Reservoir Computing with Random Skyrmion Textures

The reservoir computing paradigm posits that complex physical systems can be used to simplify pattern recognition tasks and nonlinear signal prediction. We show that random topological magnetic textures pinned by grain inhomogeneities demonstrate desirable dynamical responses for the implementation of reservoir computing as applied to ac current pulses. By harnessing the complex resistance or magnetization responses exhibited by random magnetic skyrmion textures to demonstrate simple pattern recognition, we explain how spintronics systems offer an advantage in the search for an ideal reservoir computer. The dynamical properties of compact skyrmion fabrics, coupled with their CMOS integrability operating on similar length and timescales, open the door for skyrmion-based reservoir computing applications.

Figure 1

General setup of reservoir computing for (a) a recurrent neural network and (b) a material-based reservoir. (c) Example of a skyrmion fabric reservoir with the locations of input (output) contacts identified by green (red) circles. The in-plane orientation of the magnetization is color coded and (d) shown in detail with arrows for a sample Bloch skyrmion identified by the red frame in (c).

Figure 2

(a) Randomly generated DMI grain inhomogeneities employed to pin skyrmions. (b) Sample skyrmion texture used for simulations. The locations of the electrical nanocontacts are identified by the yellow circles (size has been enhanced for visibility). (c) Current distribution through the magnetic texture shown in (b) with applied voltage ($110\mathrm{mV}$) across the nanocontacts.

Figure 3

AMR response (red) of the magnetic texture to individual sine and square voltage pulses (dashed blue) used to drive the magnetization dynamics with frequencies of (a) $1\mathrm{GHz}$ and (d) $5\mathrm{GHz}$. AMR response to identically structured pulse trains used to drive the magnetic texture with varying combinations of sine and square voltage pulses with frequencies of (b) $1\mathrm{GHz}$ and (e) $5\mathrm{GHz}$. Resistances are given in units of $R_0$, which denotes the geometry’s AMR resistance in the vanishing applied voltage limit. In (a) and (d), the ring down of the magnetic texture is exemplified by the delay between the voltage pulse ending and the AMR relaxation to equilibrium. In (b) and (e), the AMR response observed for individual pulses is superimposed consistently with the driving voltage (yellow) for comparison with the simulated AMR response to emphasize its nonlinear behavior. At frequencies much larger than the system’s FMR frequency (e) the magnetic texture’s nonlinear evolution does not have sufficient time to respond to the driving voltage patterns, leading to a close match between both the AMR response of (d) the individual pulses as well as (e) the response of the pulse train with its linear reconstruction (see the inset for details). At frequencies comparable with the FMR frequency the magnetization dynamics are highly sensitive to both the instantaneous voltage intensity and memory of past voltage values, presenting a large spike in the peak AMR resistance. This is apparent in both the AMR response to (a) individual sine and square pulses as well as (b) a strong difference between the pulse train’s response and the linear reconstruction. We characterize the AMR response observed in (b) by four reproducible and distinct resistance pulse shapes depending on whether a (c1) sine-square, (c2) square-sine, (c3) square-square, or a (c4) sine-sine pulse combination drives the dynamics; for a thorough analysis; see Sec. 4.

Figure 4

(a) Example peak AMR response to a $1\mathrm{GHz}$ pulse train driving as a function of lateral size of the magnetic geometry (vertical size is kept constant). (b) Average equilibrium AMR resistance of a $250\times 500{\mathrm{nm}}^2$ geometry as a function of temperature in the limit of vanishing applied voltage. As in previous results, resistances are given in units of $R_0$, which denotes the zero temperature equilibrium of the $250\times 500{\mathrm{nm}}^2$ geometry. Combining (a) and (b), we expect that AMR signals will still be qualitatively distinguishable for temperatures below $100\mathrm{K}$.

Figure 5

(a) Schematic of the time tracing used to train and operate the output layer (temporal axis is common for both voltage and resistance plots). The resistance response is sampled at regular intervals across the temporal window of the instantaneous—present—pulse driving the magnetic texture. (b) These resistance values are summed in weight for three different sets of weights. One set is trained to recognize the present pulse currently driving the system, the second set is trained to recognize the latent pulse preceding the present pulse, and the third set is trained to recognize the past pulse preceding the latent pulse. (c) Recognition rates of the pulses as a function of the number of resistance trace samples chosen.

Figure 6

(a) Schematic of the readout element grid used to measure averages of the out-of-plane component of the magnetic texture. Recognition rates of the voltage pulses (b) present, (c) latent, and (d) past to the readout measurement as a function of the number of grid elements used. Color coding corresponds to offset time from the beginning of the present pulse. At a $0\mathrm{ns}$ offset, the recognition rate of the present pulse is $50\mathrm{\%}$ as no information about the voltage pulse is actually present in the magnetic texture.

Figure 7

Initialization of the magnetic texture and thermal stability test. (a) An artificial skyrmion lattice is generated. (b) The lattice is relaxed under the effect of an applied external magnetic field and DMI grain inhomogeneities. (c) Thermal noise is added and allowed to act for $20\mathrm{ns}$ before being switched off. (d) The magnetic texture is relaxed again in the absence of thermal noise. (e) A $20\mathrm{ns}$ constant voltage pulse is applied to verify that skyrmions are not displaced by current-mediated transport effects.

Figure 8

Single and pulse train AMR response simulations for varying frequencies as discussed in Sec. 4: (a),(b) $0.7\mathrm{GHz}$; (c),(d) $1.6\mathrm{GHz}$; (e),(f) $1.8\mathrm{GHz}$.