Probabilistic multiplication operation via chaotic polarity switching in a single magnetic vortex

We propose a vortex-state nanomagnetic device that generates tunable, chaos-derived probabilistic bitstreams by encoding vortex-core polarity dwell times. By applying oscillating magnetic fields, the vortex enters a chaotic regime, enabling controllable bitstream probability through a single digital threshold parameter T . Using this output, we implement probabilistic multiplication of two fractional numbers via simple down-counting logic. Unlike conventional digital multipliers that require cascaded logic gates for fractional operations, our approach performs probability-domain fractional multiplication with minimal hardware. This compact, CMOS-compatible architecture provides a proof-of-concept route toward stochastic, neuromorphic, and in-memory computing. The present work demonstrates both highly irregular vortex-polarity switching and a compact single-oscillator stochastic arithmetic primitive.