Damping-like Torque Efficiency Research Articles

Direct and Inverse Spin Splitting Effects in Altermagnetic RuO2.

Recently, the altermagnetic materials with spin splitting effect (SSE), have drawn significant attention due to their potential to the flexible control of the spin polarization by the Néel vector. Here, the direct and inverse altermagnetic SSE (ASSE) in the (101)-oriented RuO2 film with the tilted Néel vector are reported. First, the spin torque along the x-, y-, and z-axis is detected from the spin torque-induced ferromagnetic resonance (ST-FMR), and the z-spin torque emerges when the electric current is along the [010] direction, showing the anisotropic spin splitting of RuO2. Further, the current-induced modulation of damping is used to quantify the damping-like torque efficiency (ξDL) in RuO2/Py, and an anisotropic ξDL is obtained and maximized for the current along the [010] direction, which increases with the reduction of the temperature, indicating the present of ASSE. Next, by way of spin pumping measurement, the inverse altermagnetic spin splitting effect (IASSE) is studied, which also shows a crystal direction-dependent anisotropic behavior and temperature-dependent behavior. This work gives a comprehensive study of the direct and inverse ASSE effects in the altermagnetic RuO2, inspiring future altermagnetic materials and devices with flexible control of spin polarization.

Giant Spin-Orbit Torque in Sputter-Deposited Bi Films.

Bismuth (Bi) has the strongest spin-orbit coupling among non-radioactive elements and is thus a promising material for efficient charge-to-spin conversion. However, previous electrical detections have reported controversial results for the conversion efficiency. In this study, an optical detection of a spin-orbit torque is reported in a Bi/CoFeB bilayer with a polycrystalline texture of (012) and (003). Taking advantage of the optical detection, spin-orbit torque is accurately separated from the Oersted field and achieves a giant damping-like torque efficiency of +0.5, verifying efficient charge-to-spin conversion. This study also demonstrates a field-like torque efficiency of -0.1. For the mechanism of the charge-to-spin conversion, the bulk spin Hall effect and the interface Rashba-Edelstein effect are considered.

Large damping-like torque and efficient current-induced magnetization reversal in Ti/Tb–Co/Cr structures

Seeking the magnetic heterostructures with large current-induced torque efficiency is currently one of the core hotspots in spintronics. In this work, we report the large and composition-dependent damping-like (DL) torque in the structure consisting of light metal Cr and Ti layers and a ferrimagnetic Tb–Co layer. The DL torque efficiency in the structures reaches a maximum (around −0.55) as the Tb content in the Tb–Co layer is in the range of 0.15–0.18. This composition-dependent behavior is different from that observed in the usual heavy-metal/ferrimagnetic structures. We also demonstrated the efficient current-induced magnetization reversal in these structures with a low threshold current density down to 8×1010 A/m2. In comparison, only very low efficiency values of −0.06 and −0.086 are obtained in the Ti/Co/Cr and Ti/Tb–Co/SiN control samples, respectively, suggesting that the large DL torque in the Ti/Tb–Co/Cr structures may originate from the orbital Hall effect in the Cr metal. By fitting the Cr layer thickness dependence of the torque efficiency with a simple orbital current diffusion model, we obtained an effective orbital Hall angle of −0.57±0.02 for the Ti/Tb0.85Co0.15/Cr samples. This work demonstrated the possibility to enhance the orbital torque effect by using the magnetic layer containing the element with strong spin–orbit coupling.

Investigation of spin–orbit torque performance with W/Cu-multilayers as spin current source

We study the W/Cu multilayers as a spin current source and the coherent spin–orbit torques in a Fe layer using the spin-torque ferromagnetic resonance (STFMR) technique. With increasing numbers of layers, the line shape of the STFMR signals changes from predominantly antisymmetric to predominantly symmetric. When using [W(0.5)/Cu(0.5)]5 as a spin current source, the symmetric amplitude increases by a factor of 5 compared to a single W layer. Simultaneously, the effective damping parameter also increases slightly due to enhanced spin pumping. Along with an increasing trend in the damping-like torque efficiency, this suggests that the extrinsic spin Hall effect is enhanced. Concurrently, the antisymmetric amplitude decreases significantly by a factor of 27, which indicates an increase in the field-like torque when multilayers are used as a spin current source.

