United States

Modern magnetic-memory technology requires all-electric control of perpendicular magnetization with low energy consumption. While spin-orbit torque (SOT) in heavy metal/ferromagnet (HM/FM) heterostructures holds promise for applications in magnetic random access memory, till today, it is limited to the in-plane direction. Such in-plane torque can switch perpendicular magnetization only deterministically with the help of additional symmetry breaking, e.g., through the application of an external magnetic field, an interlayer coupling or an asymmetric design. Instead, an out-of-plane spin-orbit torque could directly switch perpendicular magnetization. In current presentation, we report that we observe an out-of-plane spin-orbit torque in an HM/FM bilayer of &lt;i&gt;L&lt;/i&gt;1&lt;sub&gt;1&lt;/sub&gt;-ordered CuPt/CoPt and demonstrate field-free switching of the perpendicular magnetization of the CoPt layer.&lt;sup&gt;1&lt;/sup&gt; The low symmetry point group (3m1) at the CuPt/CoPt interface gives rise to this spin torque, herein after referred as 3m torque, which strongly depends on the relative orientation of current flow and crystal symmetry. We observe a 3-fold angular dependence in both the field-free switching and the current-induced out-of-plane effective field as shown in Figure 1. Because of the intrinsic nature of the 3m torque, the field-free switching in CuPt/CoPt shows good endurance in cycling experiments. Experiments with the wide variety of SOT bilayers with low-symmetry point groups at the interface may uncover further unconventional spin-torques in future.

![](https://assets.underline.io/uploads/markdown_image/1/image/e032f3aa438f0424fd4d0cd491e3db92.jpg)

Figure 1| Symmetry-dependent magnetic field-free magnetization switching. a, Schematic of the CuPt/CoPt Hall bar for electrical transport measurement. The red arrow represents the magnetization (M). The grey arrow represents the current (I) flowing. b, The definition of current flowing direction (θI). The current is applied along the Hall bar, which has an azimuth angle of θI with respect to the [1-10] direction. c, Anomalous Hall effect of the bilayer for θI = 0°. d, Current angle dependence of the SOT induced magnetization switching. The solid line is a cosine fit to the data. e, Current-induced magnetization switching with different θI.

2022 Joint MMM-INTERMAG

Symmetry Dependent Field-free Switching of Perpendicular Magnetization

#### Welcome to the 67th Annual Conference on Magnetism and Magnetic Materials, MMM 2022!

The Conference was held from October 31 to November 4 and offers both in-person and on-demand content.

MMM 2022 is sponsored jointly by AIP Publishing and the IEEE Magnetics Society. Members of the international scientific and engineering communities interested in recent developments in fundamental and applied magnetism are invited to attend and contribute to the technical sessions. The technical program will include invited and contributed papers in oral and poster sessions, invited symposia, a tutorial, and several special sessions. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

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For tickets to the event, please register at the following link: https://magnetism.org/registration

Please register for the MMM 2022 conference to join the event.

MMM 2022

This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

Modern magnetic-memory technology requires all-electric control of perpendicular magnetization with low energy consumption. While spin-orbit torque (SOT) in heavy metal/ferromagnet (HM/FM) heterostructures holds promise for applications in magnetic random access memory, till today, it is limited to the in-plane direction. Such in-plane torque can switch perpendicular magnetization only deterministically with the help of additional symmetry breaking, e.g., through the application of an external magnetic field, an interlayer coupling or an asymmetric design. Instead, an out-of-plane spin-orbit torque could directly switch perpendicular magnetization. In current presentation, we report that we observe an out-of-plane spin-orbit torque in an HM/FM bilayer of L11-ordered CuPt/CoPt and demonstrate field-free switching of the perpendicular magnetization of the CoPt layer.1 The low symmetry point group (3m1) at the CuPt/CoPt interface gives rise to this spin torque, herein after referred as 3m torque, which strongly depends on the relative orientation of current flow and crystal symmetry. We observe a 3-fold angular dependence in both the field-free switching and the current-induced out-of-plane effective field as shown in Figure 1. Because of the intrinsic nature of the 3m torque, the field-free switching in CuPt/CoPt shows good endurance in cycling experiments. Experiments with the wide variety of SOT bilayers with low-symmetry point groups at the interface may uncover further unconventional spin-torques in future.

