In-situ Probabilistic Sampling using Field-free Spin-orbit Devices with Markov Property

Markov chain Monte Carlo (MCMC) sampling uses stochastic updates to sample a target probability distribution and is widely used in scientific computing. Spintronic probabilistic bits (p-bits) provide intrinsic stochasticity, but devices with low energy barriers lack nonvolatile state retention, which complicates in-situ MCMC sampling. Here, we experimentally demonstrate initial-state-dependent stochastic switching in nonvolatile, field-free spin-orbit torque (SOT) devices. The retained magnetic state and the applied pulse amplitude jointly determine the conditional switching probabilities, allowing the devices to operate as conditional probabilistic bits (cp-bits). Micromagnetic simulations provide a qualitative interpretation of the switching mechanism. We then illustrate MCMC sampling through software simulations using an experiment-derived cp-bit model and a modified Metropolis acceptance rule; the sampling was not implemented with an array of physical devices. These results suggest a possible route toward in-memory probabilistic computing that combines state retention with stochastic updates.