Spin-Orbit torque in α-W-Based Magnetic Tunnel Junction

Using the linearized Landau–Lifshitz-Gilbert (LLG) equation in the rotation coordinate, we calculate the critical switching current density of a perpendicular magnetic tunnel junction (MTJ), where magnetization switching is achieved by the interplay of spin-transfer and spin-orbit torques. In terms of the critical current density, we find that as the current density inducing the spin-orbit torque (jSOT) increases, the current density inducing the spin-transfer torque (jSTT) decreases nonlinearly. In the presence of the spin-orbit field-like torque (β), the critical switching current density by the spin-transfer torque is proportional to the damping constant (α) as the conventional spin-transfer torque switching, while the critical switching current density by the spin-orbit torque increases with α when Heff≫HSOT . We also investigated the β dependence of the critical switching current density. For a given jSOT , the critical switching current density for the spin-transfer torque, jSTT,c decreases linearly with increasing β and nonlinearly decreases with increasing jSOT for a given β. Further, we discuss the β dependence of the critical switching current density on energy.

Spintronics plays a key role in minimizing static power consumption and enabling high-speed data transfer in neuromorphic computing architectures. In comparison to other novel nonvolatile memory architectures such as ferroelectric RAM (FRAM), resistive RAM (RRAM), and others, spin-transfer torque magneto resistance random-access memory (MRAM) (STT-MRAM) has gained considerable traction in the design of NV memory technologies due to its low power consumption, better speed, scalability, high endurance, and compatibility with CMOS processes. Irrespective of these advantages, STT-MRAM suffers from read and write latency issues due to incubation delay. Furthermore, the common read/write channel might reduce read reliability, while the write current can put a lot of strain on the magnetic tunnel junction (MTJ), and it may eventually result in the breakdown of the tunnel layer, hence resulting in memory cell degradation over time. Spin orbit torque (SOT)-MRAM has recently been presented as a solution to overcome these challenges. A heavy metal (HM) such as W, Ta, or Pt with a significant spin orbit coupling (SOC) operates as a SOC layer in most conventional SOT MRAMs, generating the SOTs required for magnetization switching. Due to the spin Hall effect (SHE) in bulk material and the Rashba-Edelstein effect (REE) at interfaces, an in-plane current passing via the HM layer produces transverse spin current, which exerts a spin torque on the adjacent ferromagnetic (FM) layer and triggers switching of magnetization. A perpendicular magnetic anisotropy (PMA) SOT MRAM offers compact scalability, improved thermal stability, read/write route isolation, and low-magnetization switching current requirements. However, utilizing an HM as a SOC layer in PMA-based systems would lead to extra device geometries, necessitating additional fabrication stages and/or the use of an external magnetic field for deterministic magnetization switching. Electrical and optoelectronic properties of two-dimensional (2D) materials such as topological insulator (TI) and transition metal dichalcogenides (TMDs) are extraordinary and highly tunable. They could be used in a variety of applications, including nanoelectronic devices, photodetectors, and sensors. TMDs have been presented as a technique to provide efficient magnetization switching in the adjoining FM layer due to strong SOC without the use of a magnetic field or a distinct fabrication procedure. Due to the breaking of inversion symmetry, which generates a range of events that drive the system out of equilibrium, TIs have a high SOC, which makes them excellent for spintronic devices. Furthermore, utilizing all van der Waals (vdW) material heterostructures to thin down heterointerfaces holds a lot of promise for further improving the SOT efficiency. TMDs have also been used as a barrier in MTJs, which are made up of TMDs such as MoS2 and WS2 sandwiched between two FM layers and provide extremely high tunneling magneto resistance (TMR). Many 2D material factors, such as thickness, quality, and surface chemical state, have a direct effect on MTJ performance. Also unknown is the relaxation of spin electrons in 2D materials, and efficient spin gating remains a difficulty.

