United States

Lateral inhibition (LI) is an important neuromorphic network functionality, modeled after the biological neuron behavior that a firing neuron deactivates its neighbors and prevents their firing. In most neuromorphic hardware platforms LI is implemented by external circuitry, thereby decreasing the energy efficiency and increasing the area overhead. Recently, the domain wall – magnetic tunnel junction (DW-MTJ) neuron is shown in modeling to be intrinsically inhibitory1. LI in DW-MTJ neurons results from magnetostatic interaction between adjacent neurons (Fig.1): the two DWs, DWN and DWI, are driven by electrical current of densities JeI&lt;JeN, so that the DW velocities vDWI&lt;vDWN and the active Neuron N fires first. DWI falls behind DWN and is subjected to the stray field of Neuron N in the −z direction. It is demonstrated that such stray field can decrease DWI velocity and prevent Neuron I from firing, thus emulating LI. However, the LI mechanism in DW-MTJ neurons has not been studied thoroughly, leading to weak inhibition only in very closely spaced devices. In our work2 we model the current- and field-driven DW motion in two adjacent DW-MTJ neurons to approach these problems. LI is maximized by an optimal magnetic interaction strength, determined by tuning the spacing between the two neurons (Fig.2). The results are explained by the current- and field-driven DW velocity characteristics and are quantified by an analytical model. We further study the influence of device parameters and demonstrate the LI behavior in an array of 1000 neurons, which renders our proposed DW-MTJ array promising for implementing a k-winner-take-all layer. With strong LI achieved, a path towards competitive learning algorithms are made possible on the DW-MTJ neurons. This work is funded by Sandia National Lab. Sandia National Lab (SNL) is managed and operated by NTESS under DOE NNSA contract DE-NA0003525References: 1. N. Hassan et al. Journal of Applied Physics, Vol.124, p.152127 (2018) 2. C. Cui et al. Nanotechnology, Vol.31(29), p.294001 (2020)

MMM 2020

Maximized Lateral Inhibition in Paired Magnetic Domain Wall Racetracks for Neuromorphic Computing

The 65th Annual Conference on Magnetism and Magnetic Materials (MMM 2020) was held in a virtual form. The COVID-19 pandemic, with its associated uncertainty about international travel and the ability to gather in large groups, meant that the Steering Committee decided to cancel the face-to-face meeting that had been planned in Palm Beach, Florida November 2-6, 2020.

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Lateral inhibition (LI) is an important neuromorphic network functionality, modeled after the biological neuron behavior that a firing neuron deactivates its neighbors and prevents their firing. In most neuromorphic hardware platforms LI is implemented by external circuitry, thereby decreasing the energy efficiency and increasing the area overhead. Recently, the domain wall – magnetic tunnel junction (DW-MTJ) neuron is shown in modeling to be intrinsically inhibitory1. LI in DW-MTJ neurons results from magnetostatic interaction between adjacent neurons (Fig.1): the two DWs, DWN and DWI, are driven by electrical current of densities JeI<JeN, so that the DW velocities vDWI<vDWN and the active Neuron N fires first. DWI falls behind DWN and is subjected to the stray field of Neuron N in the −z direction. It is demonstrated that such stray field can decrease DWI velocity and prevent Neuron I from firing, thus emulating LI. However, the LI mechanism in DW-MTJ neurons has not been studied thoroughly, leading to weak inhibition only in very closely spaced devices. In our work2 we model the current- and field-driven DW motion in two adjacent DW-MTJ neurons to approach these problems. LI is maximized by an optimal magnetic interaction strength, determined by tuning the spacing between the two neurons (Fig.2). The results are explained by the current- and field-driven DW velocity characteristics and are quantified by an analytical model. We further study the influence of device parameters and demonstrate the LI behavior in an array of 1000 neurons, which renders our proposed DW-MTJ array promising for implementing a k-winner-take-all layer. With strong LI achieved, a path towards competitive learning algorithms are made possible on the DW-MTJ neurons. This work is funded by Sandia National Lab. Sandia National Lab (SNL) is managed and operated by NTESS under DOE NNSA contract DE-NA0003525References: 1. N. Hassan et al. Journal of Applied Physics, Vol.124, p.152127 (2018) 2. C. Cui et al. Nanotechnology, Vol.31(29), p.294001 (2020)

