Harmonic Hall Measurements Research Articles

An energy efficient way for quantitative magnetization switching

Recent advancements in electrically controlled spin devices have been made possible through the use of multiferroic systems comprising ferroelectric (FE) and ferromagnetic (FM) materials. This progress provides a promising avenue for developing energy-efficient devices that allow for electrically controlled magnetization switching. In this study, we fabricated spin orbit torque (SOT) devices using multiferroic composites and examined the angular dependence of SOT effects on localized in-plane strain induced by an out-of-plane electric field applied to the piezoelectric substrate. The induced strain precisely modulates magnetization switching via the SOT effect in multiferroic heterostructures, which also exhibit remarkable capability to modulate strain along different orientations – a feature with great potential for future applications in logic device arrays. To investigate the influence of electric fields on magnetization switching, harmonic Hall measurements, synchrotron-powered x-ray magnetic circular dichroism-photoemission electron microscopy (XMCD-PEEM), x-ray diffraction (XRD), magnetic force microscopy (MFM), and micromagnetic simulation were conducted. The results demonstrate that electric-field-induced strain enables precise control of SOT-induced magnetization switching with significantly reduced energy consumption, making it highly suitable for next-generation spin logic devices.

Large out-of-plane spin–orbit torque in topological Weyl semimetal TaIrTe4

The unique electronic properties of topological quantum materials, such as protected surface states and exotic quasiparticles, can provide an out-of-plane spin-polarized current needed for external field-free magnetization switching of magnets with perpendicular magnetic anisotropy. Conventional spin–orbit torque (SOT) materials provide only an in-plane spin-polarized current, and recently explored materials with lower crystal symmetries provide very low out-of-plane spin-polarized current components, which are not suitable for energy-efficient SOT applications. Here, we demonstrate a large out-of-plane damping-like SOT at room temperature using the topological Weyl semimetal candidate TaIrTe4 with a lower crystal symmetry. We performed spin–torque ferromagnetic resonance (STFMR) and second harmonic Hall measurements on devices based on TaIrTe4/Ni80Fe20 heterostructures and observed a large out-of-plane damping-like SOT efficiency. The out-of-plane spin Hall conductivity is estimated to be (4.05 ± 0.23)×104 (ℏ ⁄ 2e) (Ωm)−1, which is an order of magnitude higher than the reported values in other materials.

Quantifying the large contribution from orbital Rashba–Edelstein effect to the effective damping-like torque on magnetization

The generation of large spin currents, and the associated spin torques, which are at the heart of modern spintronics, has long been achieved by charge-to-spin conversion mechanisms, i.e., the spin Hall effect and/or the Rashba–Edelstein effect, intrinsically linked to strong spin–orbit coupling. Recently, a novel path has been predicted and observed for achieving significant current-induced torques originating from light elements, hence possessing weak spin–orbit interaction. These findings point out to the potential involvement of the orbital counterpart of electrons, namely the orbital Hall and orbital Rashba–Edelstein effects. In this study, we aim at quantifying these orbital-related contributions to the effective torques acting on a thin Co layer in different systems. First, we demonstrate in Pt|Co|Cu|AlOx stacking a comparable torque strength coming from the conversion due to the orbital Rashba–Edelstein effect at the Cu|AlOx interface and the one from the effective spin Hall effect in the bottom Pt|Co system. Second, in order to amplify the orbital-to-spin conversion, we investigate the impact of an intermediate Pt layer in Co|Pt|Cu|CuOx. From the Pt thickness dependence of the effective torques determined by harmonic Hall measurements complemented by spin Hall magneto-resistance and THz spectroscopy experiments, we demonstrate that a large orbital Rashba–Edelstein effect is present at the Cu|CuOx interface, leading to a twofold enhancement of the net torques on Co for the optimal Pt thickness. Our findings not only demonstrate the crucial role that orbital currents can play in low-dimensional systems with weak spin–orbit coupling but also reveal that they enable more energy efficient manipulation of magnetization in spintronic devices.

