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Magnetic Tunnel Junctions (MTJs) are of great interest for non-conventional computing applications. The Toffoli gate is a universal reversible logic gate, enabling the construction of arbitrary boolean circuits. Here, we present a proof-of-concept construction of a gadget which encodes the Toffoli gate's truth table into the ground state of coupled uniaxial nanomagnets that could form the free layers of perpendicularly magnetized MTJs. This construction has three input bits, three output bits, and one ancilla bit. We numerically simulate the seven macrospins evolving under the stochastic Landau-Lifshitz-Gilbert (s-LLG) equation. We investigate the effect of the anisotropy-to-exchange-coupling strength ratio $H_A/H_\text{ex}$ on the working of the gadget. We find that for $H_A/H_\text{ex} \lesssim 0.93$, the spins evolve to the Toffoli gate truth table configurations under LLG dynamics alone, while higher $H_A/H_\text{ex}$ ratios require thermal annealing due to suboptimal metastable states. Under our chosen annealing procedure, the s-LLG simulation with thermal annealing achieves a 100% success rate up to $H_A/H_\text{ex}\simeq3.0$. The feasibility of constructing MTJ-free-layer-based Toffoli gates highlights their potential in designing new types of MTJ-based circuits.

Spin-Hall nano-oscillators (SHNO) are nanoscale spintronic devices that generate high-frequency (GHz) microwave signals useful for various applications such as neuromorphic computing and creating Ising systems. Recent research demonstrated that hybrid SHNOs consisting of a ferromagnetic metal (permalloy) and lithium aluminum ferrite (LAFO), a ferrimagnetic insulator, thin films have advantages in having lower auto-oscillation threshold currents ($I_{\text{th}}$) and generating larger microwave output power, making this hybrid structure an attractive candidate for spintronic applications. It is essential to understand how the tunable material properties of LAFO, e.g., its thickness, perpendicular magnetic anisotropy ($K_u$), and saturation magnetization ($M_s$), affect magnetic dynamics in hybrid SHNOs. We investigate the change in $I_{\text{th}}$ and the output power of the device as the LAFO parameters vary. We find the $I_{\text{th}}$ does not depend strongly on these parameters, but the output power has a highly nonlinear dependence on $M_s$ and $K_u$. We further investigate the nature of the excited spin-wave modes as a function of $K_u$ and determine a critical value of $K_u$ above which propagating spin-waves are excited. Our simulation results provide a roadmap for designing hybrid SHNOs to achieve targeted spin excitation characteristics.

We present a method to approximately solve general instances of combinatorial optimization problems using the physical dynamics of 3d rotors obeying Landau-Lifshitz-Gilbert dynamics. Conventional techniques to solve discrete optimization problems that use simple continuous relaxation of the objective function followed by gradient descent minimization are inherently unable to avoid local optima, thus producing poor-quality solutions. Our method considers the physical dynamics of macrospins capable of escaping from local minima, thus facilitating the discovery of high-quality, nearly optimal solutions, as supported by extensive numerical simulations on a prototypical quadratic unconstrained binary optimization (QUBO) problem. Our method produces solutions that compare favorably with those obtained using state-of-the-art minimization algorithms (such as simulated annealing) while offering the advantage of being physically realizable by means of arrays of stochastic magnetic tunnel junction devices.

Metal-insulator transitions (MITs) in resistive switching materials can be triggered by an electric stimulus that produces significant changes in the electrical response. When these phases have distinct magnetic characteristics, dramatic changes in spin excitations are also expected. The transition metal oxide La0.7Sr0.3MnO3 (LSMO) is a ferromagnetic metal at low temperatures and a paramagnetic insulator above room temperature. When LSMO is in its metallic phase a critical electrical bias has been shown to lead to an MIT that results in the formation of a paramagnetic resistive barrier transverse to the applied electric field. Using spin-transfer ferromagnetic resonance spectroscopy, we show that even for electrical biases less than the critical value that triggers the MIT, there is magnetic phase separation with the spin-excitation resonances varying systematically with applied bias. Thus, applied voltages provide a means to alter spin resonance characteristics of interest for neuromorphic circuits.

Large quantities of random numbers are crucial in a wide range of applications. We have recently demonstrated that perpendicular nanopillar magnetic tunnel junctions (pMTJs) can produce true random bits when actuated with short pulses. However, our implementation used high-end and expensive electronics, such as a high bandwidth arbitrary waveform generator and analog-to-digital converter, and was limited to relatively low data rates. Here, we significantly increase the speed of true random number generation (TRNG) of our stochastic actuated pMTJs (SMART-pMTJs) using Field Programmable Gate Arrays (FPGAs), demonstrating the generation of over $10^{12}$ bits at rates exceeding 10Mb/s. The resulting bitstreams pass the NIST Statistical Test Suite for randomness with only one XOR operation. In addition to a hundred-fold reduction in the setup cost and a thousand-fold increase in bitrate, the advancement includes simplifying and optimizing random bit generation with a custom-designed analog daughter board to interface an FPGA and SMART-pMTJ. The resulting setup further enables FPGA at-speed processing of MTJ data for stochastic modeling and cryptography., Comment: 4 pages, 5 figures

