Switching Characteristics of Electrically Connected Stochastically Actuated Magnetic Tunnel Junction Nanopillars

TL;DR

This work addresses how simple electrical connections between thermally activated pMTJs induce correlated stochastic switching. By extracting single-junction Poisson-switching rates and using Kirchhoff-inspired voltage redistribution, the authors build a minimal model that reproduces coupled switching probabilities; they extend this to sequential pulses with a Markov-chain framework to predict non-equilibrium steady states. They then map the resulting steady-state distributions to an Ising Hamiltonian with effective coupling $J$ and local fields $h_1,h_2$, showing that electrical control can realize tunable spin–spin interactions. The approach demonstrates programmable stochastic dynamics for Ising-machine-type computing and provides a scalable framework for engineering circuit-mediated couplings in nanoscale magnetic systems. This has implications for reconfigurable probabilistic computation and neuromorphic architectures using MTJ-based devices.

Abstract

We investigate the stochastic dynamics of nanoscale perpendicular magnetic tunnel junctions (pMTJs) and the correlations that arise when they are electrically coupled. Individual junctions exhibit thermally activated spin-transfer torque switching with transition probabilities that are well described by a Poisson process. When two junctions are connected in parallel, circuit-mediated redistribution of voltages that occurs in real time as the junction resistances change leads to correlated switching behavior. A minimal stochastic model based on single-junction statistical switching properties and Kirchhoff's laws captures the coupled switching probabilities, while a Markov-chain formalism describes nonequilibrium steady states under multi-pulse driving. Further, these circuit-mediated interactions can be mapped onto the parameters of an Ising Hamiltonian, providing an interpretation in terms of effective spin-spin interactions. Our results demonstrate how simple electrical connections can generate Ising-like couplings and tunable stochastic dynamics in nanoscale magnets.

Figures (7)

• Figure 1: (a) Schematic of the experimental setup showing the MTJ connection through a 2 k$\Omega$ resistor. (b) Hysteresis curves for two individual MTJs. Vertical dashed lines indicate reset and read voltages. (c) Example of the waveform used in the experiment. Each sequence consists of a reset pulse to initialize the MTJ state, a write pulse to induce switching, and a read pulse to measure the resulting state. The pulse durations are fixed throughout the experiment. (d) Transition probabilities for the two selected MTJs as a function of $V_A$ or $V_B$. Each point is obtained by repeating the waveform $N=10,000$. The solid lines are fitted sigmoid function as described in Eq. \ref{['eq:sigmoid']}, with fitted parameters given by Table. \ref{['tab:params']}.
• Figure 2: (a) Schematic of the experimental setup showing the MTJ connection through a 2 k$\Omega$ resistor. (b) Hysteresis curve of the resistance across the two MTJs connected in parallel. Vertical dashed lines indicate reset and read voltages. A reset voltage $V_\text{rest} = -0.6V$ set both junctions to state 1, and $V_\text{rest} = 0.6V$ set both junctions to state 0. (c) Transition probabilities for the two selected MTJs as a function of write pulse amplitude. Each point is obtained by repeating the waveform $N=100,000$.
• Figure 3: Two-step waveform for measuring the transition probability from state 01 or 10 to other four states. In the first step, the junctions are initialized to either 01 or 10. Then at second step, a variable write pulse is applied to measure the transition probability from 01 or 10 to other four states as a function of applied voltage $V$.
• Figure 4: Transition probabilities for all initial states 00, 01, 10,and 11. (a) Transition probabilities from the initial state 00 to all four possible final states. For $V_\text{write} < 0$, the transition probabilities are identical to those shown in Fig. \ref{['fig:coupled_summary']}. For $V_\text{write} > 0$, the system remains in state 00 due to the hysteresis of the junctions; positive write voltages do not induce switching from the 0 state. (b) Transition probabilities from the initial state 11 to all four possible final states. For $V_\text{write} > 0$, the transition probabilities are identical to those shown in Fig. \ref{['fig:coupled_summary']}. For $V_\text{write} < 0$, the system remains in state 11 due to the hysteresis of the junctions; that is, negative write voltages do not induce switching from the 1 state. (c) Transition probabilities from the initial state 01 to all four possible final states. (d) Transition probabilities from the initial state 10 to all four possible final states.
• Figure 5: (a) Schematic of the waveform used to measure the steady-state distribution. The same pulse sequence, $V_1$–$V_2$–Read, is applied $N = 10{,}000$ times.(b) Comparison between experimentally measured and theoretically predicted steady-state distributions for alternating pulse sequences. Two cases are shown: one with $V_1 = -0.48\,\text{V}$ and $V_2 = 0.18\,\text{V}$, and another with $V_1 = 0.195\,\text{V}$ and $V_2 = -0.455\,\text{V}$.