Spin Circuit Research Articles

VClBr2: A new two-dimensional (2D) ferromagnetic semiconductor

Magnetic van der Waals nanocrystals with intrinsic magnetic anisotropy provide an ideal platform for exploring magnetism in the low-dimensional limit. In this work, we investigated the electronic and magnetic properties of a novel 2D material VClBr2 by using spin-polarized density functional theory calculations. Various strategies were employed to tune the material properties without changing the chemical composition or introducing defects. A phase transition is observed from semiconducting → metallic → half-metallic phase with ferromagnetic and antiferromagnetic ground state(s) under the application of strain (η) and electric field (Ez). Monte-Carlo simulation based on the Heisenberg spin-chain predicted the Curie temperature (Tc) to be about 340 K under the application of an Ez=2.5 V/nm, a colossal enhancement of ∼6700% from its base value. The magnetic anisotropic energy calculation confirms the in-plane easy axis and its strain dependent modulation with a magnetization of ∼2.85 μB/V atom. The coexistence of high temperature spin-ordering along with half-metallicity, strain tunability, low formation energy, and excellent stability endow single layer VClBr2 to be of promising applications in electric field driven spin gating, room temperature spintronics, and 2D spin circuit design.

Probing the Jaynes-Cummings Ladder with Spin Circuit Quantum Electrodynamics.

We report observations of transitions between excited states in the Jaynes-Cummings ladder of circuit quantum electrodynamics with electron spins (spin circuit QED). We show that unexplained features in recent experimental work correspond to such transitions and present an input-output framework that includes these effects. In new experiments, we first reproduce previous observations and then reveal both excited-state transitions and multiphoton transitions by increasing the probe power and using two-tone spectroscopy. This ability to probe the Jaynes-Cummings ladder is enabled by improvements in the coupling-to-decoherence ratio, and shows an increase in the maturity of spin circuit QED as an interesting platform for studying quantum phenomena.

Two-dimensional Janus monolayers with tunable electronic and magnetic properties

In the post graphene era, the discovery of magnetism in two-dimensional (2D) intrinsic nanomagnets has opened up exciting possibilities for low-dimensional spintronics. In this article, we have reported three new 2D Janus nanomagnets VBrCl2, VBrI2, and VClBrI for the first time. First-principles based density functional theory calculations reveal that these monolayers are intrinsically magnetic with indirect band gap semiconducting properties and further the magnetic and electronic properties of these monolayers are enhanced with the application of biaxial strain and electric field. We observe interesting electronic and magnetic phase transitions, tunable band gap, and supreme enhancement of the Curie temperature (~ 686%). Large magnetic anisotropic energy (MAE) with high magnetic moment and tunable band gap property make these Janus materials useful candidates for future information storage, optoelectronics, and 2D spin circuit development.

Stimuli assisted electronic, magnetic and optical phase control in CrOBr monolayer

The recent emergence of two-dimensional (2D) magnetic materials with intrinsic long-range magnetic ordering have opened up the avenue of fundamental physics and low-dimensional spintronics application. In this work, First-principles based investigation has been carried out to explore the effect of pressure, strain, and electric field to tune the electronic, magnetic and optical properties of the monolayer CrOBr. Specifically, the bandgap (electronic and optical), magnetic moment, Curie temperature ( T c ), and absorption spectra could be modulated under the application of these stimuli. We examined the thermodynamical, dynamical, and mechanical stability of this system by computing the formation energy, phonon band structure, and Young’s modulus, respectively. An electro-magnetic phase crossover from ferromagnetic semiconducting to antiferromagnetic metallic state and high temperature ferromagnetic ordering ∼ 600 K was observed under the influence of external stimuli, with ∼ 350% enhancement from its unperturbed configuration. Furthermore, the CrOBr monolayer has been found to be an attractive candidate for optoelectronic applications as it is a semiconductor and shows a red shift in the absorption spectrum under the application of an external electric field. Our studies provide an improved and complete analysis of monolayer CrOBr and shed light on its potential for electronic phase engineering, optoelectronics, and 2D spin circuit design.

Two-dimensional spintronic circuit architectures on large scale graphene

Solid state electronics based on utilizing the electron spin degree of freedom for storing and processing information can pave the way for next-generation spin-based computing. However, the realization of spin communication between multiple devices in complex spin circuit geometries, essential for practical applications, is still lacking. Here, we demonstrate the spin current propagation in two-dimensional (2D) circuit architectures consisting of multiple devices and configurations using a large area CVD graphene on SiO2/Si substrate at room temperature. Taking advantage of the significant spin transport distance reaching 34 μm in commercially available wafer-scale graphene grown on Cu foil, we demonstrate that the spin current can be effectively communicated between the magnetic memory elements in graphene channels within 2D circuits of Y-junction and hexa-arm architectures. We further show that by designing graphene channels and ferromagnetic elements at different geometrical angles, the symmetric and antisymmetric components of the Hanle spin precession signal can be remarkably controlled. These findings lay the foundation for the design of complex 2D spintronic circuits, which can be integrated into efficient electronics based on the transport of pure spin currents.