Effects of post-growth annealing in YPtBi topological semimetal and Co/Pt perpendicular magnetization multilayers

We investigated the effects of post-annealing on the magnetic properties and spin orbit torque (SOT) in CoPt/YPtBi heterostructures, where YPtBi is a topological semimetal with a large spin Hall angle. From crystal structure analysis by X-ray diffraction and transmission electron microscopy, magnetization, anomalous Hall resistance, and second harmonic Hall measurements, we found that the magnetic properties and SOT performance in CoPt/YPtBi are improved by post-growth annealing up to 300 °C, while they are degraded after 350 °C annealing due to intermixing and alloying. By comparative experiments using CoPt/W, we show that YPtBi is more resistive to intermixing and alloying with CoPt than W.

Highly Efficient Spin-Orbit Torque Switching in Bi2Se3/Fe3GeTe2 van der Waals Heterostructures.

Topological insulators (TIs) have shown promise as a spin-generating layer to switch the magnetization state of ferromagnets via spin-orbit torque (SOT) due to charge-to-spin conversion efficiency of the TI surface states that arises from spin-momentum locking. However, when TIs are interfaced with conventional bulk ferromagnetic metals, the combination of charge transfer and hybridization can potentially destroy the spin texture and hamper the possibility of accessing the TI surface states. Here, we fabricate an all van der Waals (vdW) heterostructure consisting of molecular beam epitaxy grown bulk-insulating Bi2Se3 and exfoliated 2D metallic ferromagnet Fe3GeTe2 (FGT) with perpendicular anisotropy. By detecting the magnetization state of the FGT via anomalous Hall effect and magneto-optical Kerr effect measurements, we determine the critical switching current density for magnetization switching to be Jc ≈ 1.2 × 106 A/cm2, the lowest reported for the switching of a perpendicular anisotropy ferromagnet using Bi2Se3. From second harmonic Hall measurements, we further determine the SOT efficiency (ξDL) to be in the range of 1.8 ± 0.3 and 1.4 ± 0.08 between 5 and 150 K, comparable to the highest values reported for Bi2Se3. Our density functional theory calculations find that the weak interlayer interactions at the Bi2Se3/FGT interface lead to a weakened dipole at the interface and suppress the proximity induced magnetic moment on Bi2Se3. This enables direct access to the TI surface states contributed by the first quintuple layer, where the spins are singly degenerate with significant net in-plane spin polarization. Our results highlight the clear advantage of all-vdW heterostructures with weak interlayer interactions that can enhance SOT efficiency and minimize critical current density, an important step toward realizing next generation low-power nonvolatile memory and spintronic devices.

Quantitative characterization of current-induced self-spin–orbit torques in a perpendicularly magnetized (Ga,Mn)As single thin film

Quantitative characterizations of the current-induced spin–orbit torques (SOTs) are vitally important for both fundamental understanding and practical applications of SOT-based spintronic devices. Here, we study effective SOT magnetic fields in a (Ga,Mn)As single film with perpendicular magnetic anisotropy, where we can achieve highly efficient full-magnetization switching with a small critical switching current density Jc as low as 105 A/cm2. Using second harmonic Hall measurements, we estimate the SOT effective fields; the damping-like SOT effective field HDL and the field-like SOT effective field HFL are 22.1 and 18.1 Oe, respectively, at 4 K when a current of 1.43 × 105 A/cm2 is applied to the device. Based on this result, we estimate the corresponding spin-torque efficiencies ξDL and ξFL to be 1.32 and 1.08, respectively, which are one order of magnitude higher than those in conventional metal systems. The high efficiency can be partly attributed to the simple single-functional-layer structure, which can avoid the loss from spin scattering at the interface between different functional layers as observed in conventional SOT devices. Our findings will lay the foundation for studying SOT physics and devices based on ferromagnetic semiconductors.

