Abstract
Memristors are nonvolatile nanoresistors which resistance can be tuned by applied currents or voltages and set to a large number of levels. Thanks to these properties, memristors are ideal building blocks for a number of applications such as multilevel nonvolatile memories and artificial nanosynapses, which are the focus of this work. A key point towards the development of large scale memristive neuromorphic hardware is to build these neural networks with a memristor technology compatible with the best candidates for the future mainstream nonvolatile memories. Here we show the first experimental achievement of a multilevel memristor compatible with spintorque magnetic random access memories. The resistive switching in our spintorque memristor is linked to the displacement of a magnetic domain wall by spintorques in a perpendicularly magnetized magnetic tunnel junction. We demonstrate that our magnetic synapse has a large number of intermediate resistance states, sufficient for neural computation. Moreover, we show that engineering the device geometry allows leveraging the most efficient spin torque to displace the magnetic domain wall at low current densities and thus to minimize the energy cost of our memristor. Our results pave the way for spintorque based analog magnetic neural computation.
Introduction
The resistance of a memristor depends on the amplitude and duration of the successive voltages that have been previously applied between its electrodes^{1}. The resulting intricate resistance versus voltage hysteresis loops illustrated in Fig. 1a are the hallmark of memristor nanodevices. Thanks to their memory and tunability features, memristors can imitate a very important property of biological synapses: their plasticity^{2}. Synaptic plasticity is the ability of synapses to reconfigure the strength with which they connect two neurons according to the past electrical activity of these neurons. In the brain, this phenomenon allows memories to be formed and stored. In hardware, artificial synapses endowed with plasticity allow neural networks to learn and adapt to a changing environment. Today, memristors are considered as the best solution to realize such plastic nanosynapses. Fabricating memristor devices requires triggering voltage induced resistive changes at the nanoscale. Several physical effects can be harnessed for this purpose: reductionoxydation phenomena^{3}, phase changes^{4,5}, atomic displacements^{6} or ferroelectric switching^{7}. The current challenge is to go beyond the realization of single devices and to build dense and functional arrays of memristors. Given the spread of possible solutions, all of them with their respective advantages and downsides^{8}, it is likely that future neuromorphic hardware will be built using the nonvolatile memory technology that will be available on the market in the next few years. While competition is fierce in this domain, thanks to recent advances, the spintorque magnetic random access memory is among the most promising technologies^{9}.
In this report, we show the first experimental realization of a spintorque memristor with the potential to provide massive local memory access to large scale magnetic neural networks. As illustrated in Fig. 1b (left), the spintorque memristor is a magnetic tunnel junction with a single magnetic domain wall in its free layer. Thanks to the spintorque effect, the domain wall (DW) can be displaced back and forth by applying positive or negative voltages across the stripeshaped junction. As shown in Fig. 1d, when the voltage is removed, the domain wall stabilizes in different pinning sites corresponding to different positions along the track. Each domain wall position has a different resistance values thanks to the tunnel magnetoresistance effect, leading to the desired memristive features^{10,11,12}.
Multilevel switching
The magnetic tunnel junctions are fabricated by electron beam lithography and ion beam milling from a film deposited by magnetron sputtering. A side view of the samples is given in Fig. 1b, where the domain wall is the purple region of width Δ. The magnetic stack consists of a synthetic antiferromagnet [CoPt(2.4)/Ru(0.9)/CoPt(1.3)/Ta(0.2)/FeB(1)], a tunnel barrier MgO(1), a magnetic free layer [FeB(1.2)/Ta(0.3)/FeB(0.7)] and a capping layer [MgO(1)/Ta(6)], with thicknesses in nanometers^{13}. The tunnel magnetoresistance ratio is about 95% at room temperature for a minimum resistance of 36 Ω. In the case of magnetic tunnel junctions, the two extreme values of resistance in Fig. 1a correspond to the parallel (P) and antiparallel (AP) magnetizations configurations of the free layer and the top layer of the synthetic antiferromagnet. A top view of the samples is shown in Fig. 1b (right). The domain wall propagates in a micrometerlong track of width W. The samples also include a nucleation pad with larger dimensions than the track designed to facilitate the creation of the domain wall in the free layer. The samples are fabricated with three different track widths W of 90, 100 and 110 nm and with three different sizes of nucleation pad.