![](https://assets.underline.io/uploads/markdown_image/1/image/e032f3aa438f0424fd4d0cd491e3db92.jpg)

Figure 1| Symmetry-dependent magnetic field-free magnetization switching. a, Schematic of the CuPt/CoPt Hall bar for electrical transport measurement. The red arrow represents the magnetization (M). The grey arrow represents the current (I) flowing. b, The definition of current flowing direction (θI). The current is applied along the Hall bar, which has an azimuth angle of θI with respect to the [1-10] direction. c, Anomalous Hall effect of the bilayer for θI = 0°. d, Current angle dependence of the SOT induced magnetization switching. The solid line is a cosine fit to the data. e, Current-induced magnetization switching with different θI.

technical paper

The 15th Joint MMM-INTERMAG Conference (2022 Joint) is sponsored jointly by AIP Publishing and the IEEE Magnetics Society. Members of the international scientific and engineering communities interested in recent developments in fundamental and applied magnetism are invited to attend and contribute to the technical sessions. The technical program will include invited and contributed papers in oral and poster sessions, invited symposia, a plenary session, and an evening session, with about 1500 presentations overall. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

The 2022 Joint Conference will offer both in-person and prerecorded on-demand content.

For tickets to the event, please register at the following link: https://magnetism.org/register

Please register for the Joint MMM-Intermag conference to join the event.

Perpendicular Spin Transfer Torque Magnetic Random Access Memory (p-STT-MRAM) needs to combine high speed and low critical switching current at technological nodes below 30 nm. Higher STT write efficiency is therefore required. Double magnetic tunnel junctions (DMTJ) stacks have been proposed to achieve this goal [1-5]. The DMTJ critical switching current is decreased by the combined effect of the STT exerted from two antiparallel polarizers on the storage layer (SL). The retention is increased by doubling the SL/MgO interfaces contributing to the layer’s effective perpendicular anisotropy (PMA). Despite the efficiency advantage, the development of p-DMTJ presents several complexities. First, ensuring enough PMA for the top polarizer [6] and second, controlling the stray field compensation of both polarizers acting on the SL. A p-DMTJ structure having a switchable reference layer was recently proposed [7], showing through magnetic simulation similar performance as conventional p-DMTJ with static polarizers. In this work, we report experimental evidence of the working principle for this type of novel p-DMTJ. We fabricated and optimized an ASL-DMTJ structure having a switchable polarizer acting as a switching assistance layer (ASL). Fig.1.(a) and (b) show the two switching sequences, from AP to P and from P to AP states respectively. Both reversals show a transition through an intermediate resistance state (IRS). Differing from the working principles proposed in [7], the ASL is designed to switch its magnetic orientation during the write operation. This maximizes the STT efficiency independently of the switching direction, while also increasing the SL retention, since the assistance layer always aligns parallel to the SL in standby Fig.2(a)-(b). Validation of the switching sequences was possible by performing time-resolved resistance measurements Fig.2.(c)-(b).

![](https://assets.underline.io/uploads/markdown_image/1/image/0c7395b35a105c6f992d8d15bd884588.jpg)

Figure 1. (a) AP→P and (b) P→AP reversal sequence through an intermediated resistance state.

![](https://assets.underline.io/uploads/markdown_image/1/image/938d95a5c9fad68f070f40573955c5dd.jpg)

Figure 2. (a) RH of ASL-DMTJ (b) RV loops of ASL-DMTJ. (b) Real time AP→P switching sequence and (d) real time P to AP switching sequence both transiting through the IRS with (I) applied field, (II) at zero field.

