Field-like Torque Research Articles

Non-Negligible Imaginary Part of the Spin-Mixing Conductance and its Impact on Magnetization Dynamics in Heavy-Metal–Ferromagnet Bilayers

In this paper we present experimental verification of the magnitude of the imaginary part of the spin-mixing conductance in bilayers comprising heavy metals. We present results of broadband ferromagnetic resonance studies on heterostructures consisting of Finemet (${\mathrm{Fe}}_{66.5}{\mathrm{Cu}}_{1}{\mathrm{Nb}}_{3}{\mathrm{Si}}_{13.5}{\mathrm{B}}_{6}{\mathrm{Al}}_{7}$) thin films covered by $\mathrm{Pt}$ and $\mathrm{Ta}$ wedge layers with the aim of observing spin-pumping effects and evaluating both the real ($\mathrm{Re}[{g}_{\mathrm{eff}}^{\ensuremath{\uparrow}\ensuremath{\downarrow}}]$) and imaginary ($\mathrm{Im}[{g}_{\mathrm{eff}}^{\ensuremath{\uparrow}\ensuremath{\downarrow}}]$) parts of the spin-mixing conductance. In particular, we show that the imaginary part of the spin-mixing conductance cannot be regarded as negligible, and we discuss its influence on magnetization dynamics. For Finemet/$\mathrm{Ta}$ bilayers, the ratio $\mathrm{Re}[{g}_{\mathrm{eff}}^{\ensuremath{\uparrow}\ensuremath{\downarrow}}]/\mathrm{Im}[{g}_{\mathrm{eff}}^{\ensuremath{\uparrow}\ensuremath{\downarrow}}]=0.38$; that is, the fieldlike torque dominates over the dampinglike torque in such a system. The experimental results are analyzed in the framework of a recent microscopic theory that allows us to estimate the value of the interfacial spin-orbit interaction and confirm its important role. The role of material and interface parameters is also discussed.

Threshold Current Density for Perpendicular Magnetization Switching Through Spin-Orbit Torque

We theoretically investigate the threshold current density for spin-orbit-torque- (SOT) induced perpendicular magnetization switching. According to the relative sign of fieldlike torque (FLT) and dampinglike torque (DLT), we derive the corresponding analytical formulas of the threshold current density ${J}_{\mathrm{th}}$ required to switch magnetization from equilibrium states to nearly in-plane states. These formulas, which agree well with numerical results among a wide range of material parameters, indicate that SOT current density can be significantly reduced in the presence of a large FLT. The conditions are then explored to achieve complete magnetization reversal after removing the SOT currents. When the ratio of FLT to DLT \ensuremath{\eta} is negative in our sign convention, we find that SOT pulses with long enough fall time, for example, 0.2 ns in our simulations, can guarantee stable switching. In contrast, a small in-plane magnetic field or a large damping is necessary when \ensuremath{\eta} g 0. Based on the conditions, the measured threshold current densities in several reported experiments, which deviate from previous models, can be well reproduced by our derived ${J}_{\mathrm{th}}$. We further study the possible incubation delay induced by SOT, clarifying the recent contradiction on incubation time during SOT switching. Our work sheds insights on the SOT material optimization and the comprehension of magnetization switching dynamics induced by SOT.

Static and dynamic properties of bimerons in a frustrated ferromagnetic monolayer

Magnetic bimeron is a topological counterpart of skyrmions in in-plane magnets, which can be used as a spintronic information carrier. We report the static properties of bimerons with different topological structures in a frustrated ferromagnetic monolayer, where the bimeron structure is characterized by the vorticity $Q_{\text{v}}$ and helicity $\eta$. It is found that the bimeron energy increases with $Q_{\text{v}}$, and the energy of an isolated bimeron with $Q_{\text{v}}=\pm 1$ depends on $\eta$. We also report the dynamics of frustrated bimerons driven by the spin-orbit torques, which depend on the strength of the dampinglike and fieldlike torques. We find that the isolated bimeron with $Q_{\text{v}}=\pm 1$ can be driven into linear or elliptical motion when the spin polarization is perpendicular to the easy axis. We numerically reveal the damping dependence of the bimeron Hall angle driven by the dampinglike torque. Besides, the isolated bimeron with $Q_{\text{v}}=\pm 1$ can be driven into rotation by the dampinglike torque when the spin polarization is parallel to the easy axis. The rotation frequency is proportional to the driving current density. In addition, we numerically demonstrate the possibility of creating a bimeron state with a higher or lower topological charge by the current-driven collision and merging of bimeron states with different $Q_{\text{v}}$. Our results could be useful for understanding the bimeron physics in frustrated magnets.