As shown in Fig. 1b, our spintorque memristor is a two terminal device: the currents for reading and writing the resistance states are both injected perpendicularly to the magnetic layers. Figure 1c shows the evolution of the junction resistance measured as a function of the vertically injected dc current. Positive currents correspond to an electron flow from the synthetic antiferromagnet to the free layer. The measurement is performed in the presence of an external field H_{z} = 85 Oe applied along the perpendicular direction in order to suppress the stray field emitted by the synthetic antiferromagnet. Starting from a uniform state (P or AP), a domain wall is nucleated by vertical injection of current. Then, it can be displaced back and forth, towards the AP state with negative currents and towards the P state with positive currents. During its propagation, the domain wall gets pinned in random defects at the edges or the surface of the sample. This gives rise to the multiple levels of resistance observable in Fig. 1c. For each of the five samples we have measured under dc current injection, the number of observed intermediate resistance states is comprised between 15 and 20. D. Querlioz et al. have simulated a neuromorphic system where each synapse is composed of several binary magnetic tunnel junctions connected in parallel^{14}. They show (see Fig. 6 of ref. 14) that 7 to 10 binary junctions are necessary in each synapse for recognizing handwritten digits with a reasonable rate above 75%. This result, transposed to our system, means that 13 to 19 resistance levels should be sufficient for pattern classification tasks.
Due to the random nature of pinning, our memristors are subject to cycle to cycle variability, as well as variations between different devices. However, it has been shown numerically that the quality of learning is little affected by variability in memristive neural networks^{15}. In addition, the impact of this variability can be minimized in the future simply by applying short voltage pulses instead of dc currents. Indeed, when dc currents are applied, the domain wall is continuously pushed and passes over accessible defects without stopping. Applying voltage pulses of nanoseconds duration will lead to smaller domain wall displacements and smaller resistance changes. The resulting resistance versus voltage curve should thus be smoother, with many more intermediate levels, reducing at the same time devicetodevice variations.
Based on a magnetic tunnel junction, which is also the building block of the next generation of magnetic memories, our spintorque memristor has the advantages of this technology: CMOS compatibility and exceptional cyclability compared to other resistive switching devices^{9,16}. It is made of the same magnetic layers stack as magnetic memories and spintorque nanooscillators, opening the path to computing by assembling magnetic building blocks with different functionalities^{17}. In addition, magnetic domain walls can move with large speeds when pushed by spintorques in magnetic tunnel junctions, over 500 m/s, promising subnanosecond resistance variations in submicrometer stripes for applied voltages of the order of one Volt^{18}. The spintorque memristor presented here is a twoterminal device, which is promising for miniaturization and integration in neuromorphic networks^{19}. In addition, in the two terminals geometry, the currents incoming from the neurons to which the memristor is connected are not only set by the memristor’s resistance, but they can also modify its resistance depending on their respective amplitudes and durations. In this way, the transmission of two terminal artificial synapses can evolve autonomously according to local voltages, allowing unsupervised learning^{20,21}. Therefore, towards autonomous learning, classical spin torques^{22} have an advantage over spinorbit torques, which require a threeterminal geometry^{23,24,25}.
Low current densities and stochasticity
Additionally to the large number of intermediate states, the resistance versus current loops of our memristors, displayed in Fig. 1c, always show two notable features. First, domain wall displacements are obtained for current densities of the order of 10^{6} A/cm^{2}. This value is remarkably small for spintorque induced domain wall motion in perpendicularly magnetized materials^{26,27,28,29}. Secondly, the currentinduced switching between different resistance levels appears highly stochastic. Figure 2c,d show the typical experimental resistive variations associated with domain wall depinning in our samples of width 100 nm. At zero current the domain wall is in a pinning site corresponding to a resistance value of 38.5 Ω. Figure 2c shows domain wall depinning by current for several values of the external field. In that case, the domain wall motion is extremely stochastic close to the threshold current values for depinning, jumping back and forth between pinning centers separated by several hundreds of nanometers. These stochastic features, that arise when the domain wall is pushed by current, are a potential asset for neural computation^{14,30}. When the domain wall depinning is driven by a magnetic field instead of a current, the stochasticity completely disappears, as can be seen in Fig. 2d. This means that spintorques and magnetic fields exert completely different forces on the domain wall. In the following, we describe how we have engineered our magnetic tunnel junctions in order to obtain these high efficiency and stochasticity of spintorque driven domain wall motion.