technical paper

As the energy consumed by cooling systems is expected to increase over the next decades, magnetocaloric cooling systems are of high interest as a promising more energy efficient alternative to conventional vapor compression refrigerators.1–3 Heusler alloys show large magnetocaloric effects (MCE) and are therefore of high interest for possible application in magnetocaloric cooling devices.4,5 They exhibit a magnetostructural transition resulting in larger entropy changes ΔS, thus in larger adiabatic temperature changes ΔTad. We propose a phase field model based on Landau theory to simulate the magnetic domain evolution during the martensite formation, e.g. in Heusler alloys. With our model, we are able to simulate field- and pressure-induced phase transitions, including the martensite and magnetic domain evolution. This is of high interest for a multicaloric cooling cycle as proposed by Gottschall et al.6 In the model, the three order parameters η1, η2, and η3, represent the three martensite variants in a cubic to tetragonal phase transition. The energy of the martensite transformation is described by a Landau-type formulation after Cui et al.7 and is coupled with micromagnetic formulations to take magnetism into account. The 3D finite-element (FE) implementation has been performed within the MOOSE framework.8 The model is capable of reproducing the formation and evolution of domains in magnetic materials under external magnetic field (Fig. 1) or mechanical loading. Modeling field- and pressure-induced tansformation aims at investigating pressures and fields used in a multicaloric cooling cycle. The FE implementation further allows to investigate the influence of microstructure on the MCE. The authors acknowledge the support from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (Grant agreement No 743116, project CoolInnov).References: 1. C. Zimm, A. Jastrab, A. Sternberg, Adv. Cryog. Eng., 1759–1766. Springer US, Boston, MA, 1998. 2. O. Gutfleisch, M. A. Willard, E. Brück, Adv. Mater., 23(7), 821–842, 2011. 3. V. Franco, J.S. S Blázquez, B. Ingale, Annu. Rev. Mater. Res., 42(1), 305–342, 2012. 4. J. Liu, T. Gottschall, K. Skokov, Nat. Mater., 11(7), 620–626, 2012. 5. T. Gottschall, K. Skokov, D. Benke, Phys. Rev. B, 93(18), 2–7, 2016. 6. T. Gottschall, A. Gràcia-Condal, M. Fries, Nat. Mater., 17(10), 929–934, 2018. 7. S. Cui, J. Wan, X. Zuo, Int. J. Solids Struct., 109, 1–11, 2017. 8. D. R. Gaston, C. J. Permann, J. W. Peterson, Ann. Nucl. Energy, 84, 45–54, 2015.

Phase field model for ferromagnetic domain evolution during martensitic transformation of Heusler alloys

First Order Reversal Curve (FORC) distributions of magnetic hysteresis is a well-recognized tool to extract information about magnetic interactions or to fingerprint magnetic materials [1, 2]. Their success is based on the extensive modeling that allows to correlate features of the distribution with characteristics of the transition. Recently, magnetocaloric materials are starting to be studied with Temperature-FORC (TFORC) distributions, extending the technique to the analysis of their thermal hysteresis [3,4]. However, the theory supporting the interpretation of the diagrams is still lacking, limiting TFORC to a fingerprinting technique so far. This work is a first approach to correlate the modeling of first-order phase transitions, using the Bean-Rodbell model combined with a phenomenological transformation mechanism, with the features observed in TFORC distributions. The different characteristics of the transformations e.g. transition temperatures, symmetry, temperature range, etc. can be correlated to distinct features of the distributions. Fig. 1 shows some illustrative examples of situations typically found in magnetocaloric materials (magnetization curves plotted in panel (a)): 1) symmetric cooling and heating transformations with the same temperature range produce circular distributions; 2) different temperature ranges for heating and cooling transformations give rise to ellipsoidal distributions; 3) asymmetry in the transformations makes the distribution triangular. This work systematically shows how the different model parameters affect the distributions and prove that the catalogue of figures is be able to explain the experimentally observed distributions. Work supported by AEI/FEDER-UE (grants MAT-2016-77265-R and PID2019-105720RB-I00), US/JUNTA/FEDER-UE (grant US-1260179), Consejería de Economía, Conocimiento, Empresas y Universidad de la Junta de Andalucía (grant P18-RT-746), Army Research Laboratory under Cooperative Agreement Number W911NF-19-2-0212 and Sevilla University under VI PPIT-US program.References: [1] I. Mayergoyz, IEEE Transactions on Magnetics., Vol 22(5), p. 603-608 (1986). [2] C. R Pike, A. P. Roberts and K L. Verosub, Journal of Applied Physics., Vol. 85(9) p. 6660-6667 (1999). [3] V. Franco, T. Gottschall, K. P. Skokov et al., IEEE Magnetics Letters., Vol. 7 p. 6602904 (2016). [4] V. Franco, Journal of Applied Physics., Vol. 127 p. 133902 (2020).