True random number generators (TRNGs) are fundamental building blocks for many applications, such as cryptography, Monte Carlo simulations, neuromorphic computing, and probabilistic computing. While perpendicular magnetic tunnel junctions (pMTJs) based on low-barrier magnets (LBMs) are natural sources of TRNGs, they tend to suffer from device-to-device variability, low speed, and temperature sensitivity. Instead, medium-barrier magnets (MBMs) operated with nanosecond pulses - denoted, stochastic magnetic actuated random transducer (SMART) devices - are potentially superior candidates for such applications. We present a systematic analysis of spin-torque-driven switching of MBM-based pMTJs (Eb ~ 20 - 40 kBT) as a function of pulse duration (1 ps to 1 ms), by numerically solving their macrospin dynamics using a 1-D Fokker-Planck equation. We investigate the impact of voltage, temperature, and process variations (MTJ dimensions and material parameters) on the switching probability of the device. Our findings indicate SMART devices activated by short-duration pulses (< 1 ns) are much less sensitive to process-voltage-temperature (PVT) variations while consuming lower energy (~ fJ) than the same devices operated with longer pulses. Our results show a path toward building fast, energy-efficient, and robust TRNG hardware units for solving optimization problems., Comment: 7 pages, 5 figures

Nanoscale magnetic tunnel junction (MTJ) devices can efficiently convert thermal energy in the environment into random bitstreams for computational modeling and cryptography. We recently showed that perpendicular MTJs activated by nanosecond pulses can generate true random numbers at high data rates. Here, we explore the dependence of probability bias-the deviations from equal probability (50/50) 0/1 bit outcomes-of such devices on temperature, pulse amplitude, and duration. Our experimental results and device model demonstrate that operation with nanosecond pulses in the ballistic limit minimizes variation of probability bias with temperature to be far lower than that of devices operated with longer-duration pulses. Further, operation in the short-pulse limit reduces the bias variation with pulse amplitude while rendering the device more sensitive to pulse duration. These results are significant for designing TRNG MTJ circuits and establishing operating conditions., Comment: 6 pages, 4 figures

Thermally-induced transitions between bistable magnetic states of magnetic tunnel junctions (MTJ) are of interest for generating random bitstreams and for applications in stochastic computing. An applied field transverse to the easy axis of a perpendicularly magnetized MTJ (pMTJ) can lower the energy barrier ($E_b$) to these transitions leading to faster fluctuations. In this study, we present analytical and numerical calculations of $E_b$ considering both coherent (macrospin) reversal and non-uniform wall-mediated magnetization reversal for a selection of nanodisk diameters and applied fields. Non-uniform reversal processes dominate for larger diameters, and our numerical calculations of $E_b$ using the String method show that the transition state has a sigmoidal magnetization profile. The latter can be described with an analytical expression that depends on only one spatial dimension, parallel to the applied field, which is also the preferred direction of profile motion during reversal. Our results provide nanodisk energy barriers as a function of the transverse field, nanodisk diameter, and material characteristics, which are useful for designing stochastic bitstreams., Comment: 10 pages, 8 figures, 1 table. It will be submitted to a peer-reviewed journal

Magnetic tunnel junctions (MTJs), which are the fundamental building blocks of spintronic devices, have been used to build true random number generators (TRNGs) with different trade-offs between throughput, power, and area requirements. MTJs with high-barrier magnets (HBMs) have been used to generate random bitstreams with $\lesssim$ 200~Mb/s throughput and pJ/bit energy consumption. A high temperature sensitivity, however, adversely affects their performance as a TRNG. Superparamagnetic MTJs employing low-barrier magnets (LBMs) have also been used for TRNG operation. Although LBM-based MTJs can operate at low energy, they suffer from slow dynamics, sensitivity to process variations, and low fabrication yield. In this paper, we model a TRNG based on medium-barrier magnets (MBMs) with perpendicular magnetic anisotropy. The proposed MBM-based TRNG is driven with short voltage pulses to induce ballistic, yet stochastic, magnetization switching. We show that the proposed TRNG can operate at frequencies of about 500~MHz while consuming less than 100~fJ/bit of energy. In the short-pulse ballistic limit, the switching probability of our device shows robustness to variations in temperature and material parameters relative to LBMs and HBMs. Our results suggest that MBM-based MTJs are suitable candidates for building fast and energy-efficient TRNG hardware units for probabilistic computing., Comment: 10 pages, 10 figures, Accepted at ISQED 2023 for poster presentation

True random number generators are of great interest in many computing applications such as cryptography, neuromorphic systems and Monte Carlo simulations. Here we investigate perpendicular magnetic tunnel junction nanopillars (pMTJs) activated by short duration (ns) pulses in the ballistic limit for such applications. In this limit, a pulse can transform the Boltzmann distribution of initial free layer magnetization states into randomly magnetized down or up states, i.e. a bit that is 0 or 1, easily determined by measurement of the junction's tunnel resistance. It is demonstrated that bitstreams with millions of events: 1) are very well described by the binomial distribution; 2) can be used to create a uniform distribution of 8-bit random numbers; 3) pass multiple statistical tests for true randomness, including all the National Institute of Standards tests for random number generators with only one XOR operation; and 4) can have no drift in the bit probability with time. The results presented here show that pMTJs operated in the ballistic regime can generate true random numbers at GHz bitrates, while being more robust to environmental changes, such as their operating temperature, compared to other stochastic nanomagnetic devices., Comment: 8 pages, 3 figures, 2 tables, will be submitted to peer-reviewed journal