When the current is injected vertically in a magnetic tunnel junction, two spin torques are exerted on the magnetization of the free layer: the Slonczewski torque (ST) and the Fieldliketorque (FLT)^{31}. The Fieldliketorque is smaller than the Slonczewski torque and the ratio of their amplitudes, ζ, is typically 30% in magnetic tunnel junctions^{32}. We have designed our magnetic tunnel junctions in order to leverage the largest spintorque, the Slonczewski torque, to displace the domain wall. Indeed, the Slonczewski torque and the Fieldliketorque have very different actions on the domain wall depinning process. Figure 2b illustrates the energy landscape in each case. On the left is sketched the case of domain wall depinning governed by the Fieldliketorque only. In our geometry, the Fieldliketorque is equivalent to a field applied in the z direction, along the spins in the domains on each side of the wall. Therefore it has the proper symmetry to push the domain wall along the track (along the x axis in Fig. 2a), by modifying its position x. The energy barrier that the Fieldliketorque has to overcome in order to move the domain wall is directly related to the depinning field H_{c}, an intrinsic property of the pinning center. The right part of Fig. 2b shows the case of a domain wall depinning governed by the Slonczewski torque only. By symmetry this torque can modify the tilt angle ϕ of the magnetization within the domain wall (Fig. 2a). Therefore the Slonczewski torque can depin a domain wall by rotating its internal angle. The energy it has to overcome is the domain wall anisotropy K. Once the domain wall is depinned the Slonczewski torque continues to increase its ϕ angle. This drives the domain into a precessional regime known as the Walker breakdown, where the domain wall continuously oscillates between the Bloch and Néel configurations^{18,33}. Making the Slonczewski torque the most efficient spintorque to depin the domain wall requires lowering the domain wall anisotropy field H_{K} below the coercive field H_{c}. One way to reach this condition is to design an anisotropyless domain wall, that can freely oscillate between the Bloch and Néel configurations without having to overcome an energy barrier. Such an hybrid domain wall can be obtained by choosing the stripe width carefully. For large stripe widths, the spins inside the domain wall can point in the direction perpendicular to the stripe and the Bloch configuration is favoured. For small stripe widths, the transverse demagnetizing field increases and the spins inside the domain wall tend to point along the stripe, resulting in a Néel configuration. For intermediate widths at the frontier between these two regimes, the domain wall is hybrid and can easily rotate between the Néel and Bloch magnetic configurations^{34,35}.
In order to find the optimal track width W leading to a hybrid domain wall and low currentdensity propagation through the Slonczewski torque, we have performed micromagnetic simulations, using material parameters determined experimentally^{13,36} (see methods). We found that values of W in the range [90–110] nm allow creating an hybrid domain wall in the stripe. Figure 1d shows the result of micromagnetic simulations for a 100 nm width stripe. As can be seen, the angle of spins inside of the domain wall is close to 45 deg, in between the Néel and Bloch configurations as expected from an hybrid domain wall. The large difference between spintorque and field driven domain wall motion observed experimentally in Fig. 2c,d shows that our optimization was successful and that the spintorque responsible for domain wall motion is not a Fieldlike torque, but rather the Slonczewski torque. In addition, the enhanced mobility of the domain wall under current, as well as its stochastic back and forth motion, indicates that we have, as desired, created a hybrid domain wall propagating in the Walker regime when it is set in precession by the Slonczewski torque^{37}.