Setting the Basis for the Interpretation of Temperature First Order Reversal Curve (TFORC) Distributions of Magnetocaloric Materials

Magnetic refrigeration based on magnetocaloric effect (MCE) has attracted great attention due to its environmentally friendly nature and potential to improve energy efficiency. In this work, we explore the rare earth chromites (RCrO3) to understand the effect of R-site ionic radii (R= Tb and Er) on their structural and magnetic properties. Bulk powders of TbCrO3 and ErCrO3 were prepared by citrate route and characterized by x-ray diffraction (XRD) and Raman spectroscopy that revealed that both samples crystallized in the orthorhombically distorted perovskite structure (Pbnm space group). The structure was found to be more distorted for ErCrO3 (rEr= 1.062Å) as compared to TbCrO3 (rTb=1.095Å). The dc magnetization measurements revealed that the temperature decreased from 156 K to 131 K with decreasing ionic radii. Interestingly, the maximum MCE was also found to reduce with decreasing ionic radii. The maximum entropy change for TbCrO3 was calculated to be 13.4 J /kg K as compared to 10.7 J/kg K for ErCrO3. The results indicate that the structural distortions induced by the decreasing ionic radii at R-site could be a promising strategy to tune the magnetic and MCE properties in rare earth chromites.References: Gschneidner Jr, K. A., and Vitalij K. Pecharsky. Annual Review of Materials Science 30, no. 1 (2000): 387-429.

The Effect of Ionic Radii of the Rare-earth Ion on the Magnetocaloric Effect of Rare-earth Chromites

In this work, we report on an investigation of the effect of the permeability of magnetic particles on the effective macroscopic behavior of magnetorheological elastomers (MREs). MREs are a class of soft active materials known for their tunable deformation [1], [2]. Dispersed with magnetically permeable particles, these polymer-based composites deform under the action of a magnetic field. Such deformational changes in the mechanical properties of these materials are often attributed to the magnetic interaction among the filler particles [3]. Generally, for a maximum possible magnetorheological (MR) effect, particles of high relative permeability µr are required [4]. In this study, we determine the effect of the µr of the particles on the macroscopic behavior of MREs. Using a finite element simulation method based on continuum field theory, the constitutive and geometric properties on the microscale are considered in order to predict the composite’s macroscopic behavior as a function of µr by means of a computational homogenization [5]. Additionally, a magnetic flux density B ≤ 0.5T was used, below the saturation magnetization of the filler particles, hence linear constitutive relationships can be utilized. The simulations were performed for isotropic microstructures for different particle permeabilities (µr =1, 100, 10000 and 50000) and volume fractions (φ= ~10, 20 and 27%). The effective magnetic and mechanical properties are calculated as shown in Fig. 1 and Fig. 2. Fig. 1 shows the magnetic flux density distribution for isotropic MRE while Fig.2 shows the average magnetostrictive strain parallel to the direction of the magnetic field as a function of average magnetic flux density for varying permeability of the particles. The results confirmed assumptions stated in the literature whereby higher permeability of the particles caused larger deformation of the MRE (Fig.2). However, for very large permeability values (µr = 10,000 and 50,000), only negligible change in effective MRE deformation is observed.References: [1] Y. Han, A. Mohla, and L. E. Faidley Int. J. Appl. Mech., vol. 7, no. 1, pp. 1–16, 2015. [2] K. A. Kalina et al., Smart Mater. Struct., vol. 26, no. 10, 2017. [3] B. Marvalova, “Modelling of Magnetosensitive Elastomers,” Model. Simul., 2008. [4] R. Ahamed and S. Choi, “A state of art on magneto-rheological materials and their potential applications,” 2018. [5] C. Spieler, M. Kästner, and V. Ulbricht, Acta Mech., vol. 224, no. 11, pp. 2453–2469, 2013.