Spin-Hall nano-oscillators (SHNOs) are promising spintronic devices to realize current controlled GHz frequency signals in nanoscale devices for neuromorphic computing and creating Ising systems. However, traditional SHNOs -- devices based on transition metals -- have high auto-oscillation threshold currents as well as low quality factors and output powers. Here we demonstrate a new type of hybrid SHNO based on a permalloy (Py) ferromagnetic-metal nanowire and low-damping ferrimagnetic insulator, in the form of epitaxial lithium aluminum ferrite (LAFO) thin films. The superior characteristics of such SHNOs are associated with the excitation of larger spin-precession angles and volumes. We further find that the presence of the ferrimagnetic insulator enhances the auto-oscillation amplitude of spin-wave edge modes, consistent with our micromagnetic modeling. This hybrid SHNO expands spintronic applications, including providing new means of coupling multiple SHNOs for neuromorphic computing and advancing magnonics., Comment: 13 pages, 5 figures

Neuromorphic computing approaches become increasingly important as we address future needs for efficiently processing massive amounts of data. The unique attributes of quantum materials can help address these needs by enabling new energy-efficient device concepts that implement neuromorphic ideas at the hardware level. In particular, strong correlations give rise to highly non-linear responses, such as conductive phase transitions that can be harnessed for short and long-term plasticity. Similarly, magnetization dynamics are strongly non-linear and can be utilized for data classification. This paper discusses select examples of these approaches, and provides a perspective for the current opportunities and challenges for assembling quantum-material-based devices for neuromorphic functionalities into larger emergent complex network systems.

Two-dimensional (2D) magnetic semiconductors feature both tightly-bound excitons with large oscillator strength and potentially long-lived coherent magnons due to the presence of bandgap and spatial confinement. While magnons and excitons are energetically mismatched by orders of magnitude, their coupling can lead to efficient optical access to spin information. Here we report strong magnon-exciton coupling in the 2D van der Waals (vdW) antiferromagnetic (AFM) semiconductor CrSBr. Coherent magnons launched by above-gap excitation modulate the interlayer hybridization, which leads to dynamic modulation of excitonic energies. Time-resolved exciton sensing reveals magnons that can coherently travel beyond 7 micrometer, with coherence time above 5 ns. We observe this exciton-coupled coherent magnons in both even and odd number of layers, with and without compensated magnetization, down to the bilayer limit. Given the versatility of vdW heterostructures, these coherent 2D magnons may be basis for optically accessible magnonics and quantum interconnects., Comment: 14 pages, 5 figures, 30 pages Supporting Info

Spin currents are used to write information in magnetic random access memory (MRAM) devices by switching the magnetization direction of one of the ferromagnetic electrodes of a magnetic tunnel junction (MTJ) nanopillar. Different physical mechanisms of conversion of charge current to spin current can be used in 2-terminal and 3-terminal device geometries. In 2-terminal devices, charge-to-spin conversion occurs by spin filtering in the MTJ's ferromagnetic electrodes and present day MRAM devices operate near the theoretically expected maximum charge-to-spin conversion efficiency. In 3-terminal devices, spin-orbit interactions in a channel material can also be used to generate large spin currents. In this perspective article, we discuss charge-to-spin conversion processes that can satisfy the requirements of MRAM technology. We emphasize the need to develop channel materials with larger charge-to-spin conversion efficiency -- that can equal or exceed that produced by spin filtering -- and spin currents with a spin polarization component perpendicular to the channel interface. This would enable high-performance devices based on sub-20 nm diameter perpendicularly magnetized MTJ nanopillars without need of a symmetry breaking field. We also discuss MRAM characteristics essential for CMOS integration. Finally, we identify critical research needs for charge-to-spin conversion measurements and metrics that can be used to optimize device channel materials and interface properties prior to full MTJ nanopillar device fabrication and characterization., Comment: 12 pages, 3 figures, 1 table

Electrical switching of antiferromagnets is an exciting recent development in spintronics, which promises active antiferromagnetic devices with high speed and low energy cost. In this emerging field, there is an active debate about the mechanisms of current-driven switching of antiferromagnets. Harmonic characterization is a powerful tool to quantify current-induced spin-orbit torques and spin Seebeck effect in heavy-metal/ferromagnet systems. However, the harmonic measurement technique has never been verified in antiferromagnetic heterostructures. Here, we report for the first time harmonic measurements in Pt/$\alpha$-Fe$_2$O$_3$ bilayers, which are explained by our modeling of higher-order harmonic voltages. As compared with ferromagnetic heterostructures where all current-induced effects appear in the second harmonic signals, the damping-like torque and thermally-induced magnetoelastic effect contributions in Pt/$\alpha$-Fe$_2$O$_3$ emerge in the third harmonic voltage. Our results provide a new path to probe the current-induced magnetization dynamics in antiferromagnets, promoting the application of antiferromagnetic spintronic devices.

