Low-Barrier Nanomagnets as p-Bits for Spin Logic

It has recently been shown that a suitably interconnected network of tunable telegraphic noise generators or “p-bits” can be used to perform even precise arithmetic functions like a 32-bit adder. In this letter, we use simulations based on the stochastic Landau–Lifshitz–Gilbert (sLLG) equation to demonstrate that similar impressive functions can be performed using unstable nanomagnets with energy barriers as low as a fraction of a kT. This is surprising because the magnetization of low-barrier nanomagnets is not telegraphic with discrete values of <tex-math notation="LaTeX">± 1</tex-math> . Rather, it fluctuates randomly among all values between <tex-math notation="LaTeX">$-$</tex-math> 1 and +1, and the output magnets are read with a thresholding device that translates all positive values to one and all negative values to zero. We present sLLG-based simulations demonstrating the operation of a 32-bit adder, with a network of several hundred nanomagnets, exhibiting a remarkably precise correlation: The input magnets { A } and { B } as well as the output magnets { S } all fluctuate randomly and yet the quantity <tex-math notation="LaTeX">$A+B$</tex-math> <tex-math notation="LaTeX"> $-$</tex-math> <tex-math notation="LaTeX">S</tex-math> is sharply peaked around zero! If we fix { A } and { B }, the sum magnets { S } rapidly converge to a unique state with <tex-math notation="LaTeX">$S=A+B$</tex-math> so that the system acts as an adder. But unlike standard adders, the operation is invertible. If we fix { S } and { B }, the remaining magnets { A } converge to the difference <tex-math notation="LaTeX">$A=S-B$</tex-math> . These examples emphasize a new direction for the field of nanomagnetics away from stable high-barrier magnets toward stochastic low-barrier magnets that not only operate with lower currents, but are also more promising for continued downscaling.