Effect of Particle Permeability on Macroscopic Behavior of Magnetorheological Elastomers

The demand of flexibility in the existing rigid devices has introduced a new field of research ‘Flexible Spintronics’, which has enormous significance from application viewpoint [1-2]. Flexible device requires all the components of rigid spintronics in a flexible i.e. bendable, foldable, twistable and stretchable mode [3]. The ideal next generation device need to be power efficient as well as flexible. To meet such device requirement stress/strain has proven to be a potential candidate [4-5]. As magnetic thin films are prime component of every spintronic device hence the flexible counterpart of those are prerequisite. Cobalt/Platinum (Co/Pt) thin films with perpendicular magnetic anisotropy (PMA) are well studied as it has increased magnetic storage density, thermal stability etc. [6]. In our work we have prepared a PMA Co/Pt film on a flexible polyimide substrate by magnetron sputtering. Strain has been generated on the film by fixing it on semi-circular shaped molds of different radius. Here systematically we have measured the effect of both tensile and compressive stresses on the PMA, domain dynamics and relaxation mechanism by MOKE based microscopy. A minimal in-plane tensile strain has increased the coercivity of the film by 34% of its initial value, while a very small change of coercivity has been found under compressive strain (fig. 1) [7]. The size of ferromagnetic domains also decreases under tensile strain, while no change is observed under compressive stress (fig. 2). Due to stress induced anisotropy, Bloch wall formation energy has increased which hindered the domain wall motion and size of bubble domains reduced. Further, magnetization relaxation measured at sub-coercive field values yields a longer relaxation time in the tensile strained state.References: 1. P. Sheng et al., J. Semicond. 39, 011006 (2018) 2. Z. Bao et al., Adv. Mater. 28, 4177 (2016) 3. K. Harris et al., J. Mater. Sci. 51, 2771–2805 (2016) 4. A. Bukharaev et al., Phys. Uspekhi 61, 1175 (2018) 5. A. K. Biswas et al., Nano letters 17, 3478–3484 (2017) 6. B. Tudu et al., Vacuum 146, 329 (2017) 7. E. Pandey et al., Nano Express 1, 010037 (2020)

Strain Engineered Domain Structure and Their Relaxation in Perpendicularly Magnetized Co/Pt Deposited on Flexible Polyimide

Magnetic elastomers are one of the most important types of magnetoresponsive materials. They are characterized by large changes in their shape and rehological properties as a response to external magnetic fields [1]. Similarly to magnetic fluids and gels, these are hybrid materials that consist of magnetic nano- or microparticles embedded in a magnetically passive carrier material. Magnetic elastomers are candidate materials for many technological applications, like adaptive damping devices, vibrational absorbers, stiffness tunable mounts, soft actuators and micromanipulators, force sensors or artificial muscles, see [2] and references therein. Here, we study theoretically a novel microstructural design for a hybrid magnetic elastomer material that has been synthesized for the first time very recently [3-5]. This design is based on the embedding within the polymer matrix of two types of magnetic particles in different amounts: a low volume fraction of magnetically hard (MH) colloidal particles---typically, ferromagnetic particles of 5-100μm of diameter---and a high volume fraction of smaller, magnetically soft (MS) particles---paramagnetic particles with a diameter typically smaller than 5μm. We study the response of this hybrid magnetic material to external magnetic fields by means of two theoretical approaches. First, we perform extensive computer simulations with a bead-spring model of the system that takes into account the magnetic influence of the MH particles on the MS ones, as well as the mechanical coupling imposed by the polymer matrix on the rearrangements of the particles [6]. Finally, we compare the results obtained from this approach with the ones provided by a continuous magnetomechanical model. In both approaches we focus on a minimal representative volume of the material, consisting of a single MH particle surrounded by a cloud of MS ones and the mechanical coupling between all of them. We analyze the deformations of this elementary volume as a response to the external fields.References: [1] S. Odenbach. Arch. Appl. Mech., 86:269–279, (2016). [2] P. Sánchez et al., Soft Matter, 15, 175-189 (2018). [3] J.M. Linke, D.Y. Borin, S. Odenbach, RSC Adv., 6, 100407 (2016). [4] M.V. Vaganov, J. Linke, S. Odenbach, Yu.L. Raikher, J. Mag. Mag. Mat. 431, 130-133 (2017). [5] P. Sánchez et al., Soft Matter, 14, 2170-2183 (2018). [6] P. Sánchez et al., Soft Matter, 15, 7145--7158 (2019).