A 2 $\times$ 30k-Spin Multi-Chip Scalable CMOS Annealing Processor Based on a Processing-in-Memory Approach for Solving Large-Scale Combinatorial Optimization Problems

The world’s first 2 $\times $ 30k-spin multi-chip CMOS annealing processor (AP)—based on the processing-in-memory approach for solving large-scale combinatorial optimization problem—was developed. To expand the bit width of coefficients and enhance the scalability of the AP, it has three key features: an expandable and high-accuracy spin operator for local communication, a highly integrated spin circuit using direct access to SRAM, and a low-latency inter-chip interface that does not affect the runtime or results of the annealing process. The AP is fabricated on the basis of 40-nm CMOS technology. It was experimentally demonstrated that the spin-flip ratio of the processor agrees well with theoretical values based on the Gibbs distribution over a wide temperature range. As a result, under two-chip operation with 2 $\times $ 30k spins, the AP achieves an annealing time of 22 $\mu \text{s}$ , which is 455 times and 2.6 $\times $ 104 times faster than those achieved by our previous CMOS-AP and a conventional CPU, respectively. Moreover, its energy efficiency is 1.75 $\times $ 105 times higher than that of a conventional CPU-based algorithm.

A novel technique for implementing reactance in spin domain using Spin Hall Effect

This paper shows how spin current can be manipulated using charge-based analog elements. The technique proposed in this paper transforms charge-based reactance to spin-based reactance using Spin Hall Effect (SHE) and Inverse Spin Hall Effect (ISHE) simultaneously. The charge current created by ISHE provides a feedback impedance to the spin channel via SHE. The conceived circuit is theoretically verified using the spin circuit model. This technique holds great potential for realization of spin based analog devices like spin capacitors and spin inductors.

Experimental Demonstration of Efficient Spin–Orbit Torque Switching of an MTJ With Sub-100 ns Pulses

Efficient generation of spin currents from charge currents is of high importance for memory and logic applications of spintronics. In particular, generation of spin currents from charge currents in high spin–orbit coupling metals has the potential to provide a scalable solution for embedded memory. We demonstrate a net reduction in the critical charge current for spin torque-driven magnetization reversal via using spin–orbit mediated spin current generation. We scaled the dimensions of the spin–orbit electrode to 400 nm and the nanomagnet to 270 nm $\times68$ nm in a three-terminal spin–orbit torque, magnetic tunnel junction (SOT-MTJ) geometry. Our estimated effective spin Hall angle is 0.15–0.20 using the ratio of zero-temperature critical current from spin Hall switching and estimated spin current density for switching the magnet. We show bidirectional transient switching using spin–orbit generated spin torque at 100 ns switching pulses reliably followed by transient read operations. We finally compare the static and dynamic response of the SOT-MTJ with transient spin circuit modeling showing the performance of scaled SOT-MTJs to enable nanosecond class non-volatile MTJs.

Partial spin absorption induced magnetization switching and its voltage-assisted improvement in an asymmetrical all spin logic device at the mesoscopic scale

Beyond memory and storage, future logic applications put forward higher requirements for electronic devices. All spin logic devices (ASLDs) have drawn exceptional interest as they utilize pure spin current instead of charge current, which could promise ultra-low power consumption. However, relatively low efficiencies of spin injection, transport, and detection actually impede high-speed magnetization switching and challenge perspectives of ASLD. In this work, we study partial spin absorption induced magnetization switching in asymmetrical ASLD at the mesoscopic scale, in which the injector and detector have the nano-fabrication compatible device size (>100 nm) and their contact areas are different. The enlarged contact area of the detector is conducive to the spin current absorption, and the contact resistance difference between the injector and the detector can decrease the spin current backflow. Rigorous spin circuit modeling and micromagnetic simulations have been carried out to analyze the electrical and magnetic features. The results show that, at the fabrication-oriented technology scale, the ferromagnetic layer can hardly be switched by geometrically partial spin current absorption. The voltage-controlled magnetic anisotropy (VCMA) effect has been applied on the detector to accelerate the magnetization switching by modulating magnetic anisotropy of the ferromagnetic layer. With a relatively high VCMA coefficient measured experimentally, a voltage of 1.68 V can assist the whole magnetization switching within 2.8 ns. This analysis and improving approach will be of significance for future low-power, high-speed logic applications.

