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A majority gate for nanomagnetic logic with perpendicular magnetic anisotropy is presented. A novel technique of local focused ion beam irradiation generating artificial domain wall nucleation centers is used to enable directed signal flow and logic computation in an array of field-coupled nanomagnets. The switching behavior of the majority gate is characterized and logic operation is experimentally proven using magneto-optical and magnetic force microscopy. The findings are supported by numerical and micromagnetic simulations. Tolerance margins for fabrication and computing frequencies for correct operation are explored. The presented majority gate allows for complex, non-volatile logic with synchronous global clocking at room-temperature.