A. Houshang1,2, E. Iacocca1,2, P. Dürrenfeld1, S. R. Sani3, J. Åkerman1,2,3 and R. K. Dumas1,2
1Physics Department, University of Gothenburg, Gothenburg 412 96, Sweden. 
2NanOsc AB, Kista 164 40, Sweden. 
3Material Physics, School of ICT, Royal Institute of Technology, Electrum 229, Kista 164 40, Sweden.

The synchronization of multiple nanocontact spin-torque oscillators (NC-STOs) is mediated by propagating spin waves (SWs). Although it has been shown that the Oersted field generated in the vicinity of the NC can dramatically alter the emission pattern of SWs, its role in the synchronization behaviour of multiple NCs has not been considered so far. Here we investigate the synchronization behaviour in multiple NC-STOs oriented either vertically or horizontally, with respect to the in-plane component of the external field. Synchronization is promoted (impeded) by the Oersted field landscape when the NCs are oriented vertically (horizontally) due to the highly anisotropic SW propagation. Not only is robust synchronization between two oscillators observed for separations larger than 1,000 nm, but synchronization of up to five oscillators, a new record, has been observed in the vertical array geometry. Furthermore, the synchronization can no longer be considered mutual in nature.

Nature Nanotechnology 11, 280 (2016)


Fig. 1: Vertical NC array simulations for case I. 
For case I the bigger, 100 nm diameter NC is located at the bottom of the NC array. 
a) Full twodimensional FMR frequency landscape. 
b) One-dimensional line scan of the FMR frequency along x = 0 nm. The bold green line indicates that the locked mode frequency, flocked = 20.51GHz, is larger than the FMR frequency in the region between the NCs whereas the bold black line indicates that the frequency of the X mode, fX = 17.58GHz, results in a localization to a region just outside NC1. 
c) Spatial distribution of the phase-locked mode. 
d) Spatial distribution of the trapped mode. 
e) Stepwise simulations where only NC1 (red), only NC2 (blue), and both NC1 and NC2 (green) are energized. Clearly the frequency of NC1, which is towards the bottom, dominates and determines the resulting synchronized frequency.