Deterministic control of the probabilistic phase dynamics in injection-locked spin-torque nano-oscillators
Spin-torque nano-oscillators (STNOs) inherently exhibit thermally driven phase fluctuations that render their dynamics truly stochastic. Here, we demonstrate that, despite this intrinsic randomness, the probability of occupying each phase state can be deterministically and continuously programmed. We experimentally investigate a vortex-based STNO operating under second-harmonic injection-locking, where the oscillator phase settles into two degenerate attractors separated by $π$ and undergoes thermally activated phase jumps. By applying a weak radio-frequency perturbation at the free-running frequency, we tune the phase-jump rates between the two attractors without suppressing the fluctuations, achieving continuous probability control from the unbiased limit to values approaching 0 or 1. The bias phase selects which attractor is favored while the bias amplitude sets the strength of the imbalance, providing two complementary control knobs within a single nanoscale device. A phase-reduced description based on an effective quasipotential quantitatively accounts for the observations. These results establish injection-locked STNOs as programmable stochastic elements and provide a hardware primitive for probabilistic computing, Ising machines, and brain-inspired computing architectures.