The effect of spin currents on the magnetic order of insulating antiferromagnets (AFMs) is of fundamental interest and can enable new applications. Toward this goal, characterizing the spin-orbit torques (SOT) associated with AFM/heavy metal (HM) interfaces is important. Here we report the full angular dependence of the harmonic Hall voltages in a predominantly easy-plane AFM, epitaxial c-axis oriented $\alpha$-Fe$_2$O$_3$ films, with an interface to Pt. By modeling the harmonic Hall signals together with the $\alpha$-Fe$_2$O$_3$ magnetic parameters, we determine the amplitudes of field-like and damping-like SOT. Out-of-plane field scans are shown to be essential to determining the damping-like component of the torques. In contrast to ferromagnetic/heavy metal heterostructures, our results demonstrate that the field-like torques are significantly larger than the damping-like torques, which we correlate with the presence of a large imaginary component of the interface spin-mixing conductance. Our work demonstrates a direct way of characterizing SOT in AFM/HM heterostructures.

We show analytically using a macrospin approximation that easy-plane spin Hall nano-oscillators excited by a spin-current polarized perpendicularly to the easy-plane have phase dynamics analogous to that of Josephson junctions. Similarly to Josephson junctions, they can reproduce the spiking behavior of biological neurons that is appropriate for neuromorphic computing. We perform micromagnetic simulations of such oscillators realized in the nano-constriction geometry and show that the easy-plane spiking dynamics is preserved in an experimentally feasible architecture. Finally we simulate two elementary neural network blocks that implement operations essential for neuromorphic computing. First, we show that output spikes energies from two neurons can be summed and injected into a following layer neuron and second, we demonstrate that outputs can be multiplied by synaptic weights implemented by locally modifying the anisotropy., Comment: 9 pages, 11 figures

Spin torque is a promising tool for driving magnetization dynamics for novel computing technologies. These torques can be easily produced by spin-orbit effects, but for most conventional spin source materials, a high degree of crystal symmetry limits the geometry of the spin torques produced. Magnetic ordering is one way to reduce the symmetry of a material and allow exotic torques, and antiferromagnets are particularly promising because they are robust against external fields. We present spin torque ferromagnetic resonance measurements and second harmonic Hall measurements characterizing the spin torques in antiferromagnetic iron rhodium alloy. We report extremely large, strongly temperature-dependent exotic spin torques with a geometry apparently defined by the magnetic ordering direction. We find the spin torque efficiency of iron rhodium to be (330$\pm$150) % at 170 K and (91$\pm$32) % at room temperature. We support our conclusions with theoretical calculations showing how the antiferromagnetic ordering in iron rhodium gives rise to such exotic torques., Comment: 21 pages, 6 figures

Antisymmetric exchange interactions lead to non-reciprocal spin-wave propagation. As a result, spin waves confined in a nanostructure are not standing waves; they have a time-dependent phase, because counter-propagating waves of the same frequency have different wavelengths. We report on a Brillouin light scattering (BLS) study of confined spin waves in Co/Pt nanowires with strong Dzyaloshinskii-Moriya interactions (DMI). Spin-wave quantization in narrow ($\lesssim 200$ nm width) wires dramatically reduces the frequency shift between BLS Stokes and anti-Stokes lines associated with the scattering of light incident transverse to the nanowires. In contrast, the BLS frequency shift associated with the scattering of spin waves propagating along the nanowire length is independent of nanowire width. A model that considers the chiral nature of modes captures this physics and predicts a dramatic reduction in frequency shift of light scattered from higher energy spin waves in narrow wires, which is confirmed by our experiments., Comment: 9 pages, 9 figures

Solitonic magnetic excitations such as domain walls and, specifically, skyrmionics enable the possibility of compact, high density, ultrafast,all-electronic, low-energy devices, which is the basis for the emerging area of skyrmionics. The topological winding of skyrmion spins affects their overall lifetime, energetics and dynamical behavior. In this review, we discuss skyrmionics in the context of the present day solid state memory landscape, and show how their size, stability and mobility can be controlled by material engineering, as well as how they can be nucleated and detected. Ferrimagnetsnear their compensation points are important candidates for this application, leading to detailed exploration of amorphous CoGd as well as the study of emergent materials such as Mn$_4$N and Inverse Heusler alloys. Along with material properties, geometrical parameters such as film thickness, defect density and notches can be used to tune skyrmion properties, such as their size and stability. Topology, however, can be a double-edged sword, especially for isolated metastable skyrmions, as it brings stability at the cost of additional damping and deflective Magnus forces compared to domain walls. Skyrmion deformation in response to forces also makes them intrinsically slower than domain walls. We explore potential analog applications of skyrmions, including temporal memory at low density, and decorrelator for stochastic computing at a higher density that capitalizes on their interactions. We summarize the main challenges to achieve a skyrmionics technology, including maintaining positional stability with very high accuracy, electrical readout, especially for small ferrimagnetic skyrmions, deterministic nucleation and annihilation, and overall integration with digital circuits with the associated circuit overhead., Comment: 41 pages, 34 figure, review

