Variability of Binary Stochastic Neurons Employing Low Energy Barrier Nanomagnets with In-plane Anisotropy

Binary stochastic neurons (BSNs) are excellent hardware accelerators for machine learning. An ideal platform for implementing them are low- or zero-energy-barrier nanomagnets (LBMs) possessing in-plane anisotropy (e.g. circular or slightly elliptical disks) whose fluctuating magnetization encodes a probabilistic bit. Here, we show that such a BSN's activation function, the pinning current (which pins the output to a particular binary state), and the correlation time associated with the decay of the auto-correlation of the fluctuation (which determines the speed of the BSN) - all exhibit strong sensitivity to very slight geometric variations in the LBM. For example, a mere 1% change in the diameter of a circular LBM in any arbitrary direction can change the correlation time by a factor of 3-4 at room temperature and a 10% variation can change the pinning current by a factor of ~2. All this poses a design challenge. It appears that slightly elliptical LBMs may be preferable over perfectly circular LBMs. We also show that spin inertia, which gives rise to nutation during the initial few fs or ps of the magnetization dynamics and can sometimes have long-term outcomes, has no significant effect on the BSN characteristics.