Real time investigation of Double magnetic tunnel junction with switchable assistance layer for high efficiency STT-MRAM

Magnetoresistive random access memories (MRAM) based on spin-transfer torque are a scalable low-power memory solution being actively developed by industry, where the magnetization of a perpendicularly magnetized thin disk is reversed by a spin polarized current. During the switching process domain walls (DWs) can form [1-5] and understanding their dynamics in a disk geometry becomes of great interest. Here we show that DW surface tension always leads to oscillatory DW motion and instabilities that affect the switching dynamics. In a disk, a DW generally takes a circular form to minimize the sum of the surface and volume energies of the reversed domain, with the domain boundary perpendicular to the element boundary [1]. In a collective coordinate model the domain wall has two degrees of freedom, its position relative to the center of the disk q and the angle of the spins relative to the normal to the DW Φ. Here, Φ=0 is a Neel and Φ=90 deg. is a Bloch DW. We analyze the dynamics with micromagnetic and the collective coordinate model. Fig. 1a shows micromagnetic simulations of the evolution of the average perpendicular magnetization (mz) with fixed initial DW position q, such that mz&lt;0, and different initial angles Φ, with no field or current applied. Whereas both Neel and Bloch DWs states relax towards a reversed state (mz=-1), an intermediate initial angle DWs (Φ=45 deg) switches. Fig. 1b shows the (q,Φ) phase diagram indicating that the dynamics of domains close to the disk center is sensitive to small changes in Φ. Moreover, we show that the application of a spin-polarized current (I/Ic~0.2) mitigates the sensitivity of the final state to Φ. This opens a way to reduce the required power for a magnetization switching. The application of a short current pulse to nucleate a DW followed by a significant reduction of the pulse amplitude, well below the critical current, can still reliably switch the nanodisk (Fig. 2, blue curve); in this situation the power, which scales as I^2, can be drastically reduced.

![](https://assets.underline.io/uploads/markdown_image/1/image/ae7093247bc72273459ea2152e057f0d.jpg)

FIG. 1 a) Time evolution of mz for different Φ. b) (q,Φ) Relaxation phase diagram.

![](https://assets.underline.io/uploads/markdown_image/1/image/c3e1ee77b13cbb246c1c8906c9b8f14c.jpg)

FIG. 2 a) Time evolution of mz for two different currents after 5 ns. b) Spin-current amplitude as a function of the time.

Reduction of power consumption and micromagnetic instabilities associated with domain wall dynamics in perpendicular magnetic tunnel junction nanopillars

Reservoir computing (RC) is a computational framework where a fixed, non-linear reservoir maps the inputs into higher-dimensional space and the readout is trained with linear regression and classification [1]. Spintronic nanomagnetic devices are well suited for physical reservoir computing due to their interactive non-linear dynamics, recurrence characteristic, enduring lifetime, and low energy consumption [2-3]. A frustrated nanomagnet layer can also implement physical RC [4]. In this work, we demonstrate via micromagnetic simulation that a nanomagnet array excited by surface acoustic waves (SAW) can be used as a reservoir to classify sine and square waves with high accuracy. The simulated nanomagnet array has an input, 7 outputs (Fig. 1) and a 4 GHz SAW is applied to the input nanomagnet. The SAW amplitude is varied in such a way that its envelope forms a random sequence of sine and square waves of 100 MHz frequency (Fig. 2 (a)). The non-linear responses of the output nanomagnets due to this input are processed by reading the reservoir state every 1 ns while the period of the input is 10 ns. The envelopes of the output magnets’ magnetization are shown in Fig. 2 (b) which are used to train the output weights obtained by regression via Moore-Penrose pseudoinverse. For the classification, a random sequence of 100 square and sine wave samples are used. About 80 % of the total samples are trained, and the rest of the samples are used for testing. Various combination of the output nanomagnets exhibit 100 % training accuracy and 100 % testing accuracy which is indicative of the nanomagnet oscillator array being well suited for physical reservoir computing applications. Thus, this proposed strategy to implement reservoir computing could lead to energy efficient neuromorphic devices. Acknowledgment: M.F.F.C, W.A, D.B and J.A are supported in part by the National Science Foundation grant CCF-1815033.

![](https://assets.underline.io/uploads/markdown_image/1/image/ba0e1e285d3ea4a4474a2b29418b77a9.jpg)

Figure 1: A micro-magnetic snapshot of the input, the reservoir and output nanomagnets.

![](https://assets.underline.io/uploads/markdown_image/1/image/0bbde6989de89be932a0e0791dc0c7a5.jpg)

Figure 2: (a) SAW and input response (b) The envelopes of the responses vs. time (ns) of several output nanomagnets.