Spintorques quantification though domain wall depinning
In order to quantify the contribution of each spin torque to the domain wall motion in our samples, we numerically compute the evolution of the depinning current density J_{th} as a function of magnetic field and compare it to our experiments. Indeed, depending on which torque drives the depinning, the variation of J_{th} with field should be radically different. If the Fieldliketorque dominates the depinning process, the effect of current is equivalent to an applied magnetic field in the z direction and J_{th} should vary largely with the external field^{22}. On the contrary, if the Slonczewski torque drives the domain wall, the energy barrier, set by the domain wall anisotropy K, is independent of the applied field and J_{th} should depend weakly on the applied field. We simulate numerically the domain wall depinning process under each torque by solving the following system of equations^{33} describing a 1D translational domain wall motion:
In these equations, x is the domain wall position and ϕ its internal angle; γ, α and x_{c} represent the gyromagnetic ratio, the intrinsic damping constant and the spatial extension of the potential well along the x axis; H_{c} is the coercive field and H_{K} the domain wall anisotropy field. σ_{ST} and σ_{FLT} represent the amplitudes of the Slonczewski and Fieldlike torques in units of magnetic field. This model accounts for the domain wall dynamics through the two variables x and ϕ, under the effects of spin torques (σ_{FLT} and σ_{ST}), external field (H_{z}) and pinning potential (x_{c} and H_{c}). In our simulations, we vary the value of the domain wall anisotropy field H_{K} and set all the other parameters to values we have determined experimentally or through micromagnetic simulations (see methods). In particular, the coercive field H_{c} is taken to 15 Oe as in experiments. All details of numerical calculations are given in the Methods section. Figure 3 shows the computed variation of J_{th} with ΔH, defined as the difference between H_{z} and H_{c}. Two cases are analyzed, H_{K} > 2H_{c} (H_{K} = 100 Oe in Fig. 3a) and H_{K} < 2H_{c} (H_{K} = 10 Oe in Fig. 3b). For these two cases, we show the results obtained with the Slonczewski torque alone, the Fieldlike torque alone and with both torques.
In agreement with Koyama et al.^{34}, the depinning current J_{th} presents a weak dependence on ΔH = ±H_{c} − H when only the Slonczewski torque is considered (red circles in Fig. 3a,b). In the same way, a linear dependence is observed when only the Fieldlike torque is considered (black circles in Fig. 3a,b). In the case H_{K} > 2H_{c}, when the two torques are acting together, we can notice that J_{th} evolves in two different regimes. For the lowest values of ΔH, below 15 Oe, it follows the same trend as in the case where the Fieldlike torque acts alone (gray crosses in Fig. 3a). For larger ΔH, above 20 Oe, it remains constant, as in the case where only the Slonczewski torque is considered. This means that when the two torques are acting together, for a fixed value of ΔH (i.e. of the external field H_{z}), only one torque governs the domain wall depinning process. On the contrary, if H_{K} < 2H_{c}, using the two torques together is identical to using the Slonczewski torque alone (respectively gray crosses and red circles in Fig. 3b). The Fieldlike torque has no additional effect on J_{th}. Therefore, the relative values of H_{K} and 2H_{c} determine the dominant torque in the domain wall depinning process. In addition, in the case of a depinning governed only by the Slonczewski torque, the value of H_{K} also determines the order of magnitude of J_{th}. The larger H_{K}, the higher the energy barrier to overcome, the larger the current densities J_{th} necessary for depinning the domain wall.
Figure 3c shows the experimental measurements of domain wall depinning. J_{th} is plotted as a function of ΔH for two pinning sites obtained in different stripes of width W = 90 nm (blue squares in Fig. 3c) and W = 110 nm (green squares in Fig. 3c). The details of the measurements are given in the methods section. Experimentally, the maximum values of current densities needed to depin the domain wall are lower than 5.10^{6} A/cm^{2} for both stripe widths. We find that the best value of anisotropy field H_{K} describing our experimental results is H_{K} = 2H_{c} = 30 Oe. The results of simulations with this value of H_{K} are shown by circles in Fig. 3c. Clearly, the experimental curves are in better agreement with the red circles, which correspond to a domain wall depinning process governed by the Slonczewski torque rather than with the black circles corresponding to a domain wall depinning by the Fieldliketorque. The slight asymmetry of the experimental curve can be due to nonparabolic potential wells or nonlinear biasdependences of the Slonczewski torque^{22}. The qualitative and quantitative correspondence between numerical simulations and experiments indicates that in our experiments the Slonczewski torque is dominant in the domain wall depinning process.
Conclusion
To summarize, we have shown for the first time the realization of a spintorque memristor compatible with future spintorque magnetic memories. Our memristor has a large number of resistance states under dc current, between 15 and 20, which is sufficient to use it as an artificial nanosynapse. The current densities needed to drive the domain wall are low, of the order of 10^{6} A/cm^{2}. Comparing the field dependence of depinning current densities with numerical simulations indicates that the largest spintorque, the Slonczewski torque, drives the domain wall motion in our samples, also implying that we have successfully engineered our devices to accommodate hybrid domain walls. Our results are a first important step towards the realization of analog bioinspired magnetic computing hardware leveraging spintorque induced switching in multilevel magnetic tunnel junctions for learning.
