Designing Large Arrays of Interacting Spin-Torque Nano-Oscillators for Microwave Information Processing

Arrays of spin-torque nano-oscillators are promising for broadband microwave signal detection and processing, as well as for neuromorphic computing. In many of these applications, the oscillators should be engineered to have equally spaced frequencies and equal sensitivity to microwave inputs. Here we design spin-torque nano-oscillator arrays with these rules and estimate their optimum size for a given sensitivity, as well as the frequency range that they cover. For this purpose, we explore analytically and numerically conditions to obtain vortex spin-torque nano-oscillators with equally spaced gyrotropic oscillation frequencies and having all similar synchronization bandwidths to input microwave signals. We show that arrays of hundreds of oscillators covering ranges of several hundred MHz can be built taking into account nanofabrication constraints.

Figure 1

(a) Schematic illustration of the spin-torque nano-oscillator having a magnetic vortex configuration for the free layer (blue). The yellow layer illustrates the nonmagnetic layer and the gray layer corresponds to the pinned layer. The magnetization of the free layer is planar except in the vortex-core area where it becomes out of plane. (b) The schematic illustrates an array of $N$ interacting spin-torque nano-oscillators receiving microwave-frequency inputs (for more details see Appendix pp3). The different synchronization states of this array correspond to the output.

Figure 2

Lower graph: analytical auto-oscillation frequency of each nano-oscillator resulting from the application of the selected individual dc current as a function of the chosen nanodot radius. The color code indicates the corresponding free-layer thickness. Upper graph: distribution of the analytical injection locking range for a constant external microwave signal amplitude, as a function of the chosen nanodot radius for different thicknesses. The analytical injection locking range remains contained around 5 MHz.

Figure 3

Chosen applied dc current versus nanodot radius for the different selected free-layer thicknesses. Dashed lines correspond to the critical current to obtain auto-oscillations. Colors correspond to different free-layer thicknesses as in Fig. 2. The red line represents the dc current corresponding to the breakdown voltage.

Figure 4

Maximum number of nano-oscillators (black squares) and their total frequency bandwidth (white circles) in the array as a function of the frequency gap between their auto-oscillation frequencies. For small frequency gaps ${\delta }_f=1.5\mathrm{MHz}$, arrays of more than 300 nano-oscillators with suitable frequency and synchronization features can be designed.

Figure 5

Color map showing the maximum number of nano-oscillators in the array as a function of the minimum radius and thickness variations allowed for the nanopillars, for a minimum dc current variation of $\delta I=0.1\mathrm{mA}$.

Figure 6

(a) Simulated synchronization state map of the 100 coupled nano-oscillators with analytically designed free-layer dimensions and applied dc current. The $x$ and $y$ axes correspond to the frequencies of the two microwave inputs injected electrically to the array. Depending on these input frequencies, different oscillators are phase locked to one of the two microwave inputs. Each small square represents one particular synchronization state. (b) Enlargement of a square area of the main synchronization map. Colors are chosen arbitrarily to help to distinguish between synchronization-state neighbors.

Figure 7

Mean injection locking range of 10 simulated coupled spin-torque nano-oscillators as a function of the coupling-factor amplitude $k$.

Figure 8

Schematic of the electrical circuit of an array of $N$ spin-torque nano-oscillators receiving $N$ independent dc currents. The array receives the microwave input in the form of an ac magnetic field generated by an inductive line.