Damping-like Torque Research Articles

Temperature dependence of spin-orbit torques in W/CoFeB bilayers

We report on the temperature variation of spin-orbit torques in perpendicularly magnetized W/CoFeB bilayers. Harmonic Hall voltage measurements in perpendicularly magnetized CoFeB reveal increased longitudinal and transverse effective magnetic field components at low temperatures. The damping-like spin-orbit torque reaches an efficiency of 0.55 at 19 K. Scanning transmission electron microscopy and X-ray reflectivity measurements indicate that considerable interface mixing between W and CoFeB may be responsible for strong spin-orbit interactions.

Effect of Mg Oxidation Degree on Rashba-Effect-Induced Torques in Ta/CoFeB/Mg(MgO) Multilayer

Control of spin–orbit torques (SOTs) in heavy metal/ferromagnetic metal/oxide structures is critical to the realization of promising SOT magnetic random access memory devices. In this paper, the SOT-induced effective fields in Ta/CoFeB/Mg(MgO) structures with perpendicular magnetic anisotropy (PMA) were investigated through the low-current-induced lock-in technique. This paper demonstrates that the industrially preferred MgO preparation method allows us to readily manipulate the oxidation degree of the Mg(MgO) and produce a significant effect on the SOT as well as PMA. Importantly, the ratio of the field-like torque to the damping-like torque efficiency can be controlled without thinning or oxidizing the bottom Ta layer, which is the source of spin-Hall-effect-induced damping-like torque. The achieved ratio of $\sim 2.5$ satisfies the condition that is necessary for the SOT-induced switching without an external magnetic field based on the recently proposed half-precessional switching mechanism.

Enhanced spin Hall torque efficiency in Pt100−xAlx and Pt100−xHfx alloys arising from the intrinsic spin Hall effect

We report that the spin Hall torque generated by Pt can be enhanced substantially by alloying with Al or Hf. We observe damping-like spin torque efficiency per unit applied current density as high as ξDLj=0.23±0.02, nearly twice the maximum value reported for pure Pt. To achieve this maximum efficiency, a very thin (0.5 nm) Pt spacer layer is inserted between the alloy and the ferromagnet being manipulated, to avoid a degraded spin transparency at the alloy/ferromagnet interface.

Competing effect of spin-orbit torque terms on perpendicular magnetization switching in structures with multiple inversion asymmetries.

Current-induced spin-orbit torques (SOTs) in structurally asymmetric multilayers have been used to efficiently manipulate magnetization. In a structure with vertical symmetry breaking, a damping-like SOT can deterministically switch a perpendicular magnet, provided an in-plane magnetic field is applied. Recently, it has been further demonstrated that the in-plane magnetic field can be eliminated by introducing a new type of perpendicular field-like SOT via incorporating a lateral structural asymmetry into the device. Typically, however, when a current is applied to such devices with combined vertical and lateral asymmetries, both the perpendicular field-like torque and the damping-like torque coexist, hence jointly affecting the magnetization switching behavior. Here, we study perpendicular magnetization switching driven by the combination of the perpendicular field-like and the damping-like SOTs, which exhibits deterministic switching mediated through domain wall propagation. It is demonstrated that the role of the damping-like SOT in the deterministic switching is highly dependent on the magnetization direction in the domain wall. By contrast, the perpendicular field-like SOT is solely determined by the relative orientation between the lateral structural asymmetry and the current direction, regardless of the magnetization direction in the domain wall. The experimental results further the understanding of SOTs-induced switching, with implications for spintronic devices.

Spin Torque Study of the Spin Hall Conductivity and Spin Diffusion Length in Platinum Thin Films with Varying Resistivity.

We report measurements of the spin torque efficiencies in perpendicularly magnetized Pt/Co bilayers where the Pt resistivity ρ_{Pt} is strongly dependent on thickness t_{Pt}. The dampinglike spin Hall torque efficiency per unit current density ξ_{DL}^{j} varies significantly with t_{Pt}, exhibiting a peak value ξ_{DL}^{j}=0.12 at t_{Pt}=2.8-3.9 nm. In contrast, ξ_{DL}^{j}/ρ_{Pt} increases monotonically with t_{Pt} and saturates for t_{Pt}>5 nm, consistent with an intrinsic spin Hall effect mechanism, in which ξ_{DL}^{j} is enhanced by an increase in ρ_{Pt}. Assuming the Elliott-Yafet spin scattering mechanism dominates, we estimate that the spin diffusion length λ_{s}=(0.77±0.08)×10^{-15} Ω·m^{2}/ρ_{Pt}.

Wave-Number-Dependent Gilbert Damping in Metallic Ferromagnets.