Size dependent chaotic spin–orbit torque induced magnetization switching of a ferromagnetic layer with in-plane anisotropy

Understanding the magnetization switching dynamics induced by the spin–orbit torque (SOT) in a ferromagnetic layer is crucial to the design of the ultrafast and energy-saving spin–orbit torque magnetic random access memory. Here, we investigate the SOT switching dynamics of a ferromagnetic layer with in-plane anisotropy with various elliptic sizes in different easy-axis orientations using micro-magnetic simulations. The reliable and ultrafast magnetization switching can be realized by tilting the easy axis to an optimum angle with respect to the current injecting direction. The switching time, in general, decreases smoothly with an increasing current density, and the optimum tilting angle is determined for small device sizes with width smaller than 100 nm. This optimum angle is a small angle deviating from a case when the in-plane easy axis is orthogonal to the current direction. It depends on the size, the current density, and also the damping constant. However, with the device increasing to a certain size (e.g., 250 nm), especially at small tilting angles, we observe chaotic switching behavior where the switching times fluctuate locally with the current density. We attribute this size dependent chaotic switching phenomenon to the nucleation and formulation of complex multi-domains during switching. This chaotic phenomenon can be alleviated by enhancing the field-like torque in the device and thus decreasing the switching times. Consequently, the shape and size of the devices should be carefully taken into account while designing a practical fast switching and low power SOT device with in-plane anisotropy.

Spin-torque ferromagnetic resonance in electrochemically etched metallic device

We demonstrate the quantification of spin–orbit torque efficiencies using spin-torque ferromagnetic resonance (ST-FMR) combined with electrochemical etching of a Fe/Pt bilayer. The electrochemical etching of the ST-FMR device using an ionic liquid enables to study spin–orbit effective fields, as well as an Oersted field, by varying the ferromagnetic-layer thickness. This allows to disentangle the field-like (FL) effective field and Oersted field, enabling to determine the damping-like and FL torque efficiencies in the single device. This robust technique opens a possibility to explore the spin–orbit torques in exotic materials and systems.

Spin pumping and large field-like torque at room temperature in sputtered amorphous WTe2−x films

We studied the spin-to-charge and charge-to-spin conversion at room temperature in sputtered WTe2−x (x = 0.8) (t)/Co20Fe60B20(6 nm) heterostructures. Spin pumping measurements were used to characterize the spin-to-charge efficiency, and the spin efficiency was calculated to be larger than ∼0.035. Second harmonic Hall measurements were carried out to estimate the charge-to-spin conversion ratio. We found that the system exhibits a large field-like torque (spin torque efficiency ∼0.1) and small damping-like torque (spin torque efficiency ∼0.001) compared to those reported for heavy metals. High-resolution transmission electron microscopy images show that the WTe2−x layer is amorphous, which may enhance the spin swapping effect by inducing large interfacial spin–orbit scattering, thus contributing to a large field-like torque.

Deterministic field-free switching of a perpendicularly magnetized ferromagnetic layer via the joint effects of the Dzyaloshinskii–Moriya interaction and damping- and field-like spin–orbit torques: an appraisal

Field-free switching of a perpendicularly magnetized ferromagnetic layer by spin–orbit torque (SOT) from the spin Hall effect is of great interest in the applications of magnetic memory devices. In this paper we investigate by micromagnetic simulations the possibility of deterministic field-free switching by combining SOT with the Dzyaloshinskii–Moriya interaction (DMI). We confirmed that within a certain range of DMI values and charge current densities, it is possible to deterministically switch the magnetization without the assistance of an external magnetic field. SOT terms including Slonczewski-like (damping-like) torque and field-like torque (FLT) are considered when analyzing the SOT switching and domain wall dynamics. We show that the FLT could play an adverse role in blocking and slowing down the magnetization switching under certain cases of DMI and charge current-driven field-free switching. However, in other cases, FLT assists DMI in the deterministic field-free SOT switching. In addition, it is found that FLT can effectively expand the current density window for deterministic field-free SOT switching in the presence of DMI.

Nonlinear Anomalous Hall Effect for Néel Vector Detection.

