Probabilistic computing with binary stochastic neurons (BSN) implemented with low- or zero-energy barrier nanoscale ferromagnets (LBMs) possessing in-plane magnetic anisotropy has emerged as an efficient paradigm for solving computationally hard problems. The fluctuating magnetization of an LBM at room temperature encodes a p-bit which is the building block of a BSN. Its only drawback is that the dynamics of common (transition metal) ferromagnets are relatively slow and hence the number of uncorrelated p-bits that can be generated per second – the so-called “flips per second” (fps) – is insufficient, leading to slow computational speed in autonomous co-processing with p-computers. Here, we show that a simple way to increase fps is to replace commonly used ferromagnets (e.g. Co, Fe, Ni), which have large saturation magnetization Ms, with a dilute magnetic semiconductor like GaMnAs with much smaller saturation magnetization. The smaller Ms reduces the energy barrier within the LBM and increases the fps significantly. It also offers other benefits such as increased packing density for increased parallelization and reduced device to device variation. This provides a way to realize the hardware acceleration and energy efficiency promise of p-computers.

We propose and analyze a compact and non-volatile nanomagnetic (all-spin) analog matrix multiplier performing the multiply-and-accumulate (MAC) operation using two magnetic tunnel junctions – one activated by strain to act as the multiplier, and the other activated by spin-orbit torque pulses to act as a domain wall synapse that performs the operation of the accumulator. Each MAC operation can be performed in ~1 ns and the maximum energy dissipated per operation is ~100 aJ. This provides a very useful hardware accelerator for machine learning (e.g. training of deep neural networks), solving combinatorial optimization problems with Ising type machines, and other artificial intelligence tasks which often involve the multiplication of large matrices. The non-volatility allows the matrix multiplier to be embedded in powerful non-von-Neumann architectures.

Probabilistic computing algorithms require electrically programmable stochasticity to encode arbitrary probability functions and controlled stochastic interaction or correlation between probabilistic (p-) bits. The latter is implemented with complex electronic components leaving a large footprint on a chip and dissipating excessive amount of energy. Here, we show an elegant implementation with just two dipole-coupled magneto-tunneling junctions (MTJ), with magnetostrictive soft layers, fabricated on a piezoelectric film. The resistance states of the two MTJs (high or low) encode the p-bit values (1 or 0) in the two streams. The first MTJ is driven to a resistance state with desired probability via a current or voltage that generates spin transfer torque, while the second MTJ’s resistance state is determined by dipole coupling with the first, thus correlating the second p-bit stream with the first. The effect of dipole coupling can be varied by generating local strain in the soft layer of the second MTJ with a local voltage (~ 0.2 V) and that varies the degree of anti-correlation between the resistance states of the two MTJs and hence between the two streams (from 0% to 100%). This paradigm generates the anti-correlation with “wireless” dipole coupling that consumes no footprint on a chip and dissipates no energy, and it controls the degree of anti-correlation with electrically generated strain that consumes minimal footprint and is extremely frugal in its use of energy. It can be extended to arbitrary number of bit streams. This realizes an “all-magnetic” platform for probabilistic computing.