We numerically investigate the feasibility of spin wave (SW) based parallel logic operations, where the phase of SW packet (SWP) is exploited as a state variable and the phase shift caused by the interaction with domain wall (DW) is utilized as a logic inversion functionality. A designed functional element consists of parallel ferromagnetic nanowires (6nm-thick, 36nm-width, 5120nm-length, and 200nm separation) with the perpendicular magnetization and sub-μm scale overlaid conductors. The logic outputs for binary data, coded with the existence ("1") or absence ("0") of the DW, are inductively read out from interferometric aspect of the superposed SWPs, one of them propagating through the stored data area. A practical exclusive-or operation, based on 2π periodicity in the phase logic, is demonstrated for the individual nanowire with an order of different output voltage V out, depending on the logic output for the stored data. The inductive output from the two nanowires exhibits well defined three different signal levels, corresponding to the information distance (Hamming distance) between 2-bit data stored in the multiple nanowires.
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