Recently, experimental results have demonstrated that perpendicular magnetic tunnel junction (p-MTJ) with the antiferromagnetic(AFM)/ferromagnetic (FM)/oxide structure can achieve field-free spin-orbit torque (SOT) switching since the AFM metal strip can not only generate the SOT, but also provide an exchange bias (HEX), making it suitable for practical applications. However, owing to that the HEX is weak, such field-free SOT switching is incomplete, thus resulting in severe switching reliability. In addition, a large SOT switching current (ISOT) is also required, leading to high switching energy dissipation. In this paper, to address these issues, the voltage-controlled magnetic anisotropy (VCMA) is introduced to assist the SOT switching, and such novel switching method is referred as voltage-gated SOT (VGSOT). First, we develop a physics-based compact model for the three-terminal VGSOT-MTJ device, which includes three modules, i.e., the electrical module, the tunnel magnetoresistance module and the dynamic switching module. Then, the impact of the VCMA effect on the field-free SOT switching is investigated by solving a modified Landau-Lifshitz-Gilbert (LLG) equation with consideration of the VCMA, SOT and HEX. Simulation results show that thanks to the introduction of the VCMA effect, the critical ISOT can be reduced greatly, and the incomplete field-free SOT switching can be completed. With further analysis, we obtain a special switching condition, under which complete SOT field-free switching can be achieved with a shortest path and ultra-low power. Moreover, a novel write pulse scheme is proposed to achieve high speed and reliability.

We review a unified approach for computing: (i) spin-transfer torque in magnetic trilayers like spin-valves and magnetic tunnel junction, where injected charge current flows perpendicularly to interfaces; and (ii) spin-orbit torque in magnetic bilayers of the type ferromagnet/spin-orbit-coupled-material, where injected charge current flows parallel to the interface. Our approach requires to construct the torque operator for a given Hamiltonian of the device and the steady-state nonequilibrium density matrix, where the latter is expressed in terms of the nonequilibrium Green's functions and split into three contributions. Tracing these contributions with the torque operator automatically yields field-like and damping-like components of spin-transfer torque or spin-orbit torque vector, which is particularly advantageous for spin-orbit torque where the direction of these components depends on the unknown-in-advance orientation of the current-driven nonequilibrium spin density in the presence of spin-orbit coupling. We provide illustrative examples by computing spin-transfer torque in a one-dimensional toy model of a magnetic tunnel junction and realistic Co/Cu/Co spin-valve, both of which are described by first-principles Hamiltonians obtained from noncollinear density functional theory calculations; as well as spin-orbit torque in a ferromagnetic layer described by a tight-binding Hamiltonian which includes spin-orbit proximity effect within ferromagnetic monolayers assumed to be generated by the adjacent monolayer transition metal dichalcogenide.

We present a magnetic tunnel junction (MTJ) where its two ferromagnetic layers are in the form of a single ellipse (SE) and two-crossing ellipses (TCEs). The MTJ exhibits four distinct resistance states corresponding to the four remanent states of the TCE structure. Flowing current in an underlying Ta layer generates in the adjacent TCE structure spin–orbit torques, which induce field-free switching of the four-state MTJ between all its resistance states. The demonstrated four-state MTJ is an important step toward fabricating multi-level MTJs with numerous resistance states, which could be important in various spintronics applications, such as multi-level magnetic random access or neuromorphic memory.

Current-induced magnetization switching is crucial in high-performance nonvolatile memory especially when the spin-transfer torque (STT) and spin-orbit torque (SOT) are employed in the mainstream magnetic random-access memory. However, in STT devices, the intrinsic mechanism leads to a long write latency, a low endurance, and a high-power consumption, while in SOT devices, a three-terminal structure is necessary to complete the read and write operations, causing a low space efficiency. In this work, we experimentally demonstrate a NAND-like spin-torque memory unit with the interplay of STT and SOT. The spin joint effect induced magnetic reversal is verified to be more energy-efficient and faster than that of STT. It also shows a great selectivity to ensure the reliability of the write operation. The memory unit, containing 8 magnetic tunnel junctions with a shared heavy-metal nanowire, is erased by a single SOT current and written by the combination of STT and SOT, showing the great potential for the high-density, ultrafast and energy efficient memory applications.

