Spintronics: Entropy probes stochastic relaxation times of nanomagnets


Uncovering design guidelines for probabilistic computing devices

Dr. Kanai, the corresponding author of the article

As neuromorphic applications such as machine learning and artificial intelligence continue to expand, progress in p-bit research1, 2 promises to use probabilistic computing to meet their escalating energy and efficiency demands.

To this end, a recent approach that directly contributed to the p-bit hardware implementation focused on the switching volatility of stochastic magnetic tunnel junctions (MTJs). An example of this is a 2021 article by Kanai et al. from AIMR, who investigated which MTJ features control the relaxation time between the “1” and “0” states of stochastic nanomagnets3.

“Our idea was to model the stochasticity of magnetic systems using entropy,” explains Kanai. “At the time of this work, this method had never been used to study magnetization dynamics.”

Deriving a universal equation governing the entropy in magnetization dynamics, the research team discovered that the entropy rapidly increases in nanomagnets with an in-plane magnetic easy axis and larger magnitudes of perpendicular magnetic anisotropy, suggesting the in-plane easy axis to be conducive to shorter relaxation times.

These theoretical results later enabled the team to fabricate stochastic MTJs with relaxation times in the nanosecond range—100,000 time faster than the contemporaneous standard MTJs4.

“Our theoretical work on relaxation time did not only help us realize faster MTJs,” says Kanai. “It also provided design information on how to tailor the input-output properties and robustness against external magnetic fields of these devices5, 6.”

(Author: Patrick Han)


  1. Camsari, K.Y., Faria R., Sutton, B.M., & Datta, S. Stochastic p-bits for invertible logic Phys. Rev. X 7, 031014 (2017). | article
  2. Borders, W.A., Pervaiz, A.Z., Fukami S., Camsari, K.Y., Ohno, H. & Datta, S. Integer factorization using stochastic magnetic tunnel junctions Nature 573, 390 (2019). | article
  3. Kanai, S., Hayakawa, K., Ohno, H. & Fukami, S. Theory of relaxation time of stochastic nanomagnets Physical Review B 103, 094423 (2021). | article
  4. Hayakawa, K., Kanai, S., Funatsu, T., Igarashi, J., Jinnai, B., Borders, W.A., Ohno, H. & Fukami, S. Nanosecond random telegraph noise in in-plane magnetic tunnel junctions Physical Review Letters 126, 117202 (2021). | article
  5. Kobayashi, K., Borders, W. A., Kanai, S., Hayakawa, K., Ohno, H. & Fukami, S. Sigmoidal curves of stochastic magnetic tunnel junctions with perpendicular easy axis Applied Physics Letters 119, 132406(1)-(5) (2021). | article
  6. Funatsu, T., Kanai, S., Ieda, J., Fukami, S., & Ohno, H. Local bifurcation with spin-transfer torque in superparamagnetic tunnel junctions Nature Communications 13, 4079(1)-(8) (2022). | article

This research highlight has been approved by the authors of the original article and all information and data contained within has been provided by said authors.