Nicolas Locatelli1, Abbass Hamadeh2, Flavio Abreu Araujo1, Romain Lebrun1, Vladimir Naletov1,2,3,
Julie Grollier1, Olivier Klein2,3, Vincent Cros1, Grégoire de Loubens2

1Unité Mixte de Physique CNRS/Thales
2SPEC (CNRS UMR 3680), CEA Saclay
3INAC-SPINTEC, CEA/CNRS and Université Grenoble Alpes

Due to their nonlinear properties, spin transfer nano-oscillators can easily adapt their frequency to external stimuli. This makes them interesting model systems to study the effects of synchronization and brings some opportunities to improve their microwave characteristics in view of their applications in information and communication technologies and/or to design innovative computing architectures. So far, mutual synchronization of spin transfer nano-oscillators through propagating spin-waves and exchange coupling in a common magnetic layer has been demonstrated. Here we show that the dipolar interaction is also an efficient mechanism to synchronize neighboring oscillators. We experimentally study a pair of vortex-based spin transfer nano-oscillators, in which mutual synchronization can be achieved despite a significant frequency mismatch between oscillators (as large as 10% of the mean frequency). Importantly, the coupling efficiency is controlled by the magnetic configuration of the vortices, see Fig.1.

This is confirmed by a model highlighting the physics at play in the synchronization process, where we study the dependence of the coupling efficiency on the relative magnetization parameters of the vortices in the system. For this purpose, we combine micromagnetic simulations, the Thiele equation approach, and the analytical macrodipole approximation model to identify the optimized configuration for achieving phase-locking between neighboring oscillators. Notably, we compare vortices configurations with parallel core polarities (Pc) and with opposite core polarities (APc). We demonstrate that the APc configuration exhibits a coupling strength about three times higher than in the Pc configuration, see Fig.2.

Scientific Reports 5, 17039 (2015)  DOI: 10.1038/srep17039

Phys. Rev. B 92, 045419 (2015) DOI: 10.1103/PhysRevB.92.045419

Fig.1 Top: Schematic of the coupling of two V-STNOs nanopillars. (a,b) Power spectrum map versus perpendicular field measured for a case when vortices in the two pillars have (a) opposite polarities and (b) parallel core polarities. The injected current through the two pillars is Idc=38 mA.


Fig.2 Left : Evolution of the dipolar energy of two interacting vortices modeled as macrodipoles and oscillating at the same frequency. The blue curve corresponds to the identical-polarity (Pc) case; the red curve, to the opposite-polarity (APc) case. Dashed colored lines represent the corresponding mean value of the coupling energies, which differ by a factor 3. Right: Average interaction energy versus interpillar distance extracted from micromagnetic simulations for the case of two identical synchronized oscillators with radii R = 100 nm, when vortices have identical polarities (blue line and filled squares) and opposite polarities (red line and open squares).