Damping-like Torque Research Articles

Magnetization dependent spin orbit torques generated by ferrimagnetic FeCoTb alloys

Spin-orbit torques (SOTs) generated by magnetic materials have prompted a surge of interest in low-power spintronics. In this context, rare-earth doped magnetic alloys are the ideal candidate due to the low symmetry and large spin-orbit coupling. Here, we present a study on SOTs generated by ferrimagnetic FeCoTb alloys in permalloy (Ni80Fe20, Py)/Cu/FeCoTb spin valve structures, showing high-efficient damping-like and field-like torques. Crucially, the spin Hall conductivity of FeCoTb is up to 6.32 × 105 (ℏ/2e) Ω−1m−1, larger than that in conventional heavy metals. By controlling the magnetic configuration of the spin valve structure, the magnetization dependent behavior of the SOTs is achieved, which may origin from the anomalous Hall effect of FeCoTb dominated by Tb magnetization. Our results demonstrate great prospects of ferrimagnetic materials for low-power spintronic applications.

Field-Free Type- x Spin-Orbit-Torque Switching by Easy-Axis Engineering

The current-induced type-x spin-orbit-torque (SOT) switching configuration describes the orthogonal relationship between the magnetic easy axis (EA) of a ferromagnetic (FM) layer and the injected spin polarization, $\ensuremath{\sigma}$, from a heavy-metal (HM) layer, which has the potential to eclipse the conventional type-y scenario (EA parallel to $\ensuremath{\sigma}$) at the sub-nanosecond pulse regime. Here, we show that, in HM/FM bilayer heterostructures, current-driven differential planar Hall signals can serve as efficient means to probe type-x SOT switching in a simple measurement fashion. Through this approach, we demonstrate field-free type-x SOT switching in all devices with a canted EA, which are engineered via field-annealing processes. By analyzing the switching-phase diagrams, we further verify that such field-free switching stems from a z-direction effective field contributed to by both the dampinglike torque and the canted EA. Our work indicates that the canted EA, as engineered by a field-annealing process, can give rise to a robust field-free SOT switching and further reduce the critical switching current density.

Effects of Crystalline Disorder on Interfacial and Magnetic Properties of Sputtered Topological Insulator/Ferromagnet Heterostructures

Thin films of Topological insulators (TIs) coupled with ferromagnets (FMs) are excellent candidates for energy-efficient spintronics devices. Here, the effect of crystalline structural disorder of TI on interfacial and magnetic properties of sputter-deposited TI/FM, Bi2Te3/Ni80Fe20, heterostructures is reported. Ni and a smaller amount of Fe from Py was found to diffuse across the interface and react with Bi2Te3. For highly crystalline c-axis oriented Bi2Te3 films, a giant enhancement in Gilbert damping is observed, accompanied by an effective out-of-plane magnetic anisotropy and enhanced damping-like spin-orbit torque (DL-SOT), possibly due to the topological surface states (TSS) of Bi2Te3. Furthermore, a spontaneous exchange bias is observed in hysteresis loop measurements at low temperatures. This is because of an antiferromagnetic topological interfacial layer formed by reaction of the diffused Ni with Bi2Te3 which couples with the FM, Ni80Fe20. For increasing disorder of Bi2Te3, a significant weakening of exchange interaction in the AFM interfacial layer is found. These experimental results Abstract length is one paragraph.

Theory of harmonic Hall responses of spin-torque driven antiferromagnets

Harmonic analysis is a powerful tool to characterize and quantify current-induced torques acting on magnetic materials, but so far it remains an open question in studying antiferromagnets. Here we formulate a general theory of harmonic Hall responses of collinear antiferromagnets driven by current-induced torques including both field-like and damping-like components. By scanning a magnetic field of variable strength in three orthogonal planes, we are able to distinguish the contributions from field-like torque, damping-like torque, and concomitant thermal effects by analyzing the second harmonic signals in the Hall voltage. The analytical expressions of the first and second harmonics as functions of the magnetic field direction and strength are confirmed by numerical simulations with good agreement. We demonstrate our predictions in two prototype antiferromagnets, $\alpha-$Fe$_{2}$O$_{3}$ and NiO, providing direct and general guidance to current and future experiments.