Surface Acoustic Wave Induced Nano-oscillator Based Reservoir Computing

In superparamagnetic tunnel junctions (SMTJ), the energy barriers that separate the parallel and the antiparallel magnetization configurations are sufficiently small that the thermal noise causes stochastic magnetization fluctuations between the two states. Through magnetoresistance effects, those stochastic fluctuations give rise to telegraphic noise signals with two voltage levels (see Fig.1) [1, 2]. The relative average time spent in each of the two configurations can be controlled by an applied dc current via the spin-transfer torque. Due to their inherent stochastic nature, SMTJs are promising candidates for truly random number generator applications [3, 4], brain-inspired and probabilistic computing [5-10]. However, an external bias magnetic field was always required to fully operate the SMTJ’s with current, which represents a drawback to their integration with the required microelectronic circuits. In this work, we report for the first time, SMTJs that are fully controlled by DC current at zero applied magnetic field using perpendicular magnetic tunnel junctions (pMTJ). Stable pMTJs are used in densely magnetic memories [11], nevertheless their thermal stability can be strongly reduced by tuning their free layer thickness, leading to a superparamagnetic state. Here, we use pMTJ’s with a free layer thickness of t=1.6 nm, and with diameters ranging from 150 nm to 80 nm. By applying a DC current in one direction (sign), without any external bias field, we observe stochastic fluctuations in the resistance for dc currents between -0.3 mA and -0.27 mA. As shown in Fig. 2, the average probability in being in high and low resistance state is well controlled by the applied current. In order to obtain good statistics on the extracted probability, we record to stochastic transitions. We extracted the dwell time distribution, which follows an exponential distribution with a mean dwell time that is in agreement with the modified Néel-Brown model. The authors acknowledge partial funding from ERC MAGICAL No 669204, and the Nanoscience Foundation (Grenoble, France).

![](https://assets.underline.io/uploads/markdown_image/1/image/032d011551d8698e3dc1b74244af9c81.jpg)

Figure 1 : Experimental voltage time trace of the SMTJ.

![](https://assets.underline.io/uploads/markdown_image/1/image/f8c0fe8daabe77b0c738c5d388eadce3.jpg)

Figure 2 : The probability of occupancy of the high resistance state versus current.

Current controlled perpendicular superparamagnetic tunnel junctions operating at zero applied magnetic field

Spin-transfer torque (STT) based magnetoresistive random-access memory (MRAM) is of great current interest for embedded applications, due to its high speed, high endurance, and long retention time. However, state-of-the-art STT MRAM requires a large switching current that leads to reliability issues, high write energy, and limits the density scaling. In this talk, we will show that a conventional current-controlled MTJ can be changed to a voltage-controlled device if we replace the thin oxide barrier with a resonant tunneling barrier. Such a simple modification will combine two established quantum phenomena: interlayer exchange coupling and resonant tunneling within the scaled magnetic structure to enable a resonant-exchange controlled (REC) magnetization switching [1]. REC-driven magnetization switching can substantially lower the write energy, decouple the energy and speed of operations, eliminate the reliability issues, and enable denser MRAM technologies. A voltage-controlled MTJ has a high baseline resistance, which may cause compatibility issues with standard CMOS. We will discuss a magnetic gain cell structure that consists of a REC MTJ and two transistors for a large separation in the output current for the two memory states while retaining the low power advantages of a voltage-controlled write mechanism [2]. We analyze the REC MTJ using quantum-transport simulations on a CoFeB/MgO/Ru/MgO/CoFeB structure and combine the results with an empirical SPICE model to analyze the magnetic gain cell using 45 nm CMOS models in HSPICE. Our simulation results suggest approximately 103 times change in the read current in the gain cell between the two magnetic states. The expected energy and delay are 29.5 fJ/bit and 1.6 ns respectively for a write operation and 7.6 ~ 39 fJ/bit and 0.6 ~ 1 ns respectively for a read operation, thus promising for low energy, fast, and high-density REC MRAM technology.