Theoretical Modelling of Hybrid Magnetic Elastomers

Progress has been made on emulating the neuron and the synapse using magnetic devices [1], [2] especially with three-terminal magnetic tunnel junctions (3T-MTJs) [3], [4]. Increasingly more accurate biological mimics are being developed with the 3T-MTJ like the Leaky-Integrate-Fire (LIF) [5] neuron displaying lateral inhibition, and the 3T-MTJ synapse model showing spike timing dependent plasticity (STDP) [6], [7]. However, more work must be done to achieve real-time machine learning. Using an earlier developed synapse circuit [8] and a 3T-MTJ spice model [9], we show the transient behavior of a 2 by 2 crossbar array (cartoon in Fig 1). There is STDP for different delay conditions between the pre- and post-synaptic neural spikes. The shorter the time difference between the onset of the pre- and post-synaptic neuron spike, the higher the current through the ferromagnet (Fig 2). Higher current leads to higher rate of change of the domain wall (DW) position per neural event and higher DW displacement. At t=0, the initial pair of presynaptic and postsynaptic pulses helps to randomly give the DWs a head start. DW for synapse S2 (red plot) rises faster because it has the least delay of 1 ns between its pre- and post-synaptic pulse despite its pulses lagging that of S1 whose DW had a head start. Scaling this up, the 3T MTJ synapse is robust in more complex systems such as a machine learning clustering task.References: [1] S. Lequeux et al., Sci. Rep., vol. 6, no. August, 2016, doi: 10.1038/srep31510. [2] J. Torrejon et al., Nature, vol. 547, no. 7664, pp. 428–431 (2017) [3] N. K. Upadhyay, H. Jiang, Z. Wang et al, Adv. Mater. Technol., vol. 1800589, pp. 1–13 (2019) [4] N. Hassan et al., J. Appl. Phys., vol. 124, no. 15, p. 152127 (2018) [5] G. Bi and M. Poo, Annu. Rev. Neurosci., vol. 24, no. 1, pp. 139–166 (2002) [6] H. Markram, W. Gerstner, and P. J. Sjöström, Front. Synaptic Neurosci., vol. 4, pp. 2–5 (2012) [7] O. Akinola, X. Hu, C. H. Bennett et al, J. Phys. D. Appl. Phys., vol. 52, no. 49 (2019) [8] X. Hu, A. Timm, W. H. Brigner et al, IEEE Trans. Elect. Dev., vol. 66, no. 6, pp. 2817–2821 (2019)

Online Training of Spiking Neural Networks Using Domain Wall Magnetic Tunnel Junction Synapses