With the rise in in-memory computing architectures to reduce the compute-memory bottleneck, a new bottleneck is present between analog and digital conversion. Analog content-addressable memories (ACAM) are being recently studied for in-memory computing to efficiently convert between analog and digital signals. Magnetic memory elements such as magnetic tunnel junctions (MTJs) could be useful for ACAM due to their low read/write energy and high endurance, but MTJs are usually restricted to digital values. The spin orbit torque-driven domain wall-magnetic tunnel junction (DW-MTJ) has been recently shown to have multi-bit function. Here, an ACAM circuit is studied that uses two domain wall-magnetic tunnel junctions (DW-MTJs) as the analog storage elements. Prototype DW-MTJ data is input into the magnetic ACAM (MACAM) circuit simulation, showing ternary CAM function. Device-circuit co-design is carried out, showing that 8-10 weight bits are achievable, and that designing asymmetrical spacing of the available DW positions in the device leads to evenly spaced ACAM search bounds. Analyzing available spin orbit torque materials shows platinum provides the largest MACAM search bound while still allowing spin orbit torque domain wall motion, and that the circuit is optimized with minimized MTJ resistance, minimized spin orbit torque material resistance, and maximized tunnel magnetoresistance. These results show the feasibility of using DW-MTJs for MACAM and provide design parameters.

The current induced spin-orbit-torque (SOT) [1-4] is the key physical parameter describing the generation of magnetization dynamics in bilayers composed by a heavy metal (HM) layer and a ferromagnetic (FM) layer. Such bilayers, especially when associated with a magnetic tunnel junction at the FM layer (then forming the so called 3-terminal device), are considered as promising elements to be applied in novel magnetic memories, microwave generators and even bio-inspired types of computing [1]. Therefore, the robust and accurate determination of the SOT in HM/FM bilayers is of high relevance for optimizing future applications.In HM/FM bilayers the SOT is mainly caused by the spin Hall effect (SHE) of the HM layer, by which a spin current is injected into the FM layer. 3-terminal devices with application as magnetic memories adopt mainly FM films with perpendicular magnetic anisotropy, while for sensor applications also the configuration with in-plane magnetic anisotropy is of interest. The determination and quantification of the SOT can be performed in both cases by different techniques. While in a 3-terminal device the magnetization dynamics of observed via the tunnel magnetoresistance effect, in HM/FM bilayers other methods can be employed, such as the SOT-ferromagnetic resonance (FMR), the harmonic Hall voltage measurement and the spin Hall magnetoresistance (SMR). The SMR is a straightforward method when the FM layer is an insulator, while with metallic FM, in which the testing electric current in not confined in the HM layer only, it is accompanied by additional effects, such as the anisotropic magnetoresistance or the anomalous Nernst effect [5]. Therefore, it is important to analyse the measurement results by accurate models taking into account all aspects. The dominant theoretical approach for SHE-SOT is the drift-diffusion model considering spin accumulation at the interface between the FM and HM by introducing a spin mixing conductance. However, the agreement with experiments may be poor if spin dissipation at the interface (spin memory loss, spin dependent scattering, etc.) is disregarded [2].In this paper we analyze transport measurements on FM/HM bilayers as a function of the HM thickness by employing a non-equilibrium thermodynamic approach to SHE-SOT [6] with the aim to reach a semi-quantitative agreement. The study was performed on HM/FM bilayers with HM=Pt (wedge 4-19nm), Ta (wedge 4-19nm), and FM=Fe60Co20B20 (2nm) prepared at Singulus Technologies AG. All samples were annealed for 2h at 310°C in a magnetic field of 1T in order to develop an in-plane magnetic anisotropy (y axis). For the transport measurements the films were patterned into µm-size Hall bars/crosses (along x axis) by optical lithography and ion beam etching with Ti/Au contact pads. Magneto-optic Kerr effect (MOKE) and SMR measurements were performed following the protocol of [5], while SOT-FMR and harmonic Hall voltage measurements and analysis were based on references [3,4].Fig.1 shows the comparison between MOKE loops and the SMR signal. The loop along the y axis is more rectangular and indicates the magnetic easy anisotropy axis. The SMR signal is much more pronounced with the field along the x axis, while it shows a small peak close to the coercivity when the field is along the y axis. With MOKE the anisotropy was determined and a dependence on HM thickness was observed.Fig.2 presents the summary of the SOT-FMR and harmonic Hall voltage measurements for HM/FM bilayers with different thickness of HM. FMR analysis enabled determination of effective magnetization and magnetization damping (α = 0.015 for Pt and 0.0075 for Ta), while anomalous Hall effect and harmonic Hall measurements resulted in SOT efficiencies dependence vs. HM thickness. While damping-like SOT efficiency for Ta reaches ξDL-Ta = -0.35 and ξDL-Pt = 0.15 for Pt, with high resistivity difference (ρTa > 200 µΩcm and 24 < ρPt < 52 µΩcm) taken into account, the spin Hall conductivity for Pt of σSH-Pt = 2.9 (105 S/m) exceeds the one for Ta σSH-Ta = 1.7 (105 S/m) and is among the highest values reported [8].The HM thickness dependence of the SMR is analyzed by considering both the finite conductance at the interface [7] (an approach valid for small thicknesses) and thermodynamic approach [6] (valid for larger thicknesses). The results are compared with the harmonic Hall voltage measurements the SOT and the SOT efficiency and discussed in relation to the key parameters as the spin Hall angle and the spin diffusion length.Acknowledgements: WS acknowledges National Science Centre Grant No. UMO-2015/17/D/ST3/00500, Poland. Microfabrication was performed at the Academic Centre for Materials and Nanotechnology of AGH. **

