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Spin-Transfer-Torque Oscillator with an Antiferromagnetic Exchange-Coupled Composite Free Layer

We present an antiferromagnetically exchange-coupled composite (soft and hard layers) spin torque oscillator (AF-ECC STO) and demonstrate its operation via both analytical and micromagnetic modeling. The operation exploits the exchange field due to the antiferromagnetic coupling between soft and hard sublayers of the free layer as well as on the easy-plane anisotropy of the soft sublayer. Optimized AF-ECC STO structures can generate large-amplitude magnetization oscillations, which can be tuned over a broad frequency range with precessions mostly generated by the soft layer. We demonstrate that the AF-ECC STO structure offers flexibility in current control of the oscillation frequency and magnetization angle for realistic material parameters.

42 ENGINEERING↗

Heavy-ion-induced displacement damage effects in magnetic tunnel junctions with perpendicular anisotropy

Here, we evaluate the resilience of CoFeB/MgO/CoFeB magnetic tunnel junctions (MTJs) with perpendicular magnetic anisotropy to displacement damage induced by heavy ion irradiation. MTJs were exposed to 3 MeV Ta 2+ ions at different levels of ion beam fluence spanning five orders of magnitude. The devices remained insensitive to beam fluences up to 10 11 ions/cm 2 , beyond which a gradual degradation in the device magnetoresistance, coercive magnetic field, and spin-transfer-torque switching voltage were observed, ending with a complete loss of magnetoresistance at very high levels of displacement damage (>0.035 displacements per atom). The loss of magnetoresistance is attributed to structural damage at the MgO interfaces, which allows electrons to scatter among the propagating modes within the tunnel barrier and reduces the net spin polarization. Ion-induced damage to the interface also reduces the perpendicular magnetic anisotropy. This study clarifies the displacement damage thresholds that lead to significant irreversible changes in the characteristics of spin-transfer-torque magnetic random access memory (STT-MRAM) and elucidates the physical mechanisms underlying the deterioration in device properties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Permanently Magnetized Insulating Thin-Film Devices by Reduction

A reduction-based manufacturing process for creating technologically important multilayer structures from lattice-matched ferromagnetic insulators and ferromagnetic conductors is reported. The process is demonstrated by growing a permanently magnetized double-layer structure, consisting of lattice-matched conducting (Ni,Co) and insulating (Ni 0.4 Co 0.6 ) 3 O 3 layers, through a single deposition cycle. The orientation of the metal cation network is preserved after reduction. Close-packing displacements of Ni and Co take place in such a manner that the in-plane hexagonal arrangement is preserved. This is critical for ensuring high-quality interfaces joining the layers. At room temperature the hysteresis loop is centered. At low temperature the oxide layer becomes ferrimagnetically ordered, accompanied by a shift of the hysteresis loop along the magnetic field axis. The shift is assigned to exchange bias phenomenon. Biaxial compressive strain is responsible for the required ferrimagnetic ordering. Finally, spin valves and closely related magnetoresistance random access memory and spin-transfer-torque magnetic random access memory devices are addressed as potential applications.

42 ENGINEERING↗

Progress toward picosecond on-chip magnetic memory

Here, we offer a perspective on the prospects of ultrafast spintronics and opto-magnetism as a pathway to high-performance, energy-efficient, and non-volatile embedded memory in digital integrated circuit applications. Conventional spintronic devices, such as spin-transfer-torque magnetic-resistive random-access memory (STT-MRAM) and spin–orbit torque MRAM, are promising due to their non-volatility, energy-efficiency, and high endurance. STT-MRAMs are now entering into the commercial market; however, they are limited in write speed to the nanosecond timescale. Improvement in the write speed of spintronic devices can significantly increase their usefulness as viable alternatives to the existing CMOS-based devices. In this article, we discuss recent studies that advance the field of ultrafast spintronics and opto-magnetism. An optimized ferromagnet–ferrimagnet exchange-coupled magnetic stack, which can serve as the free layer of a magnetic tunnel junction (MTJ), can be optically switched in as fast as ~3 ps. Integration of ultrafast magnetic switching of a similar stack into an MTJ device has enabled electrical readout of the switched state using a relatively larger tunneling magnetoresistance ratio. Purely electronic ultrafast spin–orbit torque induced switching of a ferromagnet has been demonstrated using ~6 ps long charge current pulses. We conclude our Perspective by discussing some of the challenges that remain to be addressed to accelerate ultrafast spintronics technologies toward practical implementation in high-performance digital information processing systems.