Disentanglement of intrinsic and extrinsic side-jump scattering induced spin Hall effect in N-implanted Pt

The rapidly evolving utilization of spin Hall effect (SHE) arising from spin-orbit coupling in 5d transition metals and alloys have made giant strides in the development of designing low-power, robust and non-volatile magnetic memory. Recent studies, on incorporating non-metallic lighter elements such as oxygen, nitrogen and sulfur into 5d transition metals, have shown an enhancement in damping-like torque efficiency {\theta}_DL due to the modified SHE, but the mechanism behind this enhancement is not clear. In this paper, we study {\theta}_DL at different temperatures (100-293 K) to disentangle the intrinsic and extrinsic side-jump scattering induced spin Hall effect in N-implanted Pt. We observe a crossover of intrinsic to extrinsic side-jump mechanism as the implantation dose increases from 2*10^16 ions/cm2 to 1*10^17 ions/cm2. A sudden decrease in the intrinsic spin Hall conductivity is counterbalanced by the increase in the side-jump induced SHE efficiency. These results conclude that studying {\theta}_DL as a function of implantation dose, and also as a function of temperature, is important to understand the physical mechanism contributing to SHE, which has so far been unexplored in incorporating non-metallic element in 5d transition metals.

Giant Dampinglike-Torque Efficiency in Naturally Oxidized Polycrystalline TaAs Thin Films

We report the measurement of efficient charge-to-spin conversion at room temperature in Weyl semimetal/ferromagnet heterostructures with both oxidized and pristine interfaces. Polycrystalline films of the Weyl semimetal, TaAs, are grown by molecular beam epitaxy on (001) GaAs and interfaced with a metallic ferromagnet (Ni$_{0.8}$Fe$_{0.2}$). Spin torque ferromagnetic resonance (ST-FMR) measurements in samples with an oxidized interface yield a spin torque efficiency as large as $\xi_{\mathrm{FMR}}=0.45\pm 0.25$ for a 8 nm Ni$_{0.8}$Fe$_{0.2}$ layer thickness. By studying ST-FMR in these samples with varying Ni$_{0.8}$Fe$_{0.2}$ layer thickness, we extract a damping-like torque efficiency as high as $\xi_{\mathrm{DL}}=1.36\pm 0.66$. In samples with a pristine (unoxidized) interface, the spin torque efficiency has opposite sign to that observed in oxidized samples ($\xi_{\mathrm{FMR}}=-0.27\pm 0.14$ for a 5 nm Ni$_{0.8}$Fe$_{0.2}$ layer thickness). We also find a lower bound on the spin Hall conductivity ($424 \pm 110 \frac{\hbar}{e}$ S/cm) which is surprisingly consistent with theoretical predictions for the single crystal Weyl semimetal state of TaAs.

Spin-Orbit-Torque Efficiency and Current-Driven Coherent Magnetic Dynamics in a Pt / Ni /Py Trilayer-Based Spin Hall Nano-Oscillator

We experimentally study the current-induced effective spin-orbit torque (SOT) efficiency and the spectral characteristics of current-driven coherent magnetic dynamics in spin Hall nano-oscillators (SHNOs) based on the $\mathrm{Pt}$/$\mathrm{Ni}$/Py trilayer. We determine that the $\mathrm{Pt}$/$\mathrm{Ni}$/Py trilayer structure has an effective dampinglike torque efficiency ${\ensuremath{\xi}}_{\mathrm{DL}}\ensuremath{\sim}0.055$, comparable with the $\mathrm{Pt}$/$\mathrm{Co}$ and $\mathrm{Pt}$/$\mathrm{Fe}$ bilayer systems with a strong interfacial spin-orbit coupling and magnetic proximity effect. Furthermore, the microwave-generation spectra show that the $\mathrm{Pt}$/$\mathrm{Ni}$/Py-based SHNOs exhibit a single nonlinear self-localized bullet mode with a frequency below ${f}_{\mathrm{FMR}}$ and a significant current-dependent frequency red shift due to its strong nonlinear effect, which is very similar to that in $\mathrm{Pt}$/Py-based SHNOs, at low oblique angles $\ensuremath{\varphi}\ensuremath{\le}\phantom{\rule{0.2em}{0ex}}{50}^{\ensuremath{\circ}}$. In contrast, at high oblique angles $\ensuremath{\varphi}\ensuremath{\ge}\phantom{\rule{0.2em}{0ex}}{55}^{\ensuremath{\circ}}$, the spectra show two oscillating peaks with very similar field-, current-, and temperature-dependent behaviors, which suggests the spatial coexistence of two same-type nonlinear self-localized bullet modes at certain currents and magnetic fields. Additionally, the observed linear temperature dependence of the minimum line width, which resembles the thermal broadening of single-mode oscillation, further confirms that two localized bullet modes are independent, spatially separated, and lack thermally activated mode-transition behavior. Our results provide valuable information for the electronic control of coherent magnetic dynamics by combining bulk and interfacial spin-orbit coupling effects in the magnetic heterostructures.