Methods
Experimental measurements
To probe the intermediate resistance states available for the DW (Fig. 1c), we have applied a fixed magnetic field of 85 Oe in the z direction. Starting first from the AP state, the DW is nucleated by vertical injection of dc current. Then, we have repeated several current cycles in the range [−6.5, 6.5] mA to displace the DW and probe the different available pinning centers. To study the evolution of the depinning current J_{th} as a function of the external field, we focused on the two extreme values of stripe width W (90 and 110 nm, respectively blue and green lines in Fig. 3c). We have found a reproducible and stable pinning center in the two samples. For W = 90 nm, the pinning center is stable on the field range: [92, 118] Oe and corresponds to a resistance level of 41 Ω. In order to study the threshold current J_{th}, we swept the dc current from 0 until the DW depinning by step of 20 μA. This process was repeated between 8 and 10 times for each values of the external field in the stability range of the probed pinning center. The same procedure was used for the stripe width of 110 nm, where the pinning center, associated to a resistance level of 38.5 Ω, is stable in the field range [75, 92] Oe (Fig. 2d). Figure 2c was obtained with the memristor of 110 nm stripe width.
Numerical calculations
Micromagnetic simulations were performed with the OOMMF code^{38}. For the numerical integration of the 1D model (Eq. 1), we used a 4th order RungeKutta method (RK4) with a step time of 5 ps. In order to study the threshold current densities (J_{th}), we increased the simulated current density value using a ramp. The ramp rate was chosen to 10^{4} A/cm^{2}/ns and was verified to have no impact on the results at zero temperature. The amplitude of the spin transfer torques σ_{ST} and σ_{FLT} were described as follows: and σ_{FLT} = ζσ_{ST}, where ζ, the amplitude of the Fieldlike torque, is always of 0.3 in Fig. 3. In these expressions J is the current density and g, μ_{B} and e are respectively the Lande factor, the magnetic permeability and the elementary charge. In order to estimate the spin polarization P in our samples, we first calculated the spin polarization P_{J} from Julliere’s model: . The two measured samples in Fig. 3c present a TMR ratio of 82% and 93% (respectively for W = 90 and 110 nm), which correspond to P_{J} = 0.55 ± 0.01. J.C. Slonczewski and J.Z. Sun^{39,40} have shown that the polarization factor P in the expression of the spin torques efficiencies σ_{ST} and σ_{FLT} can be calculated as: . Using this expression, we found a spin polarization factor P of 0.422 ± 0.004. The other material parameters were determined as follows. The damping constant α of 0.005 was measured for our samples stack in ref. 36. The saturation magnetization value (M_{s}) of 1.05 10^{6} A/m was obtained from magnetization versus field measurements^{13}. The value of the perpendicular anisotropy of 7.10^{6} erg/m^{3}, used to obtain the micromagnetic simulation result shown in Fig. 1e, was estimated from the same magnetization versus field measurements, where the field is applied in the plane of the free layer. The stripe’s thickness is 2.2 nm. The pinning strength is described by two values: the spatial extension of the potential well along the x axis (x_{c} = 100 nm) and the depinning (or coercive) field H_{c} (15 Oe as in experiments). The width of the DW, 16.6 nm, was extracted from the magnetization profile of the z component along the x axis of the micromagnetic simulation result shown on Fig. 1d.
Additional Information
How to cite this article: Lequeux, S. et al. A magnetic synapse: multilevel spintorque memristor with perpendicular anisotropy. Sci. Rep. 6, 31510; doi: 10.1038/srep31510 (2016).
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Acknowledgements
The authors acknowledge financial support from the European Research Council (Starting Independent Researcher Grant No. ERC 2010 Stg 259068) and the French ministry of defense (DGA).
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J.G. conceived the experiments; S.L., J.S. and R.M. performed numerical simulations; K.Y., A.F., H.K. and S.Y. designed the junction stack and fabricated the samples; S.L. and J.S. conducted the experiments; S.L., J.S., V.C. and J.G. analyzed the results. All authors wrote and reviewed the manuscript.
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Lequeux, S., Sampaio, J., Cros, V. et al. A magnetic synapse: multilevel spintorque memristor with perpendicular anisotropy. Sci Rep 6, 31510 (2016). https://doi.org/10.1038/srep31510
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