Magnetic random-access memory, recognized as a breakthrough in spintronics, demonstrates substantial potential for next-generation nonvolatile memory and logic devices due to its unique magnetization-switching mechanism. However, realizing reliable perpendicular magnetization switching via spin–orbit torque necessitates an externally applied in-plane magnetic bias, a requirement that complicates integration in high-density device architectures. This study proposes a novel device architecture where geometric asymmetry engineering in an interlayer design generates an intrinsic equivalent in-plane magnetic field. By strategically introducing a non-symmetrical spacer between the heavy metal and ferromagnetic layers, we establish deterministic magnetization reversal while eliminating external field dependency. Furthermore, the energy barrier during magnetization switching is dynamically adjusted by applying a voltage across a perpendicular-anisotropy magnetic tunnel junction, leveraging the voltage-controlled magnetic anisotropy effect. We established a physics-driven compact model to assess the design and performance of voltage-controlled spin–orbit torque magnetic tunnel junction (VCSOT-MTJ) devices. Simulations reveal that the introduction of a minimally asymmetric light metal layer effectively resolves the issue of incomplete switching in field-free spin-orbit torque systems.

Electric-field control of magnetization is essential for the next-generation spintronic technologies such as nonvolatile magnetic memory. In particular, the voltage-control of the magnetic anisotropy (VCMA) in ferromagnets promises an energy-efficient reversal of magnetization based on the clocking scheme, which earlier has been demonstrated by using a pulsed voltage in magnetic tunnel junction (MTJ). However, the VCMA method in MTJ still requires a high gate voltage and a constant-bias magnetic field, which is a disadvantage for practical applications. In contrast, as another important method for magnetization reversal, current-induced spin-orbit torque (SOT) in topological insulator (TI) based magnetic heterostructures has been studied in recent experiments [1], which succeeded in reducing the switching power consumption by current pulse injected parallel to a bias magnetic field [2]. In this research, inspired by the VCMA and SOT approaches for magnetization control, we combine them and present two distinct clocking methods for the magnetization switching in TI based magnetic heterostructures. First, we analytically formulate the uniaxial magnetic anisotropy in magnetic TIs as a function of the Fermi energy. Next, as shown in Fig. 1, we propose a transistor-like device with the functionality of a nonvolatile magnetic memory adopting the VCMA writhing method that require no external magnetic fields and the anomalous-Hall-effect based readout scheme. For the magnetization reversal, the estimated source-drain current density and gate voltage are the orders of 104 - 105 A/cm2 and 0.1V, respectively, which are much smaller than those of traditional heavy-metal/ferromagnet heterostructures as well as the MTJs. We also discuss the possibility of using the proposed method for magnetization reversal in TI/ferromagnetic-insulator bilayers with magnetic proximity at the interface.

Nonvolatile flip-flops (NVFFs) integrating emerging spintronics devices such as magnetic tunnel junction (MTJ) are under intensive investigation. They allow computing systems to be powered-off during the standby state, hence high static power issue of conventional CMOS technology can be addressed. MTJ based on spin transfer torque (STT) effect provide non-volatility, good endurance and 3D integration with CMOS based circuits. However, it suffers from relative long switching delay, high switching power and asymmetric switching issues. In this work, we first present a multi-bit NVFF using NAND-like spintronics (NANS-SPIN) devices which are written by STT and spin orbit torque (SOT) currents. It shows advantages in terms of power consumption, area overhead and write voltage. Then, functionality and performance of the proposed NVFF will be simulated and validated.