Domain wall-magnetic tunnel junction (DW-MTJ) devices intrinsically emulate neuron [1] and synapse [2] functionalities for neuromorphic systems. While these devices efficiently emulate neurobiological components, significant CMOS overhead is required to integrate multiple perceptron layers [3]. This work proposes a four-terminal DW-MTJ neuron [4] that enables purely spintronic multilayer perceptrons that do not require CMOS. The proposed leaky integrate-and-fire neuron [5] in Fig. 1 has a ferromagnetic DW track between terminals T1 and T2 and an MTJ between terminals T3 and T4. The MTJ free layer is coupled to the DW track by an electrically insulated layer. Spin-transfer torque induced by the current through the T1-T2 path moves the DW from right to left to perform integration. DW leaking from left to right intrinsically occurs due to either dipolar magnetic field [1], anisotropy gradient along [6], or shape variation [7]. When the DW passes underneath the electrically-isolated MTJ, the free ferromagnet reorients itself to match the magnetization of the DW track due to dipolar coupling, thereby switching the MTJ between the anti-parallel resistive state and parallel conductive state. A constant voltage applied at the T3 terminal, fires by switching between low and high output currents. Additionally, by exploiting stray magnetic field interactions, these neurons perform lateral inhibition among a group of neighboring neurons [1]. In the multilayer perceptron of Fig. 2, each four-terminal DW-MTJ neuron is connected to the three-terminal analog DW-MTJ input synapses through the T1 terminal and is cascaded to the output synapses through the T4 terminal without any CMOS interface. Finally, an unsupervised learning algorithm results from feedback between the T4 terminals of the neurons and right terminals of the synapses, providing best results of 98.11% accuracy on the Wisconsin breast cancer clustering task [8].References: [1] N. Hassan, X. Hu, L. Jiang-Wei, et al., J. Appl. Phys., Vol. 124, no. 15, p. 152127 (2018) [2] O. Akinola, X. Hu, C. H. Bennett, et al., J. Phys. D: Appl. Phys., Vol. 52, no. 49, LT01 (2019) [3] A. Sengupta, Y. Shim, and K. Roy, IEEE TBioCAS, Vol. 10, no. 6, pp. 1152–1160 (2016) [4] W. H. Brigner, N. Hassan, X. Hu, et al., arXiv preprint arXiv: 2002.00862 (2020) [5] A. N. Burkitt, Biol. Cybern., Vol. 95, pp. 97–112 (2006) [6] W. H. Brigner, X. Hu, N. Hassan, et al., IEEE JXCDC, Vol. 5, no. 1, pp. 19–24 (2019) [7] W. H. Brigner, N. Hassan, L. Jiang-Wei, et al., IEEE TED, Vol. 66, no. 11, pp. 4970-4975 (2019) [8] A. Velasquez, C. H. Bennett, N. Hassan, et al., arXiv preprint arXiv: 2003.11120 (2020)

Purely Spintronic Multilayer Perceptron Enabled by Four-Terminal Domain Wall-Magnetic Tunnel Junction Neuron

Magnetic materials are already widely used for long-term data storage, but ongoing work seeks to use them as both working memory and computing architectures. Particularly, devices based on magnetic domain walls (DWs) can perform logic operations and can readily store information [1]. However, the stochasticity of DW pinning limits the feasibility of creating technologically viable devices. Here, we demonstrate how stochasticity can be changed from a technologically inhibitive behaviour into an integral property of machine learning algorithms for specialised neuromorphic devices. We first present experimental measurements that demonstrate the tunability of stochastic processes by applying external stimuli. Focused magneto-optic Kerr effect measurements were used to probe the pinning of DWs at notch-shaped defect sites in 400 nm wide Permalloy nanowires (Fig. 1). DWs were injected into the nanowires and propagated to the defect sites using a field parallel to the nanowire (Hx). The probability of the DWs being pinned at the defect sites was found to depend sigmoidally on the magnitude of a field transverse to the nanowires (Hy). The stochastic behaviour of the nanowire were then integrated into machine learning models. We have developed feedforward neural networks with the nanowires acted as binary stochastic synapses (BSS) that can be sampled by repeating the network. It is found that for a single cycle of the network it can be trained to recognise handwritten digits with an error rate of 19%. Repeated sampling of the network decreases the error rate to 9% for 128 cycles - close to mean field performance (Fig. 2). Adding a hidden layer improves performance with extra pathways for the stochastic behaviour to be averaged over. Our work illustrates how the stochasticity of DW devices can be harnessed to provide tunable bespoke hardware for machine learning tasks.References: [1] R. L. Stamps et al., J. Phys. D. Appl. Phys. Vol. 47, p. 333001 (2014)