![](https://assets.underline.io/uploads/markdown_image/1/image/8f55c819fa0feacf6498620a60124061.jpg)

A magnetic gain-cell structure for efficient voltage-controlled MRAM

Voltage control of magnetism provides a promising path toward the development of low-power spintronic devices. Magneto-ionics exploiting voltage-driven ion migration as a control mechanism has attracted interest because it can generate large magnetoelectric effects at low voltage. Here, we demonstrate the use of all-solid-state lithium-ion battery technology for reversible voltage-controlled switching between perpendicular and in-plane magnetization states in a Co/Pt bilayer. The magneto-ionic battery structure consists of a 2 nm Ta/5 nm Pt/20 nm LiCoO2/70 nm LiPON/3 nm Co/5 nm Pt crossbar junction (Fig. 1a,b). Here, the LiPON film functions as a solid-state electrolyte and the LiCoO2 acts as the Li+ storage layer. Using magneto-optical Kerr effect (MOKE) microscopy, we show that the magnetization of the Co film switches between in-plane and perpendicular directions when voltages of +2.5 V and –2 V are applied (Fig. 1c,d). The magneto-ionic switching effect is reliably reproduced over multiple cycles (Fig. 2a,b) and switching takes less than 0.5 s at room temperature (Fig. 2c). Our structure can be cycled for &gt;500 times without degradation. The magnetoelectric coupling efficiency is estimated to be 7,700 fJ/Vm at room temperature, which is the strongest magnetoelectric effect reported to date. We attribute the effect to changes in the hybridization of electron orbitals at the Co/Pt interface upon voltage-controlled insertion and deinsertion of Li+ ions. Our work sets a new benchmark for lithium-based magneto-ionics and demonstrates the relevance of battery design principles for the development of low-power spintronic devices.

![](https://assets.underline.io/uploads/markdown_image/1/image/0e0e0a222892a8e22e21ad864ff48d48.jpg)

Fig. 1 (a) Schematic of the magneto-ionic battery structure. (b) Optical microscopy image of a single crossbar junction. (c) Polar and (d) longitudinal MOKE hystersis curves recorded at –2.0 and +2.5 V.

![](https://assets.underline.io/uploads/markdown_image/1/image/7f80d4c4edc9f54a6a38f9541a3f553c.jpg)

Fig. 2 Reversible voltage-controlled switching of (a) the perpendicular magnetization and (b) the in-plane magnetization in zero magnetic field. (c) Time-resolved modulation of the longitudinal MOKE signal at room temperature recorded while toggling the voltage between –2.0 V and +2.5V in 0.5 s intervals.

Lithium-Ion Battery Technology for Voltage Control of Perpendicular Magnetization

The application of gate voltages in ferromagnet/Oxide/Heavy metal thin film multilayer has been identified as one possible candidate to manipulate their anisotropy at will [3], [1], [4]. Unfortunately, this method has proven to be unreliable in terms of the reversibility: e.g, the application of a gate voltage onMgO/CoFeB/Ta [3] causes an irreversible change of the magnetic anisotropy axis from in plane to out-of-plane, while HfO2/CoFeB/Ta stacks display a more complicated behavior, with different regimes characterized by different reversibility behaviors [2]. The microscopic origin of these phenomena remains unclear and is the object of our inquiry. In this work we performed ab-initio simulations on 6 setups comprising Fe/O, HfO2/Fe, MgO/Fe interfaces each one with frontal and interstitial oxygen atomic configurations (fig.1). The pure Fe/O interface prefers interstitial oxygen configurations while the addition of oxides seems to switch this trend around. In particular, HfO2/Fe displays a strong preference for the frontal oxygen arrangement, leading us to identify a possible hypothesis for the phenomenon of the multiple magneto-ionic regimes displayed. In it’s as grown form, HfO2/CoFeB is characterized by an underoxidized ferromagnet interface [2]. The application of a gate voltage on HfO2/CoFeB pushes some of the oxygen species in proximity of the interface where they occupy the stable frontal site. Further application of a gate voltage pushes other oxygen atoms toward the still free and more unstable interstitial sites. The occupation of these interstitial sites has the effect of destroying perpendicular magnetic anisotropy as seen both in experiments and simulations [5] [1]. Once these more mobile interstitial sites are occupied, magnetic anisotropy can be switched reversibly by inverting the gate voltage and adjusting the interstitial site occupation (fig.2)

![](https://assets.underline.io/uploads/markdown_image/1/image/40c593503d5a4f3ee9c27db4ad2dc04d.jpg)

Comparison of the different interfacial configurations in the differentsamples. The bar plots represent the ground state energies and highlight themore stable configuration

![](https://assets.underline.io/uploads/markdown_image/1/image/f5dc5807d0f4552079d7a39375420a9e.jpg)

Hypothesis for the mechanism governing magneto-ionic regimes inHfO2/FM stacks. The text highlights the magnetic properties of the interface under different oxidation conditions.

