standard rigid vortex theory. The complete phase diagram of the vortex oscillation dynamics is derived and it is shown that strong hysteretic behavior occurs in the synchronization with the external field. The complex nonlinear nature of the synchronization manifests itself also through the appearance of asymmetry in the locking frequency bands for moderate microwave field amplitudes. Predictions from the reduced order model are confirmed by full micromagnetic simulations.
Highlights
In this work, we study the synchronization mechanism between the dc current-induced vortex oscillations and a microwave external magnetic field in a thin film point-contact STNO21
Among the possible bifurcations for a two-dimensional dynamical system, for the amplitude of current (2.5 mA ≤ I ≤ 10 mA) and microwave field (Hrf ≤ 1 mT) considered, we find out that, for the dynamical system described by eq (16), just two of them occur as function of the current: the saddle-node and the homoclinic bifurcation
The central and distinctive feature of our modelling is the introduction of the current dependence in the energy and damping terms W(X, I), D(X, I) within the framework of the collective variables description (see eq (3)). Such a dependence is necessary in order to reproduce the actual behavior of the stationary vortex core orbit radius X under the action of the spin-polarized current I, as well as the free running oscillation frequency f(I) of the STNO, as shown in Fig. 4, where the comparison of theory and micromagnetic simulations is reported for two different orientations of the polarizer: out-of-plane and in-plane
Summary
We study the synchronization mechanism between the dc current-induced vortex oscillations and a microwave external magnetic field in a thin film point-contact STNO21 These oscillation regimes in micron-sized thin-film STNO have been experimentally observed[22,23] and theoretically studied mostly by means the rigid vortex theory[24]. This diagram describes all possible mechanisms of synchronization between vortex oscillations and external microwave magnetic field. The numerical one allows us to introduce an additional current dependence describing the vortex deformation that a current independent ansatz[24,32] cannot take into account
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