We present a systematic analysis of our ability to tune chiral Dzyaloshinskii-Moriya Interactions (DMI) in compensated ferrimagnetic Pt/GdCo/Pt1-xWx trilayers by cap layer composition. Using first principles calculations, we show that the DMI increases rapidly for only ~ 10% W and saturates thereafter, in agreement with experiments. The calculated DMI shows a spread in values around the experimental mean, depending on the atomic configuration of the cap layer interface. The saturation is attributed to the vanishing of spin orbit coupling energy at the cap layer and the simultaneous constancy at the bottom interface. Additionally, we predict the DMI in Pt/GdCo/X (X=Ta, W, Ir) and find that W in the cap layer favors a higher DMI than Ta and Ir that can be attributed to the difference in d-band alignment around the Fermi level. Our results open up exciting combinatorial possibilities for controlling the DMI in ferrimagnets towards nucleating and manipulating ultrasmall high-speed skyrmions., Comment: 6 pages, 5 figures

We report the direct observation of switching of the N\'eel vector of antiferromagnetic (AFM) domains in response to electrical pulses in micron-scale Pt/$\alpha$-Fe$_2$O$_3$ Hall bars using photoemission electron microscopy. Current pulses lead to reversible and repeatable switching, with the current direction determining the final state, consistent with Hall effect experiments that probe only the spatially averaged response. Current pulses also produce irreversible changes in domain structure, in and even outside the current path. In both cases only a fraction of the domains switch in response to pulses. Further, analysis of images taken with different x-ray polarizations shows that the AFM N\'eel order has an out-of-plane component in equilibrium that is important to consider in analyzing the switching data. These results show that -in addition to effects associated with spin-orbit torques from the Pt layer, which can produce reversible switching-changes in AFM order can be induced by purely thermal effects., Comment: 5 pages, 5 figures

Micromagnetic instabilities and non-uniform magnetization states play a significant role in spin transfer induced switching of nanometer scale magnetic elements. Here we model domain wall mediated switching dynamics in perpendicularly magnetized magnetic tunnel junction nanopillars. We show that domain wall surface tension always leads to magnetization oscillations and instabilities associated with the disk shape of the junction. A collective coordinate model is developed that captures aspects of these instabilities and illustrates their physical origin. Model results are compared to those of micromagnetic simulations. The switching dynamics is found to be very sensitive to the domain wall position and phase, which characterizes the angle of the magnetization in the disk plane. This sensitivity is reduced in the presence of spin torques and the spin current needed to displace a domain wall can be far less than the threshold current for switching from a uniformly magnetized state. A prediction of this model is conductance oscillations of increasing frequency during the switching process.

Temperature plays an important role in spin torque switching of magnetic tunnel junctions causing magnetization fluctuations that decrease the switching voltage but also introduce switching errors. Here we present a systematic study of the temperature dependence of the spin torque switching probability of state-of-the-art perpendicular magnetic tunnel junction nanopillars (40 to 60 nm in diameter) from room temperature down to 4 K, sampling up to a million switching events. The junction temperature at the switching voltage---obtained from the thermally assisted spin torque switching model---saturates at temperatures below about 75 K, showing that junction heating is significant below this temperature and that spin torque switching remains highly stochastic down to 4 K. A model of heat flow in a nanopillar junction shows this effect is associated with the reduced thermal conductivity and heat capacity of the metals in the junction., Comment: 7 pages, 4 figures, 1 table, submitted to peer-reviewed journal

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 in spin-transfer nanocontacts. This article reviews 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., Comment: 9 pages, 9 figures

Spin orbit torques are of great interest for switching the magnetization direction in nanostructures, moving skyrmions and exciting spin waves. The standard method of determining their efficiency is by spin torque ferromagnetic resonance (ST-FMR), a technique that involves analyzing the resonance linewidth or lineshape. On microstuctures these two analysis methods are quite consistent. Here we present ST-FMR results on permalloy (Ni$_{80}$Fe$_{20}$) nanowires -- with widths varying from $150$ to 800 nm -- that show that the standard model used to analyze the resonance linewidth and lineshape give different results; the efficiency appears greatly enhanced in nanowires when the lineshape method is used. A ST-FMR model that properly accounts for the sample shape is presented and shows much better consistency between the two methods. Micromagnetic simulations are used to verify the model. These results and the more accurate nanowire model presented are of importance for characterizing and optimizing charge-to-spin conversion efficiencies in nanostructures., Comment: 7 pages, 6 figures

Understanding the magnetization dynamics induced by spin transfer torques in perpendicularly magnetized magnetic tunnel junction nanopillars and its dependence on material parameters is critical to optimizing device performance. Here we present a micromagnetic study of spin-torque switching in a disk-shaped element as a function of the free layer's exchange constant and disk diameter. The switching is shown to generally occur by 1) growth of the magnetization precession amplitude in the element center; 2) an instability in which the reversing region moves to the disk edge, forming a magnetic domain wall; and 3) the motion of the domain wall across the element. For large diameters and small exchange, step 1 leads to a droplet with a fully reversed core that experiences a drift instability (step 2). While in the opposite case (small diameters and large exchange), the central region of the disk is not fully reversed before step 2 occurs. The origin of the micromagnetic structure is shown to be the disk's non-uniform demagnetization field. Faster, more coherence and energy efficient switching occur with larger exchange and smaller disk diameters, showing routes to increase device performance.

