Fig. 1: Operating principles of the MCA.

a MCA architecture comprising serially connected magnetic unit cells. b Structure of a single unit cell. Red and blue rectangles denote domains with –z and +z magnetization. Gold strips and pads indicate AHE readout electrodes. The domain length is \({L}_{D}\), the electrode contact length is \({L}_{P}\), and the spacing between Hall-electrode pairs is \({W}_{P}\). During readout, a current \({I}_{H}\) flows along the conduit and the transverse Hall voltage \({V}_{H}\) is measured. c Schematic of MCA-based convolution. The input domains (top) and kernel coefficients (second row) are represented by discrete values of \({L}_{D}\) and \({W}_{P}\). The device-level cartoon (third row) illustrates stationary electrodes and sequential domain shifting. The resulting Hall-voltage sequence (bottom) corresponds to the convolution output. d DW shifting driven by SOT. A charge current \(j\) generates a transverse spin current \({j}_{s}\), which applies a torque on the DWs and translates the domains along the track.