This brief introduces a 3-bit magnetic analog-to-digital converter (MADC) employing the NAND-SPIN based multi-bit device which has the same structure as the NAND-SPIN memory cell. By adjusting the physical shape of the heavy metal (HM) line, the all-in-one integrated NAND-SPIN device exhibits multiple switching thresholds which could quantify the input current into several states and store them into the corresponding Magnetic Tunnel Junctions (MTJs). In order to read data reliably, a read port is connected to each Spin Orbit Torque (SOT) MTJs so as to minimize Tunnel Magnetoresistance (TMR) degradation due to non-uniform heavy metal resistance. In addition, an HM size adjustment methodology is proposed to improve the conversion accuracy and switching reliability. Detailed micromagnetic simulation results show that the proposed MADC could achieve 5 GHz sampling rate with only 0.068 pJ conversion energy, and in-memory conversion for higher bit resolution while provides the benefit of nonvolatility.

Spintronic Neurons Spintronic neuron hardware explorations arouse a new surge of breakthroughs in neuromorphic computing. The developed magnetic domain wall devices demonstrate biological neuron characteristics driven by the synergistic interaction between spin-orbit torque and built-in field in magnetic tunnel junctions, facilitating a new trajectory of time- and energy-efficient leaky-integrate-fire-self-reset neurons implementation. More information can be found in article number 2203006 by Guozhong Xing and co-workers.

BiSb topological insulator is attractive for the spin current source in spin-orbit torque (SOT) magnetoresistive random access memory (MRAM) thanks to its giant charge-to-spin conversion efficiency. However, the large spin Hall angles have been reported so far only in BiSb deposited on top of Co/Pt and Co/Tb multilayers. In realistic SOT-MRAM application, it is essential to integrate BiSb to CoFeB/MgO junction with perpendicular magnetic anisotropy (PMA). Here, we report a large spin Hall angle of 2.8 in junctions of bottom BiSb and CoFeB/MgO with perpendicular magnetic anisotropy using a CrOx interfacial layer, which is suitable for use in magnetic tunnel junctions (MTJ). We demonstrated SOT magnetization switching by a small current density of 3.1 MA/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> at a pulse width of 50 μs, which is an order of magnitude smaller than that in heavy metals. Our work demonstrates the capability of integrating BiSb to CoFeB/MgO-based MTJ.

A ferrimagnet (FiM) has small domains consisting of oppositely polarized and unequal magnetic moments. Oppositely polarized magnetic moments have strong exchange coupling between them resulting in robust torque in FiM called bulk torque. Due to the strong bulk torque, magnetic moments in FiM do not precess around the switching axis for a long time unlike ferromagnets (FMs) leading to faster switching speed compared to FM. In this paper, we propose and model the switching of FiM (CoTb) with spin current injection from heavy metal with strong spin Hall effect (SHE) such as Pt. We carry out ab initio calculation of the Dzyaloshinskii-Moriya interaction (DMI) at the FiM(CoTb)/heavy metal(Pt) interface using spin polarized relativistic Korringa-Kohn-Rostoker (KKR) Green’s function method. We compute the exchange coupling among the magnetic moments inside the CoTb layer and model how the spin-orbit torque (SOT) along with the bulk torque can efficiently switch the FiM. Then, we consider a ferrimagnet based magnetic tunnel junction (FMTJ) with SHE metal. We perform a comprehensive simulation and performance analysis of FiM(CoTb)/MgO/CoFeB and FiM(CoTb)/MgO/FiM(CoTb) FMTJs with Pt underlayer. Using non-equilibrium Green's function (NEGF) formalism, we calculate the tunneling magnetoresistance (TMR) of the proposed FMTJs at room temperature. Furthermore, the importance of thickness in CoTb magnetization dynamics is shown using our FiM magnetization simulation framework. We analyze and show that the CoTb based FMTJ has large switching energy barrier to ensure thermal stability. Finally, we show the performance comparison (TMR, write performance and power consumption) between our proposed FMTJs and FM based MTJ and our simulation exhibits that for picosecond range switching speed, FMTJ is ∼25 times more energy efficient than FM based MTJ.