The N\'eel order of an antiferromagnet subject to a spin torque can undergo precession in a circular orbit about any chosen axis. To orient and stabilize the motion against the effects of magnetic anisotropy, the spin polarization should have components in-plane and normal to the plane of the orbit, where the latter must exceed a threshold. For biaxial antiferromagnets, the precessional motion is described by the equation for a damped-driven pendulum, which has hysteresis a function of the spin current with a critical value where the period diverges. The fundamental frequency of the motion varies inversely with the damping, and as $(x^p-1)^{1/p}$ with the drive-to-criticality ratio $x$ and the parameter $p>2$. An approximate closed-form result for the threshold spin current is presented, which depends on the minimum cutoff frequency the orbit can support. Precession about the hard axis has zero cutoff frequency and the lowest threshold, while the easy axis has the highest cutoff. A device setup is proposed for electrical control and detection of the dynamics, which is promising to demonstrate a tunable terahertz nano-oscillator.

An important goal of spintronics is to covert a charge current into a spin current with a controlled spin polarization that can exert torques on an adjacent magnetic layer. Here we demonstrate such torques in a two ferromagnet system. A CoNi multilayer is used as a spin current source in a sample with structure CoNi/Au/CoFeB. Spin torque ferromagnetic resonance is used to measure the torque on the CoFeB layer. The response as a function of the applied field angle and current is consistent with the symmetry expected for a torques produced by the planar Hall effect originating in CoNi. We find the strength of this effect to be comparable to that of the spin Hall effect in platinum, indicating that the planar Hall effect holds potential as a spin current source with a controllable polarization direction.

We investigated the low temperature performance of CoFeB/MgO based perpendicular magnetic tunnel junctions (pMTJs) by characterizing their quasi-static switching voltage, high speed pulse write error rate and endurance down to 9 K. pMTJ devices exhibited high magnetoresistance (>120%) and reliable (error rate<10-4) bi-directional switching with 2 to 200 ns voltage pulses. The endurance of the devices at 9 K surpassed that at 300 K by three orders of magnitude under the same write conditions, functioning for more than 10^12 cycles with 10 ns write pulses. The critical switching voltage at 9 K was observed to increase by 33% to 93%, depending on pulse duration, compared to that at 350 K. Ferromagnetic resonance and magnetization measurements on blanket pMTJ film stacks suggest that the increased switching voltage is associated with an increase in effective magnetic anisotropy and magnetization of free layer with decreasing temperature. Our work demonstrates that CoFeB/MgO based pMTJs have great potential to enable cryogenic MRAM and that their low temperature magnetization and effective magnetic anisotropy can be further optimized to lower operating power and improve endurance.

Spin-transfer magnetic random access memory is of significant interest for cryogenic applications where a persistent, fast, low-energy consumption and high device density is needed. Here we report the low-temperature nanosecond duration spin-transfer switching characteristics of perpendicular magnetic tunnel junction (pMTJ) nanopillar devices (40 to 60 nm in diameter) and contrast them to their room temperature properties. Interestingly, at fixed pulse voltage overdrive the characteristic switching time decreases with temperature, in contrast to macrospin model predictions, with the largest reduction in switching time occurring between room temperature and 150 K. The switching energy increases with decreasing temperature, but still compares very favorably to other types of spin-transfer devices at 4 K, with < 300 fJ required per switch. Write error rate (WER) measurements show highly reliable (WER <= 5x10^-5 with 4 ns pulses at 4 K) demonstrating the promise of pMTJ devices for cryogenic applications and routes to further device optimization., Comment: 5 pages, 4 figures, 1 table, submitted to peer-reviewed journal

We present a study of the transport properties of thermally generated spin currents in an insulating ferrimagnetic-antiferromagnetic-ferrimagnetic trilayer over a wide range of temperature. Spin currents generated by the spin Seebeck effect (SSE) in a yttrium iron garnet (YIG) YIG/NiO/YIG trilayer on a gadolinium gallium garnet (GGG) substrate were detected using the inverse spin Hall effect in Pt. By studying samples with different NiO thicknesses, the NiO spin diffusion length was determined to be 4.2 nm at room temperature. Interestingly, below 30 K, the inverse spin Hall signals are associated with the GGG substrate. The field dependence of the signal follows a Brillouin function for a S=7/2 spin ($\mathrm{Gd^{3+}}$) at low temperature. Sharp changes in the SSE signal at low fields are due to switching of the YIG magnetization. A broad peak in the SSE response was observed around 100 K, which we associate with an increase in the spin-diffusion length in YIG. These observations are important in understanding the generation and transport properties of spin currents through magnetic insulators and the role of a paramagnetic substrate in spin current generation., Comment: 5 pages, 4 figures

We present a study of the pulsed current switching characteristics of spin-valve nanopillars with in-plane magnetized dilute permalloy and undiluted permalloy free layers in the ballistic regime at low temperature. The dilute permalloy free layer device switches much faster: the characteristic switching time for a permalloy free (Ni0.83Fe0.17) layer device is 1.18 ns, while that for a dilute permalloy ([Ni0.83Fe0.17]0.6Cu0.4) free layer device is 0.475 ns. A ballistic macrospin model can capture the data trends with a reduced spin torque asymmetry parameter, reduced spin polarization and increased Gilbert damping for the dilute permalloy free layer relative to the permalloy devices. Our study demonstrates that reducing the magnetization of the free layer increases the switching speed while greatly reducing the switching energy and shows a promising route toward even lower power magnetic memory devices compatible with superconducting electronics.