Giant bulk spin–orbit torque and efficient electrical switching in single ferrimagnetic FeTb layers with strong perpendicular magnetic anisotropy

Efficient manipulation of antiferromagnetically coupled materials that are integration-friendly and have strong perpendicular magnetic anisotropy (PMA) is of great interest for low-power, fast, dense magnetic storage and computing. Here, we report a distinct, giant bulk damping-like spin–orbit torque in strong-PMA ferrimagnetic Fe100−xTbx single layers that are integration-friendly (composition-uniform, amorphous, and sputter-deposited). For sufficiently thick layers, this bulk torque is constant in the efficiency per unit layer thickness, ξDLj/t, with a record-high value of 0.036 ± 0.008 nm−1, and the damping-like torque efficiency ξDLj achieves very large values for thick layers, up to 300% for 90 nm layers. This giant bulk torque by itself switches tens of nm thick Fe100−xTbx layers that have very strong PMA and high coercivity at current densities as low as a few MA/cm2. Surprisingly, for a given layer thickness, ξDLj shows strong composition dependence and becomes negative for composition where the total angular momentum is oriented parallel to the magnetization rather than antiparallel. Our findings of giant bulk spin torque efficiency and intriguing torque-compensation correlation will stimulate study of such unique spin–orbit phenomena in a variety of ferrimagnetic hosts. This work paves a promising avenue for developing ultralow-power, fast, dense ferrimagnetic storage and computing devices.

Inactivation of damping-like torque in Tb-Gd-Fe film on Ta layer

Recently, bulk spin–orbit torques (SOTs) in transition metal-rare earth (TM-RE) ferrimagnets have been reported. In this study, to investigate bulk SOTs, we observed the current-induced effective field mediated by a damping-like torque (DLT), which is one of the components of SOTs, using TM-RE ferrimagnetic Tb x (Gd32Fe68)100-x films with a Ta layer. The DLT efficiency was inactivated by increasing the Tb composition x to be greater than 8, suggesting that the DLT was induced by the bulk SOTs of Tb x (Gd32Fe68)100-x as well as the spin Hall effect in the Ta. However, from the DLT measurement using a Tb8(Gd32Fe68)92 layer sandwiched between Ru layers, where Ru has a negligibly small DLT, was almost zero. This indicates that the inactivation of DLT cannot simply be explained by the bulk SOTs of Tb x (Gd32Fe68)100-x . However, we expect that this finding will provide meaningful insights for controlling magnetization using current.

First-principles calculations of spin-orbit torques in Mn2Au /heavy-metal bilayers

Using the nonequilibrium Green's function technique, we calculate spin-orbit torques in a ${\mathrm{Mn}}_{2}\mathrm{Au}$/heavy-metal bilayer, where the heavy metal (HM) is W or Pt. Spin-orbit coupling (SOC) in the bulk of ${\mathrm{Mn}}_{2}\mathrm{Au}$ generates a strong fieldlike torquance, which is parallel on the two sublattices and scales linearly with the conductivity, and a weaker dampinglike torquance that is antiparallel on the two sublattices. Interfaces with W or Pt generate parallel dampinglike torques of opposite signs that are similar in magnitude to those in ferromagnetic bilayers and similarly insensitive to disorder. The dampinglike torque efficiency depends strongly on the termination of the interface and on the presence of spin-orbit coupling in ${\mathrm{Mn}}_{2}\mathrm{Au}$, suggesting that the dampinglike torque is not due solely to the spin-Hall effect in the HM layer. Interfaces also induce antiparallel fieldlike and dampinglike torques that can penetrate deep into ${\mathrm{Mn}}_{2}\mathrm{Au}$.