Deep learning for spin-orbit torque characterizations with a projected vector field magnet

Spin-orbit torque characterizations on magnetic heterostructures with perpendicular anisotropy are demonstrated on a projected vector field magnet via hysteresis loop shift measurement and harmonic Hall measurement with planar Hall correction. Accurate magnetic field calibration of the vector magnet is realized with the help of deep learning models, which are able to capture the nonlinear behavior between the generated magnetic field and the currents applied to the magnet. The trained models can successfully predict the applied current combinations under the circumstances of magnetic field scans, angle scans, and hysteresis loop shift measurements. The validity of the models is further verified, complemented by the comparison of the spin-orbit torque characterization results obtained from the deep-learning-trained vector magnet system with those obtained from a conventional setup comprised of two separated electromagnets. The damping-like spin-orbit torque (DL-SOT) efficiencies (|$\xi_{DL}$|) extracted from the vector magnet and the traditional measurement configuration are consistent, where |$\xi_{DL}$| $\approx$ 0.22 for amorphous W and |$\xi_{DL}$| $\approx$ 0.02 for $\alpha$-W. Our work provides an advanced method to meticulously control a vector magnet and to conveniently perform various spin-orbit torque characterizations.

Third harmonic characterization of antiferromagnetic heterostructures

Electrical switching of antiferromagnets is an exciting recent development in spintronics, which promises active antiferromagnetic devices with high speed and low energy cost. In this emerging field, there is an active debate about the mechanisms of current-driven switching of antiferromagnets. For heavy-metal/ferromagnet systems, harmonic characterization is a powerful tool to quantify current-induced spin-orbit torques and spin Seebeck effect and elucidate current-induced switching. However, harmonic measurement of spin-orbit torques has never been verified in antiferromagnetic heterostructures. Here, we report harmonic measurements in Pt/α-Fe2O3 bilayers, which are explained by our modeling of higher-order harmonic voltages. As compared with ferromagnetic heterostructures where all current-induced effects appear in the second harmonic signals, the damping-like torque and thermally-induced magnetoelastic effect contributions in Pt/α-Fe2O3 emerge in the third harmonic voltage. Our results provide a new path to probe the current-induced magnetization dynamics in antiferromagnets, promoting the application of antiferromagnetic spintronic devices.

Modulation of spin–orbit torque by insertion of a NiO layer in a Pt/Co structure formed on Al2O3 and Si/SiO x substrate

In this study, we investigated the modulation of the spin–orbit torque (SOT) caused by inserting the NiO layer at the Pt/Co interface. A similar Pt/NiO/Co structure was deposited on two different substrates, Al2O3 and Si/SiO x substrates. We found that the damping-like torque of the Al2O3 type sample is almost independent of NiO thickness (t NiO) when t NiO < 2 nm, while that of Si/SiO x type monotonically decreased with increasing t NiO. The X-ray diffraction measurement revealed that the degree of interface roughness varies between these types. This suggests that the effect of the NiO insertion on the SOT is associated with the interface roughness.

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.

Quantifying Spin-Orbit Torques in Antiferromagnet-Heavy-Metal Heterostructures.

The effect of spin currents on the magnetic order of insulating antiferromagnets (AFMs) is of fundamental interest and can enable new applications. Toward this goal, characterizing the spin-orbit torques (SOTs) associated with AFM-heavy-metal (HM) interfaces is important. Here we report the full angular dependence of the harmonic Hall voltages in a predominantly easy-plane AFM, epitaxial c-axis oriented α-Fe_{2}O_{3} films, with an interface to Pt. By modeling the harmonic Hall signals together with the α-Fe_{2}O_{3} magnetic parameters, we determine the amplitudes of fieldlike and dampinglike SOTs. Out-of-plane field scans are shown to be essential to determining the dampinglike component of the torques. In contrast to ferromagnetic-heavy-metal heterostructures, our results demonstrate that the fieldlike torques are significantly larger than the dampinglike torques, which we correlate with the presence of a large imaginary component of the interface spin-mixing conductance. Our work demonstrates a direct way of characterizing SOTs in AFM-HM heterostructures.