Perpendicularly magnetized CoFeB layers with ultra-thin non-magnetic insertion layers are very widely used as the electrodes in magnetic tunnel junctions for spin transfer magnetic random access memory devices. Exchange interactions play a critical role in determining the thermal stability of magnetic states in such devices and their spin torque switching efficiency. Here the exchange constant of free layers incorporated in full magnetic tunnel junction layer stacks, specifically CoFeB free layers with W insertion layers is determined by magnetization measurements in a broad temperature range. A significant finding is that the exchange constant decreases significantly and abruptly with W insertion layer thickness. The perpendicular magnetic anisotropy shows the opposite trend; it initially increases with W insertion layer thickness and shows a broad maximum for approximately one monolayer (0.3 nm) of W. These results highlight the interdependencies of magnetic characteristics required to optimize the performance of magnetic tunnel junction devices., Comment: submitted to Advanced Electronic Materials

A hybrid semiconductor-superconductor nanowire on the top of a magnetic film in the stripe phase experiences a magnetic texture from the underlying fringing fields. The Zeeman interaction with the highly inhomogeneous magnetic textures generates a large synthetic spin-orbit coupling. We show that this platform can support the formation of Majorana bound states (MBS) localized at the ends of the nanowire. The transition to the topological superconducting phase not only depends on the nanowire parameters and stripe size but also on the relative orientation of the stripes with respect to the nanowire axis. Topological phase transitions with the corresponding emergence or destruction of MBS can be induced by reorienting the stripes or shifting their position, which can be achieved by passing a charge current through the magnetic film or by applying electrically-controlled strain to it. The proposed platform removes the need for external magnetic fields and offers a non-invasive electrical tuning of MBS with the perturbation (current or strain) acting only on thee magnetic film., Comment: 9 pages, 6 figures

Magnetism primarily describes the physics and materials science of systems presenting a magnetization -- a macroscopic order parameter characterizing electron angular momentum. The order parameter is associated with the electronic exchange interactions, which is fundamentally quantum mechanical. Its dynamic behavior bridges the macroscopic and the microscopic worlds. On macroscopic length and time-scales, it interacts with electromagnetic fields dictated by the Maxwells equations. On a microscopic scale, it involves the quantum-mechanical electronic states both in spin-space and momentum space, thus giving rise to a wide range of behavior that extend down to femtoseconds. Thanks to the development of modern metrology, there have been many new and noteworthy observations of magnetism-related phenomena across the entire range -- from spin-torque induced antidamping dynamics, to ultrafast laser induced femtosecond electron dynamics that involve spin current and angular momentum conservation. In this review we introduce some observations on magnetodynamics, and the scientific subjects these new results give rise to., Comment: Book chapter reviewing recent advance in magnetization dynamics, 32 pages, 9 figures

We present measurements of the spin Seebeck effect (SSE) by a technique that combines alternating currents (AC) and direct currents (DC). The method is applied to a ferrimagnetic insulator/heavy metal bilayer, Y$_3$Fe$_5$O$_{12}$(YIG)/Pt. Typically, SSE measurements use an AC current to produce an alternating temperature gradient and measure the voltage generated by the inverse spin-Hall effect in the heavy metal at twice the AC frequency. Here we show that when Joule heating is associated with AC and DC bias currents, the SSE response occurs at the frequency of the AC current drive and can be larger than the second harmonic SSE response. We compare the first and second harmonic responses and show that they are consistent with the SSE. The field dependence of the voltage response is used to characterize the damping-like and field-like torques. This method can be used to explore nonlinear thermoelectric effects and spin dynamics induced by temperature gradients., Comment: 4 pages, 5 figures

Magnetic bilayers with different magnetic anisotropy directions are interesting for spintronic appli- cations as they offer the possibility to engineer tilted remnant magnetization states. We investigate the ferromagnetic resonance (FMR) linewidth of modes associated with two interlayer exchange- coupled ferromagnetic layers, the first a CoNi multilayer with a perpendicular magnetic anisotropy, and the second a CoFeB layer with an easy-plane anisotropy. For antiferromagnetic interlayer ex- change coupling, elevated FMR linewidths are observed below a characteristic field. This is in contrast to what is found in uncoupled, ferromagnetically coupled and single ferromagnetic layers in which the FMR linewidth increases monotonically with field. We show that the characteristic field at which there is a dramatic increase in FMR linewidth can be understood using a macrospin model with Heisenberg-type exchange coupling between the layers.