A wave-number-dependent dissipative term to magnetization dynamics, mirroring the conservative term associated with exchange, has been proposed recently for ferromagnetic metals. We present measurements of wave-number-(k-)dependent Gilbert damping in three metallic ferromagnets, NiFe, Co, and CoFeB, using perpendicular spin wave resonance up to 26GHz. In the thinnest films accessible, where classical eddy-current damping is negligible, size effects of Gilbert damping for the lowest and first excited modes support the existence of a k^{2} term. The new term is clearly separable from interfacial damping typically attributed to spin pumping. Higher-order modes in thicker films do not show evidence of enhanced damping, attributed to a complicating role of conductivity and inhomogeneous broadening. Our extracted magnitude of the k^{2} term, Δα_{kE}^{*}=Δα_{0}^{*}+A_{k}^{*}k^{2}, where A_{k}^{*}=0.08-0.1 nm^{2} in the three materials, is an order of magnitude lower than that identified in prior experiments on patterned elements.

Research Update: Spin transfer torques in permalloy on monolayer MoS2

We observe current induced spin transfer torque resonance in permalloy (Py) grown on monolayer MoS2. By passing rf current through the Py/MoS2 bilayer, field-like and damping-like torques are induced which excite the ferromagnetic resonance of Py. The signals are detected via a homodyne voltage from anisotropic magnetoresistance of Py. In comparison to other bilayer systems with strong spin-orbit torques, the monolayer MoS2 cannot provide bulk spin Hall effects and thus indicates the purely interfacial nature of the spin transfer torques. Therefore our results indicate the potential of two-dimensional transition-metal dichalcogenide for the use of interfacial spin-orbitronics applications.

Spin-orbit torque in Pt/CoNiCo/Pt symmetric devices.

Current induced magnetization switching by spin-orbit torques offers an energy-efficient means of writing information in heavy metal/ferromagnet (FM) multilayer systems. The relative contributions of field-like torques and damping-like torques to the magnetization switching induced by the electrical current are still under debate. Here, we describe a device based on a symmetric Pt/FM/Pt structure, in which we demonstrate a strong damping-like torque from the spin Hall effect and unmeasurable field-like torque from Rashba effect. The spin-orbit effective fields due to the spin Hall effect were investigated quantitatively and were found to be consistent with the switching effective fields after accounting for the switching current reduction due to thermal fluctuations from the current pulse. A non-linear dependence of deterministic switching of average Mz on the in-plane magnetic field was revealed, which could be explained and understood by micromagnetic simulation.

Compact Model for Spin–Orbit Magnetic Tunnel Junctions

Electrical control of a magnetic tunnel junction (MTJ) through spin–orbit torques (SOTs) offers opportunities to introduce MTJs into high-performance, low energy applications. SOTs support a high-speed and energy-efficient three terminal MTJ with perpendicular-to-the-plane magnetization (PMTJ). The read path is separated from the write path, enhancing the reliability of the device. SOTs exhibit two coexisting contributions: 1) a damping-like torque and 2) a field-like torque. In this paper, a physics-based compact model for a three terminal PMTJ is presented, which accurately models the magnetic, electrical, and thermal behaviors of a PMTJ controlled through SOTs. The proposed compact model is validated with experimental data, exhibiting reasonable accuracy with an average error of <5.4%. The integration capability of the proposed compact model with CMOS technology is also demonstrated.

Spin-orbit torques for current parallel and perpendicular to a domain wall

We report field- and current-induced domain wall (DW) depinning experiments in Ta\Co20Fe60B20\MgO nanowires through a Hall cross geometry. While purely field-induced depinning shows no angular dependence on in-plane fields, the effect of the current depends crucially on the internal DW structure, which we manipulate by an external magnetic in-plane field. We show depinning measurements for a current sent parallel to the DW and compare its depinning efficiency with the conventional case of current flowing perpendicularly to the DW. We find that the maximum efficiency is similar for both current directions within the error bars, which is in line with a dominating damping-like spin-orbit torque (SOT) and indicates that no large additional torques arise for currents perpendicular to the DW. Finally, we find a varying dependence of the maximum depinning efficiency angle for different DWs and pinning levels. This emphasizes the importance of our full angular scans compared with previously used measurements for just two field directions (parallel and perpendicular to the DW) to determine the real torque strength and shows the sensitivity of the SOT to the precise DW structure and pinning sites.

Dependence of the efficiency of spin Hall torque on the transparency of Pt/ferromagnetic layer interfaces

We report that spin current transport across Pt-ferromagnet (FM) interfaces is strongly dependent on the type and the thickness of the FM layer and on post-deposition processing protocols. By employing both harmonic voltage measurements and spin-torque ferromagnetic resonance measurements, we find that the efficiency of the Pt spin Hall effect in exerting a damping-like spin torque on the FM ranges from < 0.05 to > 0.10 under different interfacial conditions. We also show that the temperature dependence of the spin torque efficiencies for both the damping-like torque and field-like torque is dependent upon the details of the Pt-FM interface. The "internal" spin Hall angle of the Pt thin films used in this study, after taking the interfacial spin transmission factor into account, is estimated to be ~ 0.20. This suggests that a careful engineering of Pt-FM interfaces can improve the spin-Hall-torque efficiency of Pt-based spintronic devices.