Spin-Circuit Representation of Spin Pumping

Circuit theory has been tremendously successful in translating physical equations into circuit elements in organized form for further analysis and proposing creative designs for applications. With the advent of new materials and phenomena in the field of spintronics and nanomagnetics, it is imperative to construct the spin circuit representations for different materials and phenomena. Spin pumping is a phenomenon by which a pure spin current can be injected into the adjacent layers. If the adjacent layer is a material with a high spin orbit coupling, a considerable amount of charge voltage can be generated via inverse spin Hall effect, allowing spin detection. Here we develop the spin circuit representation of spin pumping. We then combine it with the spin circuit representation for the materials having spin Hall effect to show that it reproduces the standard results in literature. We further show how complex multilayers can be analyzed by simply writing a netlist.

Spin Funneling for Enhanced Spin Injection into Ferromagnets.

It is well-established that high spin-orbit coupling (SOC) materials convert a charge current density into a spin current density which can be used to switch a magnet efficiently and there is increasing interest in identifying materials with large spin Hall angle for lower switching current. Using experimentally benchmarked models, we show that composite structures can be designed using existing spin Hall materials such that the effective spin Hall angle is larger by an order of magnitude. The basic idea is to funnel spins from a large area of spin Hall material into a small area of ferromagnet using a normal metal with large spin diffusion length and low resistivity like Cu or Al. We show that this approach is increasingly effective as magnets get smaller. We avoid unwanted charge current shunting by the low resistive NM layer utilizing the newly discovered phenomenon of pure spin conduction in ferromagnetic insulators via magnon diffusion. We provide a spin circuit model for magnon diffusion in FMI that is benchmarked against recent experiments and theory.

Scaling Limits on All-Spin Logic

Scaling limits on all-spin logic (ASL) are theoretically studied using the spin circuit theory and the stochastic Landau–Lifshitz–Gilbert equation under the macrospin approximation. It is found that as ASL circuits are scaled, the device delay significantly increases due to a stronger dipole coupling between the input and the output magnets. The effect of the dipole interaction can be mitigated by increasing the input current and by using smaller magnets with stronger material anisotropy and weaker saturation magnetization. Furthermore, the presence of the leakage current modifies the device delay. Finally, both delay and energy of ASL dramatically increase as the shunt path is shortened. Possible solutions to eliminate the leakage current and the shunt path are discussed.

Spin Circuit Model for 2D Channels with Spin-Orbit Coupling.

In this paper we present a general theory for an arbitrary 2D channel with “spin momentum locking” due to spin-orbit coupling. It is based on a semiclassical model that classifies all the channel electronic states into four groups based on the sign of the z-component of the spin (up (U), down (D)) and the sign of the x-component of the velocity (+, −). This could be viewed as an extension of the standard spin diffusion model which uses two separate electrochemical potentials for U and D states. Our model uses four: U+, D+, U−, and D−. We use this formulation to develop an equivalent spin circuit that is also benchmarked against a full non-equilibrium Green’s function (NEGF) model. The circuit representation can be used to interpret experiments and estimate important quantities of interest like the charge to spin conversion ratio or the maximum spin current that can be extracted. The model should be applicable to topological insulator surface states with parallel channels as well as to other layered structures with interfacial spin-orbit coupling.

Spin Circuit Representation for the Spin Hall Effect

Spin circuits with four component voltages and currents have been developed and used in the past to analyze various structures, which include non-collinear ferromagnets. Recent demonstrations of large spin orbit torques in heavy metals like Pt, Ta, and W open up new possibilities in spintronic applications by providing an alternative way to write information into a magnet. Here, we extend the four component (one charge and three spins) conductance matrix to include materials with spin Hall effect based on the standard diffusion equation. Our proposed spin circuit successfully reproduces standard results like spin Hall effect (SHE), inverse spin Hall effect, and spin Hall magnetoresistance. This circuit representation also makes it straightforward to analyze new configurations. We present two examples, namely, 1) the possibility of spin injection using giant SHE (GSHE) materials into semiconductors without tunneling barriers, and 2) the effect of spin ground on one surface to enhance spin current injection from the opposite surface in a thin GSHE sample. Finally, we provide an elemental conductance matrix for a small cubic structure which can be used as a building block to analyze any arbitrarily shaped GSHE material.

Dynamic Circuit Model for Spintronic Devices

In this work we propose a finite-difference scheme based circuit model of a general spintronic device and benchmark it with other models proposed for spintronic switching devices. Our model is based on the four-component spin circuit theory and utilizes the widely used coupled stochastic magnetization dynamics/spin transport framework. In addition to the steady-state analysis, this work offers a transient analysis of carrier transport. By discretizing the temporal and spatial derivatives to generate a linear system of equations, we derive new and simple finite-difference conductance matrices that can, to the first order, capture both static and dynamic behaviors of a spintronic device. We also discuss an extension of the spin modified nodal analysis (SMNA) for time-dependent situations based on the proposed scheme.