Reversible anisotropy manipulation via gate voltages in ferromagnet/oxide multilayers

Magnetoionics (MI) is a much-in-demand feature for spintronics devices due to its great potential for improving energy efficiency in memory devices. The main feature of MI is to allow for the nonvolatile modulation of magnetic properties [1–5], making MI reversibility a fundamental quality for high device performance. Various studies have addressed issues impacting reversibility such as the presence of different types of ions, oxides and the degree of oxidation at the oxide/ferromagnetic interface [3, 5–8], while the influence of annealing temperature on reversibility has been largely overlooked. Annealing is commonly used to induce crystallization in CoFeB layers leading to the enhancement of perpendicular magnetic anisotropy (PMA), interfacial Dzyaloshinskii-Moriya interaction (iDMI), and tunnel magnetoresistance [9–11], therefore its impact on MI is of great interest. In this study, we show that W/CoFeB/HfO2 thin films annealed at 350°C and 390°C show a significant but irreversible dependence of PMA and DMI on gate voltage. However, an annealing program using a slow ramp that minimizes the exposure to the highest temperatures allows to induce PMA and iDMI while also showing a MI reversibility of 71% in remanence with respect to PMA. This dependence of MI reversibility on annealing profiles and temperatures could be related to the different degrees of crystallinity obtained under different annealing conditions. Such structural differences, such as size and distribution of crystallites, can greatly impact the ion mobility inside the stack and be responsible for observed modulation of the MI reversibility. Our results therefore show that annealing parameters need to be optimized to obtain enhanced magnetic properties without compromising MI performance.

![](https://assets.underline.io/uploads/markdown_image/1/image/54d50bab8c546ddbc8fd33ecfea28690.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/bf6e6dbd3a0f9277642eaa6aab5dd034.jpg)

Effect of Annealing on Magnetoionics in W/CoFeB/HfO2

Effect of Annealing on Magnetoionics in W/CoFeB/HfO2

The Ising machine is an unconventional computing architecture that can be used to solve NP-hard combinatorial optimization problems more efficiently than traditional von Neumann architectures. GHz spin Hall nano-oscillators (SHNOs) are a particularly attractive technology for building fast, energy-efficient, and scalable Ising machines; however, electrical coupling mechanisms which allow for full programmability among different oscillator nodes have not yet been fully demonstrated in such a network. Here, we develop a general analytical framework that can describe injection locking of SHNOs with arbitrary oscillation orbits at both the fundamental frequency and harmonics. With this compact analytical framework, we integrate the SHNO into a Verilog-A device model that can emulate the oscillator’s injection locking behavior in circuit simulations, where the dynamics of coupled oscillator networks are simulated together with conventional electronic components (Fig. 1). While our abstract circuit simulations achieve similar accuracy as full micromagnetic simulations, the device model we developed leads to more than 100 times improvement in simulation efficiency and allows us to evaluate the performance using realistic circuits. Using circuit-level simulations, we further study the effects of phase noise and scalability in networks of up to hundreds of coupled oscillators to show that the SHNO-based Ising machine can be operated robustly at room temperature. Compared with existing technologies, SHNO networks exhibit orders of magnitude improvement in time, space, and energy efficiency (Table 1). Our results provide analytical tools and design insights that will be useful for the realization of a CMOS-integrated SHNO Ising machine.

![](https://assets.underline.io/uploads/markdown_image/1/image/a0dab57c9a06319f78760697037422fd.jpg)

Fig. 1: (a) Electrical coupling circuit linking two SHNOs in the oscillator-based Ising machine. (b) Phases of oscillators in a 4-node coupled network solving the Ising model in circuit simulations (HSPICE) using our abstract device model and in micromagnetic simulations (MuMax3).

