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The tearing mode stability of an inverse aspect-ratio expanded tokamak plasma equilibrium of general shape is investigated using asymptotic matching techniques. Particular emphasis is placed on the conservation of toroidal electromagnetic angular momentum. The TJ code, which is a specific implementation of the results of the investigation, is described.
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.
A number of improvements to the TJ toroidal tearing mode code [Fitzpatrick, Phys. Plasmas 31, 102507 (2024)] are documented. The TJ code is also successfully benchmarked against the STRIDE toroidal tearing mode code [Glasser and Koleman, Phys. Plasmas 25, 082502 (2018)]. Finally, the new capabilities of the TJ code are used to investigate the stability of tearing modes in tokamak plasmas as an ideal stability boundary, associated with either an external-kink or an internal-kink mode, is approached. All elements of the tearing stability matrix are found to tend to infinity as an ideal stability boundary is approached. Furthermore, as the stability boundary is approached, the eigenfunctions of the various tearing modes in the plasma, which are decoupled by sheared plasma rotation, are all found to morph into that of the marginally stable ideal mode. However, the growth-rates and real frequencies of the various “ideal-tearing-modes” are different from one another. Moreover, the growth-rate of the ideal-tearing-mode that reconnects magnetic flux at the rational surface that lies closest to the edge of the plasma is the one that tends to a very large value as the stability boundary is approached. A relatively simple test for ideal stability that is capable of detecting stability boundaries for external-kink and internal-kink modes, even in the presence of a very close-fitting ideal wall, is described and verified.
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.
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.
Lateral inhibition is an important functionality in neuromorphic computing, modeled after the biological neuron behavior that a firing neuron deactivates its neighbors belonging to the same layer and prevents them from firing. In most neuromorphic hardware platforms lateral inhibition is implemented by external circuitry, thereby decreasing the energy efficiency and increasing the area overhead of such systems. Recently, the domain wall—magnetic tunnel junction (DW-MTJ) artificial neuron is demonstrated in modeling to be intrinsically inhibitory. Without peripheral circuitry, lateral inhibition in DW-MTJ neurons results from magnetostatic interaction between neighboring neuron cells. However, the lateral inhibition mechanism in DW-MTJ neurons has not been studied thoroughly, leading to weak inhibition only in very closely-spaced devices. This work approaches these problems by modeling current- and field- driven DW motion in a pair of adjacent DW-MTJ neurons. We maximize the magnitude of lateral inhibition by tuning the magnetic interaction between the neurons. The results are explained by current-driven DW velocity characteristics in response to an external magnetic field and quantified by an analytical model. Dependence of lateral inhibition strength on device parameters is also studied. Finally, lateral inhibition behavior in an array of 1000 DW-MTJ neurons is demonstrated. Our results provide a guideline for the optimization of lateral inhibition implementation in DW-MTJ neurons. Finally, with strong lateral inhibition achieved, a path towards competitive learning algorithms such as the winner-take-all are made possible on such neuromorphic devices.
Tunneling spectroscopy between parallel two-dimensional (2D) electronic systems provides a powerful method to probe the underlying electronic properties by measuring tunneling conductance. Here, in this work, we present a theoretical framework for spin transport in 2D-to-2D tunneling systems, driven by spin pumping. This theory applies to a vertical heterostructure where two layers of metallic 2D electron systems are separated by an insulating barrier, with one layer exchange coupled to a magnetic layer driven at resonance. Utilizing a nonperturbative Floquet-Keldysh formalism, we derive general expressions for the tunneling spin and charge currents across a broad range of driving frequencies, extending beyond the traditional adiabatic pumping regime. At low frequencies, we obtain analytical results that recover the known behaviors in the adiabatic regime. However, at higher frequencies, our numerical findings reveal significant deviations in the dependence of spin and charge currents on both frequency and precession angle. This work offers fresh insights into the role of magnetization dynamics in tunneling transport, opening up new avenues for exploring nonadiabatic spin pumping phenomena.
Spintronic nano-oscillators and diodes with reduced nonlinearity benefit from low phase noise and improved device properties. Moreover, they could offer key advantages for realizing neuromorphic applications, such as spike-based neurons and frequency multiplexing in neural networks. Here, in this work, we experimentally demonstrate the reduction in nonlinearity of a spin Hall nano-oscillator (SHNO) by compensation of its effective magnetic anisotropy. The study involves optimization of Co/Ni multilayer growth to achieve the compensation, followed by spin-diode measurements on patterned microstrips to quantify their anisotropy. The relationship between the second- (H k 2 = 0.47 mT) and first-order ($H^{eff}_{k_1}$ = -0.8 mT) anisotropy fields reveals the existence of an easy cone, thereby validating the presence of compensation. Furthermore, we demonstrate a compensated spin diode that has a fixed frequency when the input power is varied. We then study the current-induced auto-oscillation properties of SHNOs on compensated films by patterning nanoconstrictions of 200 and 100 nm wide. The invariance of the resonance frequency and linewidth of the compensated SHNO with applied dc current indicates the absence of nonlinearity. This independence is maintained irrespective of the applied external fields and their orientations. The compensated SHNO obtained has a linewidth of 1.1 MHz and a peak output power of up to 1 pW/MHz.