42 ENGINEERING↗

Magnetic tunnel junction random number generators applied to dynamically tuned probability trees driven by spin orbit torque

Abstract Perpendicular magnetic tunnel junction (pMTJ)-based true-random number generators (RNGs) can consume orders of magnitude less energy per bit than CMOS pseudo-RNGs. Here, we numerically investigate with a macrospin Landau–Lifshitz-Gilbert equation solver the use of pMTJs driven by spin–orbit torque to directly sample numbers from arbitrary probability distributions with the help of a tunable probability tree. The tree operates by dynamically biasing sequences of pMTJ relaxation events, called ‘coinflips’, via an additional applied spin-transfer-torque current. Specifically, using a single, ideal pMTJ device we successfully draw integer samples on the interval [0, 255] from an exponential distribution based on p -value distribution analysis. In order to investigate device-to-device variations, the thermal stability of the pMTJs are varied based on manufactured device data. It is found that while repeatedly using a varied device inhibits ability to recover the probability distribution, the device variations average out when considering the entire set of devices as a ‘bucket’ to agnostically draw random numbers from. Further, it is noted that the device variations most significantly impact the highest level of the probability tree, with diminishing errors at lower levels. The devices are then used to draw both uniformly and exponentially distributed numbers for the Monte Carlo computation of a problem from particle transport, showing excellent data fit with the analytical solution. Finally, the devices are benchmarked against CMOS and memristor RNGs, showing faster bit generation and significantly lower energy use.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Electrical control of magnetism by electric field and current-induced torques

The remanent magnetization of ferromagnets has long been studied and used to store binary information. While early magnetic memory designs relied on magnetization switching by locally generated magnetic fields, key insights in condensed matter physics later suggested the possibility of doing it by electrical means instead. In the 1990s, Slonczewski and Berger formulated the concept of current-induced spin torques in magnetic multilayers through which a spin-polarized current generated by a first ferromagnet may be used to switch the magnetization of a second one. This discovery drove the development of spin-transfer-torque magnetic random-access memories (MRAMs). More recent fundamental research revealed other types of current-induced torques named spin-orbit torques (SOTs) and will lead to a new generation of devices including SOT MRAMs and skyrmion-based devices. Parallel to these advances, multiferroics and their magnetoelectric coupling, first investigated experimentally in the 1960s, experienced a renaissance. Dozens of multiferroic compounds with new magnetoelectric coupling mechanisms were discovered and high-quality multiferroic films were synthesized (notably of BiFeO 3 ), also leading to novel device concepts for information and communication technology such as the magnetoelectric spin-orbit (MESO) transistor. The story of the electrical switching of magnetization, which is discussed in this review, is that of a dance between fundamental research (in spintronics, condensed matter physics, and materials science) and technology (MRAMs, MESO transistors, microwave emitters, spin diodes, skyrmion-based devices, components for neuromorphics, etc.). This pas de deux has led to major scientific and technological breakthroughs in recent decades (such as the conceptualization of pure spin currents, the observation of magnetic skyrmions, and the discovery of spin-charge interconversion effects). As a result, this field has not only propelled MRAMs into consumer electronics products but also fueled discoveries in adjacent research areas such as ferroelectrics or magnonics. Here, in this review, recent advances in the control of magnetism by electric fields and by current-induced torques are covered. Fundamental concepts in these two directions are reviewed first, their combination is then discussed, and finally current various families of devices harnessing the electrical control of magnetic properties for various application fields are addressed. The review concludes by giving perspectives in terms of both emerging fundamental physics concepts and new directions in materials science.