Antiferromagnetic (AFM) spintronics exploits the Néel vector as a state variable for novel spintronic devices. Recent studies have shown that the fieldlike and antidamping spin-orbit torques (SOTs) can be used to switch the Néel vector in antiferromagnets with proper symmetries. However, the precise detection of the Néel vector remains a challenging problem. In this Letter, we predict that the nonlinear anomalous Hall effect (AHE) can be used to detect the Néel vector in most compensated antiferromagnets supporting the antidamping SOT. We show that the magnetic crystal group symmetry of these antiferromagnets combined with spin-orbit coupling produce a sizable Berry curvature dipole and hence the nonlinear AHE. As a specific example, we consider the half-Heusler alloy CuMnSb, in which the Néel vector can be switched by the antidamping SOT. Based on density-functional theory calculations, we show that the nonlinear AHE in CuMnSb results in a measurable Hall voltage under conventional experimental conditions. The strong dependence of the Berry curvature dipole on the Néel vector orientation provides a new detection scheme of the Néel vector based on the nonlinear AHE. Our predictions enrich the material platform for studying nontrivial phenomena associated with the Berry curvature and broaden the range of materials useful for AFM spintronics.

Spin–Orbit Torque Switching in Low-Damping Magnetic Insulators: A Micromagnetic Study

Magnetic insulators, in particular, rare-earth iron garnets, have low damping compared to metallic ferromagnetic materials due to lack of conduction electrons. In analogy to spin-transfer-torque devices, the low-damping nature is presumed to be an advantage for spintronic applications. We report that perpendicular magnetic anisotropy material with low damping actually does not favor reliable spin–orbit torque (SOT) switching. Increasing damping, introducing interfacial Dzyaloshinskii–Moriya interactions, or field-like torques may help SOT switching in some cases. Having notches in a nanometer-scale element, which is a more realistic size for practical applications, can also improve switching stability.

Modulation of field-like spin orbit torque in heavy metal/ferromagnet heterostructures.

Spin orbit torque (SOT) has drawn widespread attention in the emerging field of magnetic memory devices, such as magnetic random access memory (MRAM). To promote the performance of SOT-MRAM, most efforts have been devoted to enhance the SOT switching efficiency by improving the damping-like torque. Recently, some studies noted that the field-like torque also plays a crucial role in the nanosecond-timescale SOT dynamics. However, there is not yet an effective way to tune its relative amplitude. Here, we experimentally modulate the field-like SOT in W/CoFeB/MgO trilayers through tuning the interfacial spin accumulation. By performing spin Hall magnetoresistance measurement, we find that the CoFeB with enhanced spin dephasing, either generated from larger layer thickness or from proper annealing, can distinctly boost the spin absorption and enhance the interfacial spin mixing conductance Gr. While the damping-like torque efficiency increases with Gr, the field-like torque efficiency is found to decrease with it. The results suggest that the interfacial spin accumulation, which largely contributes to the field-like torque, is reduced by higher interfacial spin transparency. Our work shows a new path to further improve the performance of SOT-based ultrafast magnetic devices.

Effects of transition metal spacers on spin-orbit torques, spin Hall magnetoresistance, and magnetic anisotropy of Pt/Co bilayers

We studied the effect of inserting 0.5-nm-thick spacer layers (Ti, V, Cr, Mo, W) at the Pt/Co interface on the spin-orbit torques, the Hall effect, magnetoresistance, saturation magnetization, and magnetic anisotropy. We find that the dampinglike spin-orbit torque decreases substantially for all samples with a spacer layer compared to the reference Pt/Co bilayer, consistently with the opposite sign of the atomic spin-orbit coupling constant of the spacer elements relative to Pt. The reduction of the dampinglike torque is monotonic with atomic number for the isoelectronic $3d,4d$, and $5d$ elements, with the exception of V that has a stronger effect than Cr. The fieldlike spin-orbit torque almost vanishes for all spacer layers irrespective of their composition, suggesting that this torque predominantly originates at the Pt/Co interface. The anomalous Hall effect, magnetoresistance, and saturation magnetization are also all reduced substantially, whereas the sheet resistance is increased in the presence of the spacer layer. Finally, we evidence a correlation between the amplitude of the spin-orbit torques, the spin-Hall-like magnetoresistance, and the perpendicular magnetic anisotropy. These results highlight the significant influence of ultrathin spacer layers on the magnetotransport properties of heavy-metal/ferromagnetic systems.