Variation of spin-orbit torque and spin transport properties by V alloying in β-W-based magnetic heterostructures

Of transition metals, β-W exhibits the maximum charge-to-spin conversion efficiency. However, due to the lack of phase stability, the β-W-based alloy has rarely been investigated as a spin current generating layer. This study examines W–V alloy layers with various W100-xVx/CoFeB/MgO/Ta heterostructure compositions. X-ray diffraction confirms that the β-W matrix is conserved up to a V content of 20 at%. We attain a maximum damping-like torque efficiency of −0.45 ± 0.04 for the W80V20 alloy-based heterostructure through the harmonic response method. Furthermore, we determine the spin diffusion length of the W80V20 layer and specify the interfacial spin transparency of the W80V20/CoFeB structure by adopting the spin diffusion model. Consequently, we suggest an intrinsic spin-Hall angle of −0.86. In addition, we observe in-plane current-induced switching. Our results establish the potential of the β-phase W-V alloy layer as a spin current source layer in spintronic devices.

Highly dose dependent damping-like spin–orbit torque efficiency in O-implanted Pt

Damping-like torque (DLT) arising from the spin Hall effect (SHE) in heavy metals and their alloys has been widely explored for applications in spin–orbit torque MRAM, auto-oscillations, spin waves, and domain wall motion. In conventional materials, the DLT efficiency is limited by intrinsic properties, while attaining strong spin–orbit coupling and higher spin-charge interconversion, with no compromise to electric properties, is the need of the hour. In this Letter, we report more than 3.5 times increase in DLT efficiency, θDL, of modified Pt-oxide by employing a better approach of low energy 20 keV O+ ion implantation. The highest fluence of O+ implantation (1 × 1017 ions cm−2) in Pt enhanced the DLT efficiency from 0.064 to 0.230 and improved the spin transmission for a smaller trade-off in the longitudinal resistivity (ρPt to ρPt−Oxide) from 55.4 to 159.5 μΩ cm, respectively. The transverse spin Hall resistivity, ρSH, is found to be proportional to the square of the longitudinal resistivity, i.e., ρSHimp∝ρimp2, implying that the enhanced SHE in O-implanted Pt is due to a side-jumping mechanism. Further, no break in the twofold as well as mirror symmetry of torques from the O-implanted Pt allows the use of spin-torque ferromagnetic resonance-based line shape analysis to quantify such torques.

Tunable spin–orbit torque efficiency in in-plane and perpendicular magnetized [Pt/Co]n multilayer

Despite the great promise for very efficient and fast switching of magnetization in embedded memory and computing applications, the performance of spin–orbit torque (SOT) lags behind conventional technologies due to the low spin-Hall conductivity of the spin Hall materials. This work reports an advantageous spin Hall material, periodic [Pt/Co]n multilayer, which combines a low resistivity with a widely tunable spin Hall effect along with magnetization as evidenced with an in-plane CoFeB ferromagnetic detector. Three detection methods have been employed to illustrate the trends of magnetic orientation, interlayer exchange coupling, spin transport, and SOT efficiency as a function of Co thickness, which casts insight into the mechanisms of the SOTs in the [Pt/Co]n multilayer. With the varying Co thickness in the [Pt/Co]n multilayer, it is found that the damping-like torque efficiency is negative and the field-like torque efficiency is 8.2–31.5 times larger. The [Pt/Co]n multilayers have two spin reorientation transition states where the spin Hall angle θSH is maximized with a low resistivity of ∼ 40 μΩ cm, at tCo = 0.507 nm and 0.159 nm. We simulated the magnetization trajectories and time-domain responses of SOT switching with a current pulse and demonstrated a much faster switching in the spin reorientation transition states based on the coupled Landau–Lifshitz–Gilbert equation.

Spin-orbit torques originating from the bulk and interface in Pt-based structures

We investigated spin-orbit torques in prototypical Pt-based spintronic devices. We found that, in Pt/Ni and Pt/Fe bilayers, the damping-like torque efficiency depends on the thickness of the Pt layer. We also found that the damping-like torque efficiency is almost identical in the Pt/Ni and Pt/Fe bilayers despite the stronger spin memory loss at the Pt/Fe interface. These results suggest that although the dominant source of the damping-like torque is the bulk spin Hall effect in the Pt layer, a sizable damping-like torque is generated by the interface in the Pt/Fe bilayer due to the stronger interfacial spin-orbit coupling. In contrast to the damping-like torque, whose magnitude and sign are almost identical in the Pt/Ni and Pt/Fe bilayers, the field-like torque strongly depends on the choice of the ferromagnetic layer. The sign of the field-like torque originating from the bulk spin Hall effect in the Pt layer is opposite between the Pt/Ni and Pt/Fe bilayers, which can be attributed to the opposite sign of the imaginary part of the spin-mixing conductance. These results demonstrate that the spin-orbit torques are quite sensitive to the electronic structure of the FM layer.