36 MATERIALS SCIENCE↗

Magnetic droplet solitons

Magnetic droplet solitons are dynamical magnetic textures that form due to an attractive interaction between spin waves in thin films with perpendicular magnetic anisotropy. Spin currents and the spin torques associated with these currents enable their formation as they provide a means to excite non-equilibrium spin-wave populations and compensate their decay. Recent years have seen rapid advances in experiments that realize and study magnetic droplets. Important advances include the first direct x-ray images of droplets, determination of their threshold and sustaining currents, measurement of their generation and annihilation time, and evidence for drift instabilities, which can limit their lifetime. This perspective discusses these studies and contrasts these solitons to other types of spin-current excitations, such as spin-wave bullets, and static magnetic textures, including magnetic vortices and skyrmions. Magnetic droplet solitons can also serve as current controlled microwave frequency oscillators with potential applications in neuromorphic chips as nonlinear oscillators with memory.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Interfacial spin–orbit torques

Spin–orbit torques offer a promising mechanism for electrically controlling magnetization dynamics in nanoscale heterostructures. While spin–orbit torques occur predominately at interfaces, the physical mechanisms underlying these torques can originate in both the bulk layers and at interfaces. Classifying spin–orbit torques based on the region that they originate in provides clues as to how to optimize the effect. While most bulk spin–orbit torque contributions are well studied, many of the interfacial contributions allowed by symmetry have yet to be fully explored theoretically and experimentally. To facilitate progress, we review interfacial spin–orbit torques from a semiclassical viewpoint and relate these contributions to recent experimental results. In this study, we show the relationship between different interface transport parameters within the same model. For charges and spins flowing perpendicular to the interface, interfacial spin–orbit coupling both modifies the mixing conductance of the magnetoelectronic circuit theory and gives rise to spin memory loss. For in-plane electric fields, interfacial spin–orbit coupling gives rise to torques described by spin–orbit filtering, spin swapping, and precession. In addition, these same interfacial processes generate spin currents that flow into the non-magnetic layer. For in-plane electric fields in trilayer structures, the spin currents generated at the interface between one ferromagnetic layer and the non-magnetic spacer layer can propagate through the non-magnetic layer to produce novel torques on the other ferromagnetic layer.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A domain wall-magnetic tunnel junction artificial synapse with notched geometry for accurate and efficient training of deep neural networks

Inspired by the parallelism and efficiency of the brain, several candidates for artificial synapse devices have been developed for neuromorphic computing, yet a nonlinear and asymmetric synaptic response curve precludes their use for backpropagation, the foundation of modern supervised learning. Spintronic devices—which benefit from high endurance, low power consumption, low latency, and CMOS compatibility—are a promising technology for memory, and domain-wall magnetic tunnel junction (DW-MTJ) devices have been shown to implement synaptic functions such as long-term potentiation and spike-timing dependent plasticity. In this work, we propose a notched DW-MTJ synapse as a candidate for supervised learning. Using micromagnetic simulations at room temperature, we show that notched synapses ensure the non-volatility of the synaptic weight and allow for highly linear, symmetric, and reproducible weight updates using either spin transfer torque (STT) or spin–orbit torque (SOT) mechanisms of DW propagation. We use lookup tables constructed from micromagnetics simulations to model the training of neural networks built with DW-MTJ synapses on both the MNIST and Fashion-MNIST image classification tasks. Accounting for thermal noise and realistic process variations, the DW-MTJ devices achieve classification accuracy close to ideal floating-point updates using both STT and SOT devices at room temperature and at 400 K. Our work establishes the basis for a magnetic artificial synapse that can eventually lead to hardware neural networks with fully spintronic matrix operations implementing machine learning.

42 ENGINEERING↗

Absorption of transverse spin current in ferromagnetic NiCu: Dominance of bulk dephasing over spin-flip scattering

In ferromagnetic metals, transverse spin currents are thought to be absorbed via dephasing—i.e., destructive interference of spins precessing about the strong exchange field. Yet, due to the ultrashort coherence length of ≈1 nm in typical ferromagnetic thin films, it is difficult to distinguish dephasing in the bulk from spin-flip scattering at the interface. Here, to assess which mechanism dominates, we examine transverse spin-current absorption in ferromagnetic NiCu alloy films with reduced exchange fields. We observe that the coherence length increases with decreasing Curie temperature, as weaker dephasing in the film bulk slows down spin absorption. Moreover, nonmagnetic Cu impurities do not diminish the efficiency of spin-transfer torque from the absorbed spin current. Our findings affirm that the transverse spin current is predominantly absorbed by dephasing inside the nanometer-thick ferromagnetic metals, even with high impurity contents.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