Spin orbit torques in ferrimagnetic GdFeCo with various compositions

Compositional dependence of spin–orbit torque (SOT) of the bilayer comprised of Ta and ferrimagnetic GdFeCo was investigated. Critical current density of SOT switching Jsw of the GdFeCo/Ta bilayers did not vary with Gd composition x, and were found to exhibit roughly Jsw = 11 MA cm−2. Two orthogonal components of SOT, damping-like torque τDL and field-like torque τFL were estimated by measuring harmonic Hall resistance under in-plane fields parallel and perpendicular to the AC current, respectively. The absolute values of SOT, ∣τ DL∣ and ∣τFL∣, were confirmed to be roughly constant within 22 ≤ x ≤ 28. On the other hand, the sign of τFL changed across the compensation composition. These results suggest that the injected spin current is considered to exert a torque to the transition metal FeCo moment rather than to the rare earth Gd moment.

Detection of torque effects in Co/Pt via ferromagnetic resonance

Charge-current-induced torque effects on the magnetization dynamics of ferromagnetic/metal bilayer is interesting from the aspect of fundamental physics as well as the applications in spintronic devices. The torque-induced variation of damping constant of magnetization can be foreseen from the change of the linewidth of ferromagnetic resonance spectrum. The Oersted torque (τOe) and current-induced torque (τC) are induced by charge current; while the spin-orbit torque (τSO) and field-like torque (τFL) are induced by spin current. However, the torque effects often were hindered due to the heating-induced artifacts. In this work, we particularly pay attention to minimize the Joule heating effects in order to investigate the intrinsic torque effects in cobalt (Co)/platinum (Pt) bilayer with an applied charge current ranging from −60 to 60 mA. In this range, the Oersted field is estimated as 0.25 Oe which is much smaller than the experimental result of ΔHr (∼0.7 Oe), implying some contribution from the spin-current induced field like torque. The current-polarization-induced asymmetry of linewidth ΔW, ΔW≡W+Jc−W−Jc, increases from 0 to 0.15 with Jc changing from 0 to 60 mA, which is attributed to the spin-orbit torque.

Investigation of spin orbit torque driven dynamics in ferromagnetic heterostructures

We use time-resolved (TR) measurements based on the polar magneto-optical Kerr effect (MOKE) to study the magnetization dynamics excited by spin orbit torques in Py (Permalloy)/Pt and Ta/CoFeB bilayers. The analysis reveals that the field-like (FL) spin orbit torque (SOT) dominates the amplitude of the first oscillation cycle of the magnetization precession and the damping-like (DL) torque determines the final steady-state magnetization. In our bilayer samples, we have extracted the effective fields, hFL and hDL, of the two SOTs from the time-resolved magnetization oscillation spectrum. The extracted values are in good agreement with those extracted from time-integrated DCMOKE measurements, suggesting that the SOTs do not change at high frequencies. We also find that the amplitude ratio of the first oscillation to steady state is linearly proportional to the ratio hFL/hDL. The first oscillation amplitude is inversely proportional to, whereas the steady state value is independent of, the applied external field along the current direction.

Tunable damping-like and field-like spin-orbit-torque in Pt/Co/HfO2 films via interfacial charge transfer

The spin–orbit-torque (SOT) consists of dampinglike torque (DLT) and fieldlike torque (FLT), where the combined effects of these two torques need further consideration for efficient SOT switching. Here, the tunable correlation between the DLT and FLT is investigated in Pt/Co/HfO2 multilayers with different annealing temperatures (Ta). With increasing Ta, the FLT decreases monotonously, while both the sign and the magnitude of DLT are changed. Interfacial analysis results reveal that the tunable correlation of them is strongly dependent on the interfacial electron structure between the Co and HfO2 layer. The interfacial charge transfer between the Co, O, and Hf atoms could modify interfacial spin–orbit coupling and the crystal electric field (ECEF), which promotes the interface-generated SOT. This work demonstrates an effective method to tune the correlation of the two SOT components, a desirable feature which will be beneficial for the design of SOT-based devices.

Magnetodynamics in orthogonal nanocontact spin-torque nano-oscillators based on magnetic tunnel junctions

We demonstrate field and current controlled magnetodynamics in nanocontact spin-torque nano-oscillators based on orthogonal magnetic tunnel junctions. We systematically analyze the microwave properties (frequency f, linewidth Δf, power P, and frequency tunability df/dI) with their physical origins—perpendicular magnetic anisotropy, dampinglike and fieldlike spin transfer torque (STT), and voltage-controlled magnetic anisotropy (VCMA). These devices present several advantageous characteristics: high emission frequencies (f>20 GHz), high frequency tunability (df/dI=0.25 GHz/mA), and zero-field operation (f∼4 GHz). Furthermore, detailed investigation of f(H, I) reveals that df/dI is mostly governed by the large VCMA [287 fJ/(V m)], while STT plays a negligible role.

