Phase locking, intermittency and chaos, of an array of magnon-ic crystal cavities driven by spin torque nano oscillators

Abstract

Magnonic crystals created by an array of periodically arranged holes on a thin ferromagnetic film show frequency bandgaps in their spin wave spectrum. By removing a few holes, or anti-dots, from the array, we are able to create magnonic crystal cavities (MCCs) where spin waves of a particular wavelength are resonant. By adding a nano-contact and driving spin polarized current, or a spin torque nano-contact oscillator (STNO) to each cavity, we are able to simulate a gain element within that cavity. The combination of gain and a resonant cavity, lead to the creation of a SWASER, whose optical analogue is the commonly used LASER. We have previously reported how a MCC can be designed to generate a narrow linewidth spin wave excitation [1]. The aim of the present work is to demonstrate how arrays of these cavities can be arranged to transfer power, in phase, to an adjacent magnonic crystal waveguide (MCW). The radius of the anti-dot and the lattice constant of the magnonic crystal are 40 nm and 150 nm, respectively. The full geometry consists of 49 x 49 unit cells, and the MCW was created by removing one row of anti-dots. The MCCs were placed on either side of the MCW, again separated by one row of anti-dots. Each MCC was created by removing 3 anti-dots, and a STNO placed at the center of the MCC. We work with the magnetic properties of permalloy, assume a damping constant of 0.01, and apply a static external field along the direction of the MCW. The simulation data was probed in a region of the MCW and saved every 10 ps, with sufficient resolution to observed spin wave oscillations up to 50 GHz. Other aspects of the simulation methodology have been previously reported [1]. The locations of the MCCs, relative to each other and the adjacent waveguide, are restricted by the very nature of the peridocity of the underlyig lattice. We use the GPU accelerated parallel micromagnetic solver, MuMax [2], to study the performance of different numbers of MCCs, and observe that the coupling between cavities can cause a loss of resonant spin wave precession. However, this can be mitigated by changing the spin polarized current that drives the spin torque within each cavity. We find that it is possible to lock adjacent cavities using 20% lower spin polarized currents, as compared to a single cavity. The same (lower) spin polarized current when applied to a single cavity requires a much longer time to drive the spin waves into resonance, as shown in Figure 1. Our studies thus establish one means to scale the spin wave power that can be generated using spin polarized current pumping into nano-contacts. This has immense practical significance, as it has been thus far difficult to use arrays of nano-contacts to generate sufficent spin wave amplitudes that can be used in RF devices. Changing the spin polarized current in the STNO allows us to tune the wavelength of the SWs in the cavity, and find the correct phase locking between cavities. However, we must be cautious to report that in the process of scaling to arrays of SWASERs, we have observed the onset of intermittency and chaos in the SW oscillations that are reminiscent of similar phenomena in LASERs [3]. These nonlinear phenomena have been traditionally observed in SW propagation in magnetic films [4]. However, we believe that these are the first observations, albeit through simulations, of the possible onset of these nonlinearities in coupled SWASER cavities.