The effect of output-input isolation on the scaling and energy consumption of all-spin logic devices

All-spin logic (ASL) is a novel approach for digital logic applications wherein spin is used as the state variable instead of charge. One of the challenges in realizing a practical ASL system is the need to ensure non-reciprocity, meaning the information flows from input to output, not vice versa. One approach described previously, is to introduce an asymmetric ground contact, and while this approach was shown to be effective, it remains unclear as to the optimal approach for achieving non-reciprocity in ASL. In this study, we quantitatively analyze techniques to achieve non-reciprocity in ASL devices, and we specifically compare the effect of using asymmetric ground position and dipole-coupled output/input isolation. For this analysis, we simulate the switching dynamics of multiple-stage logic devices with FePt and FePd perpendicular magnetic anisotropy materials using a combination of a matrix-based spin circuit model coupled to the Landau–Lifshitz–Gilbert equation. The dipole field is included in this model and can act as both a desirable means of coupling magnets and a source of noise. The dynamic energy consumption has been calculated for these schemes, as a function of input/output magnet separation, and the results show that using a scheme that electrically isolates logic stages produces superior non-reciprocity, thus allowing both improved scaling and reduced energy consumption.

Scrutiny on the produced spin current in spin circuit considering Nano-magnetic nodes and copper Nano-channel

Electronics of spin or spintronics is a newfangled field which its purpose is to study the role of electron's spin in solid-state devices. spintronic devices require spin current. Spin current is a difference between spin-up and spin-down electric currents. This article reviews the spin current. In this paper, we intend to calculate spin current in two spin circuits' branches. Also we investigate simultaneously effects of nano-channel length and cross section area variations on it. Our findings show that spin current in series branch increase by simultaneously length of nano-channel reduction and rising of cross section area. For spin flip branches, we can reduce dissipation by simultaneously length and cross section area nano-channel reduction. We choose copper metal as nano-channel because of longer spin diffusion length, less spin current dissipation and equality of its lattice constant with those of permalloy.

Calculation of Spin Conduction Matrix in Spin Circuit Considering Nano-Magnetic Nodes and Copper Nano-Channel

In this work, we intend to calculate spin conduction matrixes of T-shaped spin circuits' branches. Also we investigate simultaneously effects of gold nano-channel length and cross section area variations on its non-zero elements. Our findings show that G 11 and G 22 elements of series branches increase with simultaneously channel length reduction and channel cross section area grow up. For spin flip branches, G 22 element decreases with simultaneously nano-channel length and cross section area reduction. We choose copper metal as nano-channel because of its high conductance and lattice constant.

Spin Ensembles Coupled to Superconducting Resonators: A Scalable Architecture for Solid-State Quantum Computing

A design is proposed for scalable solid-state quantum computing, which is based on collectively enhanced magnetic coupling between nitrogen-vacancy center ensembles and superconducting transmission line resonators interconnected by current-biased Josephson junction superconducting phase qubit. In this hybrid system, we realize distant multi-qubit controlled phase gate operations and generate distant multi-qubit entangled W-like states, being indispensable resource to quantum computation. Our proposed architecture consists of solid-state spin ensembles and circuit QED, and could achieve quantum computing in a solid-state environment with high-fidelity and scalable way. The experimental feasibility is discussed, and the implementation efficiency is demonstrated numerically.

Nuclear-spin noise and spontaneous emission.

Spontaneous emission from nuclear spins is measured for the first time, we believe. This is possible because of the use of a low-noise SQUID amplifier with noise temperature (~0.2 K) less than that of the 1.5 K helium bath. The spontaneous emission power is ~5-10% of the background circuit Nyquist noise, which corresponds to the ratio of the effective spin resistance Rs (proportional to the nuclear susceptibility) and circuit resistance R. Although only one spin flip occurs per 108 yr due to spontaneous omission, the effect is magnified, because all 1022 spins in the sample contribute independent of the temperature. This technique implies that spectra of spins can be measured without the requirement of a net polarization and might be useful for samples where spin lattice relaxation times are impracticaily long. Radiation damping terms which are added to the Bloch equations allow for spin noise analysis of power flow between the spin system and cavity. The equivalence is obtained of predictions of Nyquist's theorem at all spin temperatures Ts and bath temperatures T in conformity with the predictions of the Einstein detailed balance equation for spontaneous emission. The model of a macroscopic spin pendulum applies where fluctuation through a mean square angle 〈θ2〉 from magnetization alignment along the polarizing field accounts for coupling of the fluctuating spins to the single-cavity mode. Several aspects of the model for spin noise analysis are applicable to inverted two-level systems.