Spin–orbit torque in perpendicularly magnetized [Pt/Ni] multilayers

The performance of spin–orbit torque (SOT) in heavy metal/ferromagnetic metal periodic multilayers has attracted widespread attention. In this paper, we have successfully fabricated a series of perpendicular magnetized [Pt(2–t)/Ni(t)]4 multilayers, and studied the SOT in the multilayers by varying the thickness of Ni layer t. The current induced magnetization switching was achieved with a critical current density of 1 × 107 A/cm2. The damping-like SOT efficiency ξ DL was extracted from an extended harmonic Hall measurement. We demonstrated that the ξ DL can be effectively modulated by t Pt/t Ni ratio of Pt and Ni in the multilayers. The SOT investigation about the [Pt/Ni] N multilayers might provide new material candidates for practical perpendicular SOT-MRAM devices.

Spin current generation from an epitaxial tungsten dioxide WO2

We report on efficient spin current generation at room temperature in rutile-type WO2 grown on an Al2O3(0001) substrate. The optimal WO2 film has a (010)-oriented monoclinically distorted rutile structure with metallic conductivity due to 5d2 electrons, as characterized by x-ray diffraction, electronic transport, and x-ray photoelectron spectroscopy. By conducting harmonic Hall measurement in a Ni81Fe19/WO2 bilayer, we estimate two symmetries of the spin–orbit torque (SOT), i.e., dampinglike (DL) and fieldlike ones, to find that the former is larger than the latter. By comparison with the Ni81Fe19/W control sample, the observed DL SOT efficiency ξDL of WO2 (+0.174) is about two-thirds of that of W (−0.281) in magnitude, with a striking difference in their signs. The magnitude of the ξDL of WO2 exhibits a comparable value to those of widely reported Pt and Ta, and Ir oxide IrO2. The positive sign of the ξDL of WO2 can be explained by the preceding theoretical study based on the 4d oxides. These results highlight that the epitaxial WO2 offers a great opportunity of rutile oxides with spintronic functionalities, leading to future spin–orbit torque-controlled devices.

Observation of large spin conversion anisotropy in bismuth

While the effective g-factor can be anisotropic due to the spin-orbit interaction (SOI), its existence in solids cannot be simply asserted from a band structure, which hinders progress on studies from such viewpoints. The effective g-factor in bismuth (Bi) is largely anisotropic; especially for holes at T-point, the effective g-factor perpendicular to the trigonal axis is negligibly small (<0.112), whereas the effective g-factor along the trigonal axis is very large (62.7). We clarified in this work that the large anisotropy of effective g-factor gives rise to the large spin conversion anisotropy in Bi from experimental and theoretical approaches. Spin-torque ferromagnetic resonance was applied to estimate the spin conversion efficiency in rhombohedral (110) Bi to be 17 to 27%, which is unlike the negligibly small efficiency in Bi(111). Harmonic Hall measurements supportthelarge spin conversion efficiency in Bi(110). A large spin conversion anisotropy as the clear manifestation of the anisotropy of the effective g-factor is observed. Beyond the emblematic case of Bi, our study unveiled the significance of the effective g-factor anisotropy in condensed-matter physics and can pave a pathway toward establishing novel spin physics under g-factor control.

Strong higher-order angular dependence of spin-orbit torque in W/CoFeB bilayer

The symmetry of normal metal/ferromagnet bilayers allows spin-orbit torques (SOTs) to simultaneously have two distinct angular dependences on the magnetization direction $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathrm{m}}$. The most well-studied forms of SOT consist of the conventional fieldlike and dampinglike torques, which we label as ``lowest-order'' SOT. There are additional SOT forms associated with spin polarization different from that of the lowest-order SOT, and which contain an extra factor of $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathrm{m}}$ dependence. We label these as ``higher-order'' SOT. Understanding SOT-driven magnetization dynamics requires detailed information about the full angular dependence. In this paper, we measure both the lowest-order and higher-order angular dependences of SOTs in three types of bilayers, Pt/Co, Ta/CoFeB, and W/CoFeB, using harmonic Hall measurements. It is found that the higher-order SOT is negligible for Pt/Co and Ta/CoFeB, whereas it is dominant over the lowest-order one for W/CoFeB. Macrospin simulations show that the higher-order SOT can significantly affect the magnetization dynamics, which is qualitatively in line with SOT-induced switching experiments.