Enhanced spin–orbit torque efficiency in Pt/Co/Ho heterostructures via inserting Ho layer

Spin–orbit torque (SOT) is a promising approach to manipulate the magnetization for high-performance spintronic applications. In conventional SOT heterostructures with heavy metal (HM)/ferromagnet layers, the SOT efficiency is determined by the charge-to-spin conversion, characterized by the spin Hall angle θSH of the HM layer. Researchers have investigated various HMs with different θSH to enhance the SOT efficiency while it is still limited because of the HM’s intrinsic properties. In this study, we employ a rare-earth holmium (Ho) layer on top of a ferromagnetic Co layer (Pt/Co/Ho) to enhance the SOT efficiency. An increased damping-like SOT efficiency up to 200% is achieved at an optimized thickness of 2-nm Ho, corresponding to a lower switching current density, which is 60% less compared to the sample without a Ho layer. The damping-like torque efficiency per current density is estimated at around 0.256 for Pt/Co/Ho heterostructures. Our results, herein, demonstrate that inserting a rare-earth metal affords an additional spin current and/or improves the spin transparency to enhance the SOT efficiency, providing a route for energy-efficient spintronic devices.

Interfacial spin transmission and spin–orbit torques in as-grown and annealed W/Co2FeAl/MgO multilayers

The interfacial spin transmission and spin–orbit torques (SOTs) in as-grown and annealed W/Co2FeAl(CFA)/MgO multilayers are studied by the spin-torque ferromagnetic resonance (ST-FMR) technique. The effective spin-mixing conductance of 4.40×1014 Ω−1 m−2 and the interfacial spin transparency Tin of 0.47 are obtained for the as-grown samples, which are comparable to those of the widely employed W/CoFeB bilayer. The annealing influence on the W/CFA/MgO multilayer is subsequently studied. The damping-like torque efficiency (ξDL) and field-like torque efficiency (ξFL) are extracted for different annealing temperatures via modulation of damping measurements and the angular dependence of ST-FMR spectra. Importantly, the ξDL value is fairly large (0.3–0.5) and does not degrade even when the annealing temperature is increased up to 420 °C. Our results indicate that the studied W/CFA/MgO multilayers could be promising candidate materials for designing and developing SOT-driven spintronic devices.

Impact of the crystal orientation on spin-orbit torques in Fe/Pd bilayers

Spin-orbit torques in ferromagnetic/non-magnetic heterostructures offer more energy-efficient means to realize spin-logic devices; however, their strengths are determined by the heterostructure interface. This work examines the impact of crystal orientation on the spin-orbit torque efficiency in different Fe/Pd bilayer systems. Results from spin torque ferromagnetic resonance measurements evidence that the damping-like torque efficiency is higher in epitaxial than in polycrystalline bilayer structures while the field-like torque is negligible in all bilayer structures. The strength of the damping-like torque decreases with deterioration of the bilayer epitaxial quality. The present finding provides fresh insight for the enhancement of spin-orbit torques in magnetic heterostructures.

Characterization of Spin-Orbit Torque Efficiency in Magnetic Heterostructures with Perpendicular Magnetic Anisotropy via Spin-Torque Ferromagnetic Resonance

Characterization of spin-orbit torques (SOTs) in the perpendicular magnetic anisotropy (PMA) system is of great importance for fundamental studies and technological applications in spintronic devices. Here, we report a spin Hall magnetoresistance (SMR) based spin-torque ferromagnetic resonance (ST FMR) study of SOT efficiency in perpendicularly magnetized $\mathrm{W}$/${\mathrm{Co}}_{40}{\mathrm{Fe}}_{40}{\mathrm{B}}_{20}$/$\mathrm{Mg}\mathrm{O}$ structures. A full analysis of the ST FMR spectrum is developed for the PMA sample. A typical ST FMR spectrum of the PMA system shows two resonance modes, i.e., in-plane and out-of-plane magnetization precession modes. By performing modulation of the damping measurement for the in-plane mode, the dampinglike torque efficiency is determined to be \ensuremath{-}0.38, which is consistent with the reference value obtained in samples with in-plane magnetic anisotropy. The dampinglike torque efficiency of \ensuremath{-}0.31 is also obtained from the out-of-plane resonance mode, in which the significant contribution of the spin-pumping-induced inverse spin Hall effect is carefully considered. The obtained values of dampinglike torque efficiency by different means are consistent with each other. The present work provides useful insights to determine the dampinglike torque efficiency of the PMA sample via ST FMR measurements.

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.