We utilize simulations of spin-polarized electron scattering by a chain of localized quantum spins to show that energy and linear momentum conservation laws impose strong constraints on the properties of magnetic excitations induced by spin transfer. In turn, orbital and spin dynamics of conduction electrons depends on the dynamical characteristics of the local spins. Furthermore, our results suggest the possibility to achieve precise control of spin-transfer-driven magnetization dynamics by tailoring the spectral characteristics of the magnetic systems and of the driving electrons.
We utilize simulations of electron scattering by a chain of dynamical quantum spins to analyze the interplay between the spin transfer effect and the magnetization dynamics.We show that the complex interactions between the spin-polarized electrons and the dynamical states of the local spins can be decomposed into separate processes involving electron reflection and transmission, as well as absorption and emission of magnons—the quanta of magnetization dynamics. Analysis shows that these processes are substantially constrained by the energy and momentum conservation laws, resulting in a significant dependence of spin transfer on the electron’s energy and the dynamical state of the local spins. Here, our results suggest that exquisite control of spin transfer efficiency and of the resulting dynamical magnetization states may be achievable by tailoring the spectral characteristics of the conduction electrons and of the magnetic systems.
We compare thermal-gradient-driven transverse voltages in ferrimagnetic-insulator/heavy-metal bilayers (Tm 3 Fe 5 O 12 /W and Tm 3 Fe 5 O 12 /Pt) to corresponding electrically driven transverse resistances at and above room temperature. We find for Tm 3 Fe 5 O 12 /W that the thermal and electrical effects can be explained by a common spin-current detection mechanism, the physics underlying spin Hall magnetoresistance (SMR). However, for Tm 3 Fe 5 O 12 /Pt the ratio of the electrically driven transverse voltages (planar Hall signal/anomalous Hall signal) is much larger than the ratio of corresponding thermal-gradient signals, a result which is very different from expectations for a SMR-based mechanism alone. Here, we ascribe this difference to a proximity-induced magnetic layer at the Tm 3 Fe 5 O 12 /Pt interface.
Spin-accumulation and spin-current profiles are calculated for a disordered Pt film subjected to an in-plane electric current within the nonequilibrium Green's function approach. In the bulklike region of the sample, this approach captures the intrinsic spin Hall effect found in other calculations. Near the surfaces, the results reveal qualitative differences with the results of the widely used spin-diffusion model, even when the boundary conditions are modified to try to account for them. One difference is that the effective spin-diffusion length for transverse spin transport is significantly different from its longitudinal counterpart and is instead similar to the mean-free path. Furthermore, this feature may be generic for spin currents generated via the intrinsic spin Hall mechanism because of the differences in transport mechanisms compared to longitudinal spin transport. Orbital accumulation in the Pt film is only significant in the immediate vicinity of the surfaces and has a small component penetrating into the bulk only in the presence of spin-orbit coupling, as a secondary effect induced by the spin accumulation.
In this paper, we report the temperature-field phase diagram as well as present a comprehensive study of the electronic structure and three-dimensional fermiology of the triangular-lattice magnet EuAg 4 Sb 2 , utilizing quantum oscillation measurements, angle-resolved photoemission spectroscopy, and first-principles calculations. The complex magnetic phase diagram of EuAg 4 Sb 2 highlights many transitions through nontrivial AFM states. Shubnikov-de Haas and de Haas-van Alphen oscillations were observed in the polarized ferromagnetic state of EuAg 4 Sb 2 , revealing three pairs of distinct spin-split frequency branches with small effective masses. A comparison of the angle-dependent oscillation data with first-principles calculations in the ferromagnetic state and angle-resolved photoemission spectra shows good agreement, identifying tubular hole pockets and hourglass-shaped hole pockets at the Brillouin zone center, as well as diamond-shaped electron pockets at the zone boundary. As the temperature increases, the frequency branches of the tiny hourglass pockets evolve into a more cylindrical shape, while the larger pockets remain unchanged. This highlights that variations in exchange splitting, driven by changes in the magnetic moment, primarily impact the small Fermi pockets without significantly altering the overall band structure. As a result, this is consistent with first-principles calculations, which show minimal changes near the Fermi level across ferromagnetic and simple antiferromagnetic states or under varying on-site Coulomb repulsion.
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Machine drives are versatile systems that can be programmed to emulate a variety of mechanical loads. In this paper, we walk through the modeling and control framework of a shaft-coupled dual-motor drive system that is programmed to emulate a fictitious mechanical system. We quantitatively evaluate the control performance of such a system and derive a theoretical limit that explains its inaccuracy at high operating frequencies. To overcome this problem, we propose an alternate control structure that achieves the same control objective at high frequencies as well. After suitable adjustments are made to the controller, we validate its performance using simulation results.
Legged humanoid robots promise revolutionary mobility and effectiveness in environments built for humans. However, inefficient use of energy significantly limits their practical adoption. The humanoid biped walking anthropomorphic novelly-driven efficient robot for emergency response (WANDERER) achieves versatile, efficient mobility, and high endurance via novel drive-trains and passive joint mechanisms. Results of a test in which WANDERER walked for more than 4 h and covered 2.8 km on a treadmill, are presented. Results of laboratory experiments showing even more efficient walking are also presented and analyzed in this article. WANDERER's energetic performance and endurance are believed to exceed the prior literature in human-scale humanoid robots. This article describes WANDERER, the analytical methods and innovations that enable its design, and system-level energy efficiency results.