Giant response to spin-orbit torques in heavy-metal/ferromagnetic bilayers associated with magnetic reversal

Using bilayer films of $\ensuremath{\beta}$-Ta (5 nm)/${\mathrm{Ni}}_{0.8}{\mathrm{Fe}}_{0.2}$ (2 nm), we fabricate elliptical structures which exhibit uniaxial magnetic anisotropy, resulting in single magnetic domain behavior. We study induced spin-orbit torques (SOTs) in these devices with first- and second-order harmonic Hall measurements for current flowing along the long axis of the ellipses and external magnetic field applied in the film plane. We observe a giant response to the SOTs associated with magnetization reversal of the NiFe layer, and we correlate it quantitatively with a $d{\ensuremath{\varphi}}_{m}/d{\ensuremath{\varphi}}_{H}$ term, where ${\ensuremath{\varphi}}_{m}$ and ${\ensuremath{\varphi}}_{H}$ are the in-plane angles of the magnetization and the magnetic field, respectively. We discuss theoretical and applicative implications of this intriguing behavior.

Large Exotic Spin Torques in Antiferromagnetic Iron Rhodium

Spin torque is a promising tool for driving magnetization dynamics for computing technologies. These torques can be easily produced by spin-orbit effects, but for most conventional spin source materials, a high degree of crystal symmetry limits the geometry of the spin torques produced. Magnetic ordering is one way to reduce the symmetry of a material and allow exotic torques, and antiferromagnets are particularly promising because they are robust against external fields. We present spin torque ferromagnetic resonance (ST-FMR) measurements and second harmonic Hall measurements characterizing the spin torques in antiferromagnetic iron rhodium alloy. We report extremely large, strongly temperature-dependent exotic spin torques with a geometry apparently defined by the magnetic ordering direction. We find the spin torque efficiency of iron rhodium to be (207 \ifmmode\pm\else\textpm\fi{} 94)% at 170 K and (88 \ifmmode\pm\else\textpm\fi{} 32)% at room temperature. We support our conclusions with theoretical calculations showing how the antiferromagnetic ordering in iron rhodium gives rise to such exotic torques.

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.

Spin–orbit torque generation in bilayers composed of CoFeB and epitaxial SrIrO3 grown on an orthorhombic DyScO3 substrate

We report on the highly efficient spin–orbit torque (SOT) generation in epitaxial SrIrO3 (SIO), which is grown on an orthorhombic DyScO3(110) substrate. By conducting harmonic Hall measurement in Co20Fe60B20 (CoFeB)/SIO bilayers, we characterize two kinds of the SOTs, i.e., dampinglike (DL) and fieldlike ones to find that the former is much larger than the latter. By comparison with the Pt control sample with the same CoFeB thickness, the observed DL SOT efficiency ξDL of SIO (∼0.32) is three times higher than that of Pt (∼0.093). The ξDL is nearly constant as a function of the CoFeB thickness, suggesting that the SIO plays a crucial role in the large SOT generation. These results on the CoFeB/SIO bilayers highlight that the epitaxial SIO is promising for low-current and reliable spin–orbit torque-controlled devices.

Continuous film spin–orbit torque characterization via four probe measurement

Spin–orbit torque (SOT) characterization techniques generally require the Hall cross that generally demands lithography resources and time. It is highly desirable to characterize SOT efficiencies with minimal sample processing time. Here, we demonstrate a lithography-free technique to determine the spin–orbit torque efficiency in a perpendicular magnetic anisotropy ferromagnetic heterostructure. By