Critical current destabilizing perpendicular magnetization by the spin Hall effect

The critical current needed to destabilize the magnetization of a perpendicular ferromagnet via the spin Hall effect is studied. Both the dampinglike and fieldlike torques associated with the spin current generated by the spin Hall effect is included in the Landau-Lifshitz-Gilbert equation to model the system. In the absence of the fieldlike torque, the critical current is independent of the damping constant and is much larger than that of conventional spin torque switching of collinear magnetic systems, as in magnetic tunnel junctions. With the fieldlike torque included, we find that the critical current scales with the damping constant as $\alpha^{0}$ (i.e., damping independent),$\alpha$, and $\alpha^{1/2}$ depending on the sign of the fieldlike torque and other parameters such as the external field. Numerical and analytical results show that the critical current can be significantly reduced when the fieldlike torque possesses the appropriate sign, i.e. when the effective field associated with the fieldlike torque is pointing opposite to the spin direction of the incoming electrons. These results provide a pathway to reducing the current needed to switch magnetization using the spin Hall effect.

Comparison of spin-orbit torques and spin pumping across NiFe/Pt and NiFe/Cu/Pt interfaces

We experimentally investigate spin-orbit torques and spin pumping in NiFe/Pt bilayers with direct and interrupted interfaces. The damping-like and field-like torques are simultaneously measured with spin-torque ferromagnetic resonance tuned by a dc bias current, whereas spin pumping is measured electrically through the inverse spin Hall effect using a microwave cavity. Insertion of an atomically thin Cu dusting layer at the interface reduces the damping-like torque, field-like torque, and spin pumping by nearly the same factor of ~1.4. This finding confirms that the observed spin-orbit torques predominantly arise from diffusive transport of spin current generated by the spin Hall effect. We also find that spin-current scattering at the NiFe/Pt interface contributes to additional enhancement in magnetization damping that is distinct from spin pumping.

Angular dependence of spin-orbit spin-transfer torques

In ferromagnet/heavy metal bilayers, an in-plane current gives rise to spin-orbit spin transfer torque which is usually decomposed into field-like and damping-like torques. For two-dimensional free-electron and tight-binding models with Rashba spin-orbit coupling, the field-like torque acquires nontrivial dependence on the magnetization direction when the Rashba spin-orbit coupling becomes comparable to the exchange interaction. This nontrivial angular dependence of the field-like torque is related to the Fermi surface distortion, determined by the ratio of the Rashba spin-orbit coupling to the exchange interaction. On the other hand, the damping-like torque acquires nontrivial angular dependence when the Rashba spin-orbit coupling is comparable to or stronger than the exchange interaction. It is related to the combined effects of the Fermi surface distortion and the Fermi sea contribution. The angular dependence is consistent with experimental observations and can be important to understand magnetization dynamics induced by spin-orbit spin transfer torques

Spin-transfer torque in spin filter tunnel junctions

Spin-transfer torque in a class of magnetic tunnel junctions with noncollinear magnetizations, referred to as spin filter tunnel junctions, is studied within the tight-binding model using the nonequilibrium Green's function technique within Keldysh formalism. These junctions consist of one ferromagnet (FM) adjacent to a magnetic insulator (MI) or two FM separated by a MI. We find that the presence of the magnetic insulator dramatically enhances the magnitude of the spin-torque components compared to conventional magnetic tunnel junctions. The fieldlike torque is driven by the spin-dependent reflection at the MI/FM interface, which results in a small reduction of its amplitude when an insulating spacer (S) is inserted to decouple MI and FM layers. Meanwhile, the dampinglike torque is dominated by the tunneling electrons that experience the lowest barrier height. We propose a device of the form FM/(S)/MI/(S)/FM that takes advantage of these characteristics and allows for tuning the spin-torque magnitudes over a wide range just by rotation of the magnetization of the insulating layer.

Current induced torques and interfacial spin-orbit coupling: Semiclassical modeling

In bilayer nanowires consisting of a ferromagnetic layer and a non-magnetic layer with strong spin-orbit coupling, currents create torques on the magnetization beyond those found in simple ferromagnetic nanowires. The resulting magnetic dynamics appear to require torques that can be separated into two terms, damping-like and field-like. The damping-like torque is typically derived from models describing the bulk spin Hall effect and the spin transfer torque, and the field-like torque is typically derived from a Rashba model describing interfacial spin-orbit coupling. We derive a model based on the Boltzmann equation that unifies these approaches. We also consider an approximation to the Boltzmann equation, the drift-diffusion model, that qualitatively reproduces the behavior, but quantitatively fails to reproduce the results. We show that the Boltzmann equation with physically reasonable parameters can match the torques for any particular sample, but in some cases, it fails to describe the experimentally observed thickness dependences.