Enhancement of spin-orbit torque efficiency by tailoring interfacial spin-orbit coupling in Pt-based magnetic multilayers

We study inserting Co layer thickness-dependent spin transport and spin–orbit torques (SOTs) in the Pt/Co/Py trilayers by spin-torque ferromagnetic resonance. The interfacial perpendicular magnetic anisotropy (IPMA) energy density (K s = 2.7 erg/cm2, 1 erg = 10−7 J), which is dominated by interfacial spin–orbit coupling (ISOC) in the Pt/Co interface, total effective spin-mixing conductance ) and two-magnon scattering (β TMS = 0.46 nm2) are first characterized, and the damping-like torque (ξ DL = 0.103) and field-like torque (ξ FL = –0.017) efficiencies are also calculated quantitatively by varying the thickness of the inserting Co layer. The significant enhancement of ξ DL and ξ FL in Pt/Co/Py than Pt/Py bilayer system originates from the interfacial Rashba–Edelstein effect due to the strong ISOC between Co-3d and Pt-5d orbitals at the Pt/Co interface. Additionally, we find a considerable out-of-plane spin polarization SOT, which is ascribed to the spin anomalous Hall effect and possible spin precession effect due to IPMA-induced perpendicular magnetization at the Pt/Co interface. Our results demonstrate that the ISOC of the Pt/Co interface plays a vital role in spin transport and SOTs-generation. Our finds offer an alternative approach to improve the conventional SOTs efficiencies and generate unconventional SOTs with out-of-plane spin polarization to develop low power Pt-based spintronic via tailoring the Pt/FM interface.

Bifurcation of a topological skyrmion string

Manipulation of three-dimensional (3D) topological objects is of both fundamental interest and practical importance in many branches of physics. Here, we show by spin dynamics simulations that the bifurcation of a 3D skyrmion string in a layered frustrated system could be induced by the dampinglike spin-orbit torque. The bifurcation of a skyrmion string happens when the skyrmion string carries a minimal topological charge of $Q=2$. We demonstrate that three types of bifurcations could be realized by applying different current injection geometries, which lead to the transformation from I-shaped skyrmion strings to Y-, X-, and O-shaped ones. Besides, different branches of a bifurcated skyrmion string may merge into an isolated skyrmion string spontaneously. The mechanism of bifurcation should be universal to any skyrmion strings with $Q\geq 2$ in the layered frustrated system and could offer a general approach to manipulate 3D stringlike topological objects for spintronic functions.

Sign Change of Spin-Orbit Torque in Pt/NiO/CoFeB Structures.

Antiferromagnetic insulators have recently been proved to support spin current efficiently. Here, we report the dampinglike spin-orbit torque (SOT) in Pt/NiO/CoFeB has a strong temperature dependence and reverses the sign below certain temperatures, which is different from the slight variation with temperature in the Pt/CoFeB bilayer. The negative dampinglike SOT at low temperatures is proposed to be mediated by the magnetic interactions that tie with the "exchange bias" in Pt/NiO/CoFeB, in contrast to the thermal-magnon-mediated scenario at high temperatures. Our results highlight the promise to control the SOT through tuning the magnetic structure in multilayers.

Tilted spin current generated by the collinear antiferromagnet ruthenium dioxide

We report measurements demonstrating that when the Neel vector of the collinear antiferromagnet RuO2 is appropriately canted relative to the sample plane, the antiferromagnet generates a substantial out of plane damping-like torque. The measurements are in good accord with predictions that when an electric field, E is applied to the spin split band structure of RuO2 it can cause a strong transverse spin current even in the absence of spin-orbit coupling. This produces characteristic changes in all three components of the E induced torque vector as a function of the angle of E relative to the crystal axes, corresponding to a spin current with a well defined tilted spin orientation s approximately (but not exactly) parallel to the Neel vector, flowing perpendicular to both E and S. This angular dependence is the signature of an antiferromagnetic spin Hall effect with symmetries that are distinct from other mechanisms of spin-current generation reported in antiferromagnetic or ferromagnetic materials.

Finite element modeling of spin–orbit torques

Using a spin drift–diffusion model for coupled spin and charge transport, including the spin Hall effect and the inverse spin Hall effect, spin–orbit torques acting on the magnetization in heavy metal/ferromagnet bilayers are evaluated employing a finite element approach. The behavior of the resulting spin accumulation and torques is analyzed for different magnetization orientations of the ferromagnetic layer and varying thicknesses of the heavy metal layer. A strong damping-like torque component, consistent with experimental results, is observed. In addition, sub-ns switching simulations based on solving the Landau–Lifshitz–Gilbert equation are demonstrated.

