Mutual control of stochastic switching for two electrically coupled superparamagnetic tunnel junctions

TL;DR

This work demonstrates mutual coupling between two stochastic SMTJs using a simple linear dc-coupled circuit, inducing correlated switching without complex peripherals. It combines a Néel-Brown based parameterization of uncoupled dwell times with a four-state Markov model to predict the coupled dynamics, confirming agreement with experiments. The coupling is strongest in the mid-superparamagnetic regime and enhances with higher TMR and device similarity, with the correlation sign tunable by bias polarity. The approach offers a scalable, energy-efficient path toward networks of SMTJs for probabilistic computing, supported by predictive modeling for larger arrays.

Abstract

Superparamagnetic tunnel junctions (SMTJs) are promising sources for the randomness required by some compact and energy-efficient computing schemes. Coupling SMTJs gives rise to collective behavior that could be useful for cognitive computing. We use a simple linear electrical circuit to mutually couple two SMTJs through their stochastic electrical transitions. When one SMTJ makes a thermally induced transition, the voltage across both SMTJs changes, modifying the transition rates of both. This coupling leads to significant correlation between the states of the two devices. Using fits to a generalized Néel-Brown model for the individual thermally bistable magnetic devices, we can accurately reproduce the behavior of the coupled devices with a Markov model.

Figures (11)

• Figure 1: Schematic of the electrical circuit used to couple two superparamagnetic tunnel junctions and the four metastable configurations they take. Each panel shows the constant voltage source $V_0$, the series resistor $R_0$, the two SMTJs in parallel with each other, and a voltmeter representing the oscilloscope measurement of the shared voltage across the SMTJs. The yellow arrows connecting the four panels represent thermally driven transitions between the different configurations of the SMTJs. Panel (a) shows both SMTJs in the parallel (P) state, with the free layer (bottom) magnetization parallel to the fixed layer (top) magnetization. When the magnetization in the free layer of either SMTJ flips, panels (b) and (c), the resistance of the now antiparallel SMTJ (indicated by a purple free layer) increases so the voltage across both SMTJs increases. The voltages in these two cases differ due to differences in the magnetoresistance of the two devices. If both free layers flip, the system goes to the configuration in panel (d), with both SMTJs in the antiparallel (AP) state and the largest magnitude voltage across both SMTJs.
• Figure 2: (a) Experimental evolution of the dc resistance of the studied SMTJs versus the applied in-plane magnetic field, swept from 6 mT to 10 mT and back. Those characteristics were obtained for a constant applied dc voltage $V_0=-0.1$ V and a series resistor of $R_0=473~\Omega$. (b) Experimental time trace of the voltage of a single SMTJ $\mu_0H= 6.9$ mT, $V_0=-0.45$ V, in parallel with a static resistor of $R_{eq}=1085~\Omega$. This panel covers a single transition from the antiparallel to the parallel state illustrating the effects of $RC$ time constants on the transitions. Fit to an exponential gives a time constant $\tau_{RC}$ for the measurement of (71$\pm$14) ns. (c) Longer time trace showing approximately 50 transitions over 1 ms. The different noise levels around the two voltage states reflect that the measurement is being taken in an asymmetric configuration; the lower voltage state is relatively stabilized by the applied voltage, and consequently undergoes weaker thermal fluctuations. (d) Histogram of measured voltages over 2 s containing roughly $10^5$ transitions. Note logarithmic $x$-axis; $y$-axis is shared with (c).
• Figure 3: (a) Time trace of the voltage of two coupled SMTJs, for $\mu_0H=6.9\;\text{mT}$, $V_0=-0.45\;\text{V}$ and $R_0=473~\Omega$. (b) Histogram of measured voltages over 20 s. Note the logarithmic scale on the horizontal axis.
• Figure 4: (b) Probabilities of occupancy for the different joint configurations of two coupled SMTJs, with $V_0=-0.45\;\text{V}$. (a) Determinant of the probabilities in (b) as in Eq. \ref{['eq:p-matrix']}. Error bars indicate single standard deviation uncertainties.
• Figure 5: Auto- and cross-correlation for the states of two coupled SMTJs. Solid lines are derived from experimental data at $\mu_0H= 7.6$ mT, $V_0=-0.3$ V. Dashed lines are derived from the Néel-Brown model fit with the parameters of Table \ref{['tab:table1']} (Appendix \ref{['app:neelbrown']}) at the same field and voltage, and a Markov model for the coupling (Appendix \ref{['app:markov']}). In the log scale inset, the gray line is the geometric mean of the model-predicted coupled autocorrelations, which serves as an asymptotic upper bound for the cross-correlation.