High-speed tunable generation of random number distributions using actuated perpendicular magnetic tunnel junctions

Perpendicular magnetic tunnel junctions (pMTJs) actuated by nanosecond pulses are emerging as promising devices for true random number generation (TRNG) due to their intrinsic stochastic behavior and high throughput. In this work, we demonstrate the tunability and quality of random number distributions generated by pMTJs operating at a frequency of 104 MHz. First, changing the pulse amplitude is used to systematically vary the probability bias. The variance of the resulting bitstreams closely matches the expected binomial distribution, demonstrating consistency with an underlying sequence of Bernoulli trials. Second, the quality of uniform distributions of 8-bit random numbers generated with a probability bias of 0.5 is considered. A reduced chi-square analysis of these data shows that only two XOR operations are sufficient to achieve this distribution with p-values greater than 0.05. Finally, we show that there is a correlation between long-term probability bias variations and pMTJ resistance. These findings suggest that variations in the characteristics of the pMTJ underlie the observed variation of probability bias. In conclusion, our results highlight the potential of stochastically actuated pMTJs for high-speed, tunable TRNG applications, showing the importance of the stability of pMTJ device characteristics in achieving reliable, long-term performance.

Magnetic tunnel junctions↗

Magnus force induced magnetic diode effect in skyrmion systems

We show that skyrmions can exhibit a “magnetic diode effect,” where there is a nonreciprocal response in the transport when the magnetic field is reversed. This effect can be achieved for skyrmions moving in channels with a sawtooth potential on one side and a reversed sawtooth potential on the other side. We consider the cases of both spin-transfer torque (STT) and spin–orbit torque (SOT). When the magnetic field is held fixed, the velocity response of the skyrmion is the same for current applied in either direction for both torques, so there is no current diode effect. When the magnetic field is reversed, under STT driving the velocity of the skyrmion reverses and its absolute value changes. Under SOT driving, the velocity remains in the same direction but drops to a much lower value, resulting in negative differential conductivity. For a fixed current, we find a nonreciprocal skyrmion velocity as a function of the applied field’s sign, in analogy to the velocity–current curves observed in the usual diode effect. The nonreciprocity is generated by the Magnus force, which causes skyrmions to interact preferentially with one side of the channel. Since the channel sides have opposite asymmetry, a positive magnetic field can cause the skyrmion to interact with the “hard” asymmetry side of the channel, while a negative magnetic field causes the skyrmion to interact with the “easy” asymmetry side. This geometry could be used to create new kinds of magnetic-field-induced diode effects that can be harnessed in new types of skyrmion-based devices.

36 MATERIALS SCIENCE↗

Thermal stability and magnetization switching of composite free layer with perpendicular magnetic anisotropy

We present a micromagnetic study of a ferromagnetically exchange-coupled composite free layer design for perpendicular magnetic tunnel junctions. The thermal stability factor and critical switching current density depend on the exchange coupling strength and effective anisotropy ratio between the sublayers of the composite free layer. The energy barrier increases with an increase of the exchange coupling strength until it reaches a plateau in the strong-coupling limit. An optimal exchange coupling strength exists that leads to the minimal critical switching current and a significant improvement of the figure of merit defined as the ratio between the energy barrier and critical switching current. This behavior is obtained for smaller device sizes with uniform reversal and larger sizes with domain wall reversal.

36 MATERIALS SCIENCE↗

Linearized frequency domain Landau-Lifshitz-Gilbert equation formulation

We present a general finite element linearized Landau-Lifshitz-Gilbert equation (LLGE) solver for magnetic systems under weak time-harmonic excitation field. The linearized LLGE is obtained by assuming a small deviation around the equilibrium state of the magnetic system. Inserting such expansion into LLGE and keeping only first order terms gives the linearized LLGE, which gives a frequency domain solution for the complex magnetization amplitudes under an external time-harmonic applied field of a given frequency. We solve the linear system with an iterative solver using generalized minimal residual method. We construct a preconditioner matrix to effectively solve the linear system. The validity, effectiveness, speed, and scalability of the linear solver are demonstrated via numerical examples.

36 MATERIALS SCIENCE↗