![](https://assets.underline.io/uploads/markdown_image/1/image/56041ec137cf8fc9052b69c276e29915.jpg)

Table 1: Comparison of speed, energy, and space metrics between the SHNO Ising machine and existing technologies. Values are standardized to a 100-node network.

Using Machine Based on Electrically Coupled Spin Hall Nano-Oscillators

In order to go beyond the traditional CMOS logic technology, novel spin-based logic architectures are being developed to provide nonvolatile data retention, near-zero leakage, and scalability. In particular, architectures based on magnetic domain walls take the advantage of the fast motion, high density, non-volatility and flexible design of domain walls to process and store information in three dimensions [1,2]. Such logic schemes have so far relied on domain wall manipulation and clocking using an external magnetic field, which hinders their industrial implementation. Here we demonstrate a method for performing all-electric logic operations and cascading using domain wall racetracks [3]. Our concept is based on the recently developed chiral coupling mechanism between adjacent magnets where the magnetic anisotropy competes with the interfacial Dzyaloshinskii–Moriya interaction (DMI) in Pt/Co/AlOx trilayers [4,5]. When a narrow in-plane (IP) magnetized region is incorporated into an out-of-plane (OOP) magnetized track, it couples to its surrounding, leading to the antiferromagnetic alignment of the OOP magnetization on the left and right of the IP region. This is enforced by interfacial DMI favouring a fixed magnetization winding direction, which is left-handed in our Pt/Co/AlOx trilayers. When a current-driven domain wall propagating in the track encounters such a region, the magnetization of the IP regions flips, leading to the annihilation of the incoming domain wall and the nucleation of a new domain wall of opposite polarity on the other side of the IP region (Fig. 1a). The chiral OOP-IP-OOP structure therefore serves as a domain wall inverter, the essential building block for all implementations of Boolean logic. Based on this principle, we fabricated reconfigurable NAND and NOR logic gates, making our concept for current-driven DW logic functionally complete. We also cascaded several NAND gates to build XOR and full adder gates, demonstrating electrical control of magnetic data and device interconnection in logic circuits (Fig. 1b). The functionality of logic circuits can be also expanded by the realization of a domain wall diode based on a geometrically tailored inverter [7]. We also broadened the application of chiral coupling towards dynamic computation with oscillators [8]. By imprinting the magnetic configuration of an IP magnetized disk in an OOP magnetized slab containing sizeable DMI, a chiral polar vortex texture can be established as a ground state in the patterned region (Fig. 2a). By means of micromagnetic calculations, we show that such an oscillator can be driven and manipulated by an injected spin current. We investigated the mutual synchronization of such oscillators via spin wave and dipolar interactions (Fig. 2b) and demonstrated their potential for neuromorphic computing with a neural network of six oscillators.

![](https://assets.underline.io/uploads/markdown_image/1/image/28a28fb12e8a66f07e883d8cc0fb0ebe.jpg)

Fig. 1. Current-driven DW logic. (a) Schematic of current-driven DW inversion, occurring as the DW moves across the in-plane region. After selective oxidization, the magnetizations of neighboring OOP and IP regions align with a left-handed chirality in Pt/Co/AlOx. Here a down│up DW is inverted to an up│down DW. (b) Left panel: Schematic of a full adder gate obtained by cascading several NAND gates. Right panel: Full adder gate with “a=0” and “b=1” inputs resulting in “Sum=1” with a “Carry = 0”.

![](https://assets.underline.io/uploads/markdown_image/1/image/b552ddf811e6fdfc165e88837fcab20a.jpg)

Fig. 2. Computation with chiral oscillators. (a) Equilibrium magnetic texture in the DMI-based nano-oscillator with 100 nm diameter. The oscillator has two equivalent states, depending on the magnetization direction in the OOP region. Magnetization along the +z and –z direction is indicated in white and black, while the IP magnetization direction is given by the color wheel. (b) Synchronization pattern of two oscillators separated by 60 nm distance. The current density in the left oscillator is fixed (j1=0.8×109 A/m2), while the current density of the oscillator on the right (j2) is swept.

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