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 +/- 1. Rather, it fluctuates randomly among all values between -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 A + B-S is sharply peaked around zero! If we fix {A} and {B}, the sum magnets {S} rapidly converge to a unique state with S = A + B 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 A = S - B. 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.