Harnessing Stochastic Domain Wall Pinning for Machine Learning

Modeling computer architecture after the human brain is a promising approach to the ever-increasing demands for real-time processing of massive amounts of data. But, the building blocks of the brain, i.e. neurons and synapses, have more detailed behavior than simply how they are connected, and this behavior is central to their computing efficiency. If we want to capture the energy efficiency of such a neuromorphic architecture, we need devices themselves that can capture the behavior of the biological elements. Magnetic materials and devices have many properties similar to the brain that make them attractive candidates as artificial neurons and synapses. We will present our recent work on designing and modeling three-terminal domain wall-magnetic tunnel junctions (DW-MTJs) that can act as both leaky, integrate, and fire neurons with inherent lateral inhibition [1-2] and as synapses with online learning and spike-timing dependent plasticity behavior [3]. The DW-MTJ neuron consists of a perpendicularly magnetized wire containing a single DW and an MTJ on top of the wire. When current is applied to the wire, the DW propagates through spin transfer torque (STT) or spin orbit torque (SOT). The MTJ defines the firing point of the neuron: when the DW moves past the junction, the MTJ resistance switches to generate a spiking current at the MTJ output terminal. We will show results of integration, firing, and inherent leaking of the device. When assembled into a crossbar array, 1-10 digit identification is simulated by measuring which of ten neurons reach the firing point first. Lateral inhibition (LI) is an important function in neuromorphic computing, modeled after the biological neuron behavior that a neuron prevents its less active neighbors in the same layer from firing. In most neuromorphic hardware platforms, LI is implemented with external circuitry, thereby decreasing the energy efficiency and increasing the area overhead of such systems. We show that the DW-MTJ neuron has inherent LI via magnetic interactions. We will show results from modeling current- and field-driven DW motion in adjacent DW-MTJ neurons. Figure 1 shows that with 90 nm spacing between two 50 nm wide DW-MTJs, the slower device’s DW velocity is drastically reduced from 75 m/s to 20 m/s and a LI of 75% is achieved. The results are explained by current-driven DW velocity characteristics in response to external magnetic fields and are quantified by an analytical model based on the Landau-Lifshitz-Gilbert (LLG) equation. We will show results of arrays of DW-MTJs implementing a soft winner-take-all function and application of the effect to image recognition. We will furthermore present simulation results of the DW-MTJ showing synaptic behavior when the MTJ is made long. By constructing a small circuit around the device we implement spike-timing-dependent plasticity (STDP), where the current flowing through the synapse, which will determine its resistive synaptic weight, is determined by the delay between input and output neurons (Fig. 2). We will show that the STDP synapses can process time-dependent input data. The results will be compared with other emerging nonvolatile devices for artificial neural networks. The work presented shows that DW-MTJs can provide a monolithic platform for neuromorphic computing circuits, where both synapses and neurons can be made from the same thin film stack, and motivate further study of magnetic devices for neuromorphic computing. SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525.References: 1. N. Hassan, X. Hu, L. Jiang-Wei, W. H. Brigner, O. G. Akinola, F. Garcia-Sanchez, M. Pasquale, C. H. Bennett, J. A. C. Incorvia & J. S. Friedman. Magnetic domain wall neuron with lateral inhibition. J. Appl. Phys. 124, (2018). 2. C. Cui, O. G. Akinola, N. Hassan, H. Christopher, M. J. Marinella, J. S. Friedman & J. A. C. Incorvia. Maximized Lateral Inhibition in Paired Magnetic Domain Wall Racetracks for Neuromorphic Computing. IOP Nanotechnology 31, 29 (2020). 3. O. G. Akinola, X. Hu, C. H. Bennett, M. Marinella, J. S. Friedman & J. A. C. Incorvia. Three-terminal magnetic tunnel junction synapse circuits showing spike-timing-dependent plasticity. J. Phys. D. Appl. Phys. 52, 49LT01 (2019).

Modeling biological behavior in domain wall-magnetic tunnel junction artificial neurons and synapses for energy-efficient neuromorphic computing INVITED

Maximized Lateral Inhibition in Paired Magnetic Domain Wall Racetracks for Neuromorphic Computing

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Phase field model for ferromagnetic domain evolution during martensitic transformation of Heusler alloys

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