Magnetic droplet solitons were first predicted to occur in materials with uniaxial magnetic anisotropy due to a long-range attractive interaction between elementary magnetic excitations, magnons. A non-equilibrium magnon population provided by a spin-polarized current in nanocontacts enables their creation and there is now clear experimental evidence for their formation, including direct images obtained with scanning x-ray transmission microscopy. Interest in magnetic droplets is associated with their unique magnetic dynamics that can lead to new types of high frequency nanometer scale oscillators of interest for information processing, including in neuromorphic computing. However, there are no direct measurements of the time required to nucleate droplet solitons or their lifetime---experiments to date only probe their steady-state characteristics, their response to dc spin currents. Here we determine the timescales for droplet annihilation and generation using current pulses. Annihilation occurs in a few nanoseconds while generation can take several nanoseconds to a microsecond depending on the pulse amplitude. Micromagnetic simulations show that there is an incubation time for droplet generation that depends sensitively on the initial magnetic state of the nanocontact. An understanding of these processes is essential to utilizing the unique characteristics of magnetic droplet solitons oscillators, including their high frequency, tunable and hysteretic response., Comment: 12 pages, 4 figures

A spin-polarized current in a nanocontact to a magnetic film can create collective magnetic oscillations by compensating the magnetic damping. In particular, in materials with uniaxial magnetic anisotropy, droplet solitons have been observed a self-localized excitation consisting of partially reversed magnetization that precesses coherently in the nanocontact region. It is also possible to generate topological droplet solitons, known as \emph{dynamical skyrmions}. Here we study the conditions that promote either droplet or dynamical skyrmion formation and describe their stability in magnetic films without Dzyaloshinskii-Moriya interactions. We show that Oersted fields from the applied current as well as the initial magnetization state can determine whether a droplet or dynamical skyrmion forms. Dynamical skyrmions are found to be more stable than droplets. We also discuss electrical characteristics that can be used distinguish these magnetic objects.

A voltage-controlled topological-spin switch (vTOPSS) that uses a hybrid topological insulator-magnetic insulator multiferroic is presented that can implement Boolean logic operations with sub-10 aJ energy-per-bit and energy-delay product on the order of $10^{-27}$ Js. The device uses a topological insulator (TI), which has the highest efficiency of conversion of electric field to spin torque yet observed at room temperature, and a low-moment magnetic insulator (MI) that can respond rapidly to a given spin torque. We present the theory of operation of vTOPSS, develop analytic models of its performance metrics, elucidate performance scaling with dimensions and voltage, and benchmark vTOPSS against existing spin-based and CMOS devices. Compared to existing spin-based devices, such as all-spin logic and charge-spin logic, vTOPSS offers 100$\times$ lower energy dissipation and (40-100)$\times$ lower energy-delay product. With experimental advances and improved material properties, we show that the energy-delay product of vTOPSS can be lowered to $10^{-29}$ Js, competitive against existing CMOS technology. Finally, we establish that interconnect issues that dominate the performance in CMOS logic are relatively less significant for vTOPSS, implying that highly resistive materials can indeed be used to interconnect vTOPSS devices., Comment: 12 pages, 10 figures

We present experimental results and macrospin simulations of the switching characteristics of orthogonal spin-transfer devices incorporating an out-of-plane magnetized polarizing layer and an in-plane magnetized spin valve device at cryogenic temperatures. At $T=4$ K we demonstrate: high speed deterministic switching at short pulse lengths - down to 100 ps - with sufficient measurement statistics to establish a switching error rate of $10^{-5}$; coherent precessional switching at longer times; and ensemble decoherence effects at even longer times. Finite temperature macrospin models capture the precessional switching well but fail to fully reproduce all the decoherence and switching error behavior., Comment: 5 pages, 5 figures

We present an x-ray magnetic dichroism (XMCD) and soft x-ray absorption spectroscopy (XAS) study to address the nature of emerging magnetic order in metallic Copper as Cobalt is added to the matrix. For this purpose line shape and energy position of XAS and XMCD spectra will be analyzed for a series of Co/Cu alloys as well as a multilayer reference. We observe an increased hybridization between Cu and Co sites as well as increased localization of the Cu d-electrons and an induced magnetic moment in Cu. The emergence of long range magnetic order in non-magnetic materials that are in proximity to a ferromagnet is significant for a comprehensive interpretation of transport phenomena at ferromagnetic/non-magnetic interfaces, like e.g. the giant magnetoresistance effect. The presented results will further enable us to interpret Cu XMCD and XAS spectra acquired from unknown Co/Cu samples to identify the environment of Cu atoms exhibiting proximity induced magnetism., Comment: 6 pages, 4 figures. To be submitted to Physical Review B

A versatile control of magnetic systems, widely used to store information, can also enable manipulating Majorana bounds states (MBS) and implementing fault-tolerant quantum information processing. The proposed platform relies on the proximity-induced superconductivity in a two-dimensional electron gas placed next to an array of magnetic tunnel junctions (MTJs). A change in the magnetization configuration in the MTJ array creates tunable magnetic textures thereby removing several typical requirements for MBS: strong spin-orbit coupling, applied magnetic field, and confinement by one-dimensional structures which complicates demonstrating non-Abelian statistics through braiding. Recent advances in fabricating two-dimensional epitaxial superconductor/semiconductor heterostructures and designing tunable magnetic textures support the feasibility of this novel platform for MBS., Comment: 7 pages, 5 figures