Electrically programmable probabilistic bit anti-correlator on a nanomagnetic platform

Execution of probabilistic computing algorithms require electrically programmable stochasticity to encode arbitrary probability functions and controlled stochastic interaction or correlation between probabilistic (p-) bits. The latter is implemented with complex electronic components leaving a large footprint on a chip and dissipating excessive amount of energy. Here, we show an elegant implementation with just two dipole-coupled magneto-tunneling junctions (MTJ), with magnetostrictive soft layers, fabricated on a piezoelectric film. The resistance states of the two MTJs (high or low) encode the p-bit values (1 or 0) in the two streams. The first MTJ is driven to a resistance state with desired probability via a current or voltage that generates spin transfer torque, while the second MTJ’s resistance state is determined by dipole coupling with the first, thus correlating the second p-bit stream with the first. The effect of dipole coupling can be varied by generating local strain in the soft layer of the second MTJ with a local voltage (~ 0.2 V) and that varies the degree of anti-correlation between the resistance states of the two MTJs and hence between the two streams (from 0 to 100%). This paradigm generates the anti-correlation with “wireless” dipole coupling that consumes no footprint on a chip and dissipates no energy, and it controls the degree of anti-correlation with electrically generated strain that consumes minimal footprint and is extremely frugal in its use of energy. It can be extended to arbitrary number of bit streams. This realizes an “all-magnetic” platform for generating correlations or anti-correlations for probabilistic computing. It also implements a simple 2-node Bayesian network.

shows the soft layer of MTJ A schematically. We initialize the magnetization state of this layer with a very large spin polarized current which makes the magnetization point in the direction that represents bit 0 (i.e.  = 0 0 or m z = +1). Next, varying magnitude of spin polarized current, with spin polarized along the direction representing bit 1, is injected perpendicular to the plane of the layer to make the magnetization point in the direction representing bit 1 (i.e.  = 180 0 or m z = -1) with varying probability. The probability depends on the magnitude of the current and we calculate the probability as a function of the current's magnitude.
The probability is calculated by simulating the magneto-dynamics in the soft layer using the stochastic Landau-Lifshitz-Gilbert equation which is Equation (1) in the text, except in this case, there is Since the spin polarized current through the MTJ will be the dominant determinant of magneto-dynamics, we can ignore the dipole field. the direction representing the bit 0. Current with spin polarized in the opposite direction along the major axis is injected and we calculate the probability that the magnetization flips to represent bit 1. This is the probability P(1). We run the simulation following Equation (1) of the text until steady state is reached and the magnetization has settled to one of the two stable orientations along the major (easy) axis, i.e.   1), as a function of the spin polarized current magnitude. Clearly, we can control the probability to be anything between 0% and 100% with the magnitude of the spin polarized current.
We have also examined a situation where the initial condition is the magnetization of the soft layer of MTJ A is initially made to point along the minor (hard) axis. This can be ensured with an in-plane magnetic field in the direction of the minor axis that is initially turned on and then turned off. Fig. S2(b) plots the probability in this case as a function of the magnitude and sign of the spin polarized current. The sign is positive when the spin polarization is in the direction representing bit 1 and negative when it represents bit 0. In this case, we ran only 1000 simulations. Note that in this case, we need a much lower magnitude of the spin polarized current (an order of magnitude lower), which will reduce the energy dissipation. The disadvantage is that we will need to turn on and off an in-plane magnetic field each time we reset the probability generator. To produce the magnetic field will also require dissipating some energy.

Exchange coupled MTJ for high magnetostriction and high tunneling magneto-resistance ratio (TMR)
In our simulation, we considered an MTJ whose soft layer is made of Terfenol-D which provides high magnetostriction. This reduces the voltage needed to produce a given amount of strain in the piezoelectric and hence in the soft layer. Ultimately, that reduces the energy required to modulate the correlation.
However, the TMR of MTJs with Terfenol-D soft layer is not known. The highest TMRs are obtained in MTJs with CoFeB/MgO/CoFeB layers. One can engineer the best of both worlds by fabricating the structure shown below:

Fig. S4: An exchange coupled MTJ
In this structure, the bottom Terfenol-D and CoFeB layers are exchange coupled and hence their magnetization rotations are synchronized, i.e. when one rotates, the other does too. There could, however, be a potential lattice mismatch issue between Terfenol-D and CoFeB. An ultrathin texture break interlayer, e.g. Ta, which could maintain the exchange coupling between Terfenol-D and CoFeB, can be used to further optimize the performance of the composite soft layer (CoFeB/Ta(0.6-0.8nm)/Terfenol-D). This idea has been proposed and demonstrated (albeit with a different material system), and is used in today's STT-RAM product [1].

Correlator versus anti-correlator
If MTJ A and MTJ B are placed such that the line joining the centers of their elliptical soft layers is collinear with their minor axes (hard axes), as shown in Fig. S5(a), then dipole coupling prefers "antiferromagnetic ordering", i.e. the magnetizations of the two layers tend to be mutually antiparallel. This would lead to an anti-correlator. However, if MTJ A and MTJ B are placed such that the line joining the centers of their elliptical soft layers is collinear with their major axes (easy axes), as shown in Fig. S5(b), then dipole coupling prefers "ferromagnetic ordering", i.e. the magnetizations of the two layers tend to be mutually parallel. This would lead to a correlator. The system is not reconfigurable, i.e. the same pair cannot be made to act as either a correlator, or an anti-correlator, at will. However, this is not needed for most applications in probabilistic computing and belief networks.