Spin-orbit torques from intrinsic spin-orbit couplings in a periodically buckled honeycomb lattice

In this paper, we study the spin-orbit torques (SOTs) originated from the spin-orbit coupling (SOC) of intrinsic type in a periodically buckled honeycomb nanoribbon such as silicene. Using the Green function formalism with density matrix expressions, we analyze the SOT contributions from the Fermi-level and -sea electrons. We find that the intrinsic-SOC-induced inverse spin galvanic effect generates spin accumulations perpendicular to the honeycomb plane. The anti-damping torque results purely from the Fermi-level contribution, while the field-like torque from both the Fermi-level and -sea contributions. At zero bias voltage, the SOT is symmetric with respect to the Fermi energy (i.e., an even function of the Fermi energy), whereas the presence of bias further introduces the anti-symmetric torque components. When the ferromagnet magnetization lies in the honeycomb plane, all Fermi-sea contributions disappear. The maximum SOT among different Fermi energies is also inspected. For large enough in-plane magnetization compared to the staggered potential, the field-like torque has a maximum at zero Fermi energy. When the magnetization is smaller than some value characterized by the intrinsic SOC, the maximum of the anti-damping torque occurs at the cross point of the two Dirac linear bands in the leads. More importantly, we find that the anti-damping torques responsible for magnetic switching as well as the torkance require staggered potential from an applied out-of-plane electric field, i.e., lattice buckling is essential to the switching. When the electric field is reversed, the anti-damping torque and the torkance are also reversed. Accordingly, full electric control of the SOTs can be realized in this buckled system.

Stabilization of the skyrmion crystal phase and transport in thin-film antiferromagnets

We investigate the formation and stability of the skyrmion crystal phase in antiferromagnetic thin films subjected to fieldlike torques such as, e.g., those induced by an electric current in CuMnAs and Mn$_{2}$Au via the inverse spin-galvanic effect. We show that the skyrmion lattice represents the ground state of the antiferromagnet in a substantial area of the phase diagram, parametrized by the staggered field and the (effective) uniaxial anisotropy constant. Skyrmion motion can be driven in the crystal phase by the spin transfer effect. In the metallic scenario, itinerant electrons experience an emergent SU$(2)$-electromagnetic field associated with the (N\'{e}el) skyrmion background, leading to a topological spin-Hall response. Experimental signatures of the skyrmion crystal phase and readout schemes based on topological transport are discussed.

Power and phase dynamics of injection-locked spin torque nano-oscillators under conservative and dissipative driving signals

To describe all possible injection locking configurations of spin torque nano-oscillators (STNO), previous analytical descriptions are extended by introducing the most general form of the driving force: ℱ ∝ +. We provide the expressions of the corresponding forcing functions ℱ for the six basic conservative and dissipative forcing torques (~ × and ~ × × with = , ,), and demonstrate at the example of a uniform in-plane magnetized STNO, that the general case (| | | |) as well as special cases, can occur depending on: (i) the nature of the forcing torque, (ii) the direction with respect to the equilibrium direction, (iii) the harmonic order and (iv) the operation point (dc current). These relations provide a straightforward means to analyze more complex forcing torques such as a rotating field or the superposition of damping-like and field-like spin transfer torques. Besides the phase properties we also address in detail the power properties of the injection locked state for which two new parameters are introduced: the locking power range and the power angle. They can provide important complementary information on the driving forces from experiment. The general description presented here is not limited to STNOs and is valid for any non-isochronous auto-oscillator driven by an elliptical forcing of conservative or dissipative nature.

Current-Induced Modulation of Coercive Field in the Ferromagnetic Oxide SrRuO3

We investigated the coercive field $H_{\text {c}}$ for domain wall (DW) motion as a function of the current ${I}$ in the ferromagnetic oxide SrRuO3, a model system with narrow DWs for fabricating high-density spintronics devices. The DW is moved by ${I}$ in the direction of the current, and $H_{\text {c}}$ is modulated linearly in ${I}$ . This linear relationship is consistent with an effective magnetic field $H_{\text {eff}}$ driving the DW. The direction of DW motion and the magnitude of $H_{\text {eff}}$ are well described by a model based on the field-like torque arising from the spin relaxation of conduction electrons in the DW.