Current-induced out-of-plane torques in a single permalloy layer with lateral structural asymmetry

We investigated current-induced torques in a single permalloy layer connected to nonmagnetic electrodes with lateral inversion asymmetry by spin-torque ferromagnetic resonance. Considering the symmetry of the spin-torque ferromagnetic resonance spectrum with respect to the magnetic field direction, we successfully separated various types of torque. In addition to in-plane damping-like and field-like torques, we detected two additional components of out-of-plane (OOP) torques, the symmetries of which with respect to the magnetic field direction correspond to an OOP field-like torque and an OOP damping-like torque. We obtained the OOP torques in particular by breaking a lateral inversion symmetry of the nonmagnetic electrodes, and the sign of the torques is reversed by inverting the electrode structure. The microwave frequency dependence of the OOP torques indicates that the OOP torques are not attributable to a spin current but to the Oersted field generated by a nonuniform charge current, ${B}_{\mathrm{Oersted}}$, and an inductive field, ${B}_{\mathrm{induc}.}$ (which originates from ${B}_{\mathrm{Oersted}}$). We propose an external field-free and fast magnetization switching of a ferromagnetic layer with perpendicular magnetic anisotropy by using ${B}_{\mathrm{induc}.}$, which can be achieved only by fabricating the electrodes asymmetrically.

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.

All-Electrical Control of Compact SOT-MRAM: Toward Highly Efficient and Reliable Non-Volatile In-Memory Computing.

Two-dimensional van der Waals (2D vdW) ferromagnets possess outstanding scalability, controllable ferromagnetism, and out-of-plane anisotropy, enabling the compact spintronics-based non-volatile in-memory computing (nv-IMC) that promises to tackle the memory wall bottleneck issue. Here, by employing the intriguing room-temperature ferromagnetic characteristics of emerging 2D Fe3GeTe2 with the dissimilar electronic structure of the two spin-conducting channels, we report on a new type of non-volatile spin-orbit torque (SOT) magnetic tunnel junction (MTJ) device based on Fe3GeTe2/MgO/Fe3GeTe2 heterostructure, which demonstrates the uni-polar and high-speed field-free magnetization switching by adjusting the ratio of field-like torque to damping-like torque coefficient in the free layer. Compared to the conventional 2T1M structure, the developed 3-transistor-2-MTJ (3T2M) cell is implemented with the complementary data storage feature and the enhanced sensing margin of 201.4% (from 271.7 mV to 547.2 mV) and 276% (from 188.2 mV to 520 mV) for reading “1” and “0”, respectively. Moreover, superior to the traditional CoFeB-based MTJ memory cell counterpart, the 3T2M crossbar array architecture can be executed for AND/NAND, OR/NOR Boolean logic operation with a fast latency of 24 ps and ultra-low power consumption of 2.47 fJ/bit. Such device to architecture design with elaborated micro-magnetic and circuit-level simulation results shows great potential for realizing high-performance 2D material-based compact SOT magnetic random-access memory, facilitating new applications of highly reliable and energy-efficient nv-IMC.

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 ${\mathrm{Mn}}_{2}\mathrm{Au}$.

Effect of interfacial intermixing on spin-orbit torque in Co/Pt bilayers

Using the first-principles non-equilibrium Green's function technique with supercell disorder averaging, we study the influence of interfacial intermixing on the spin-orbit torque in Co$\mid$Pt bilayers. Intermixing is modeled by inserting one or more monolayers of a disordered CoPt alloy between Co and Pt. Dampinglike torque is moderately enhanced by interfacial intermixing, while the fieldlike torque, which is small for abrupt interfaces, is strongly enhanced and becomes comparable to the dampinglike torque. The enhancement of the fieldlike torque is attributed to the interface between Co and the intermixed region. The planar Hall-like torque increases with intermixing but remains relatively small. The behavior of the torques is similar for bilayers with (111) and (001)-oriented interfaces. Strong dependence of the fieldlike torque on intermixing could provide a way to tune the fieldlike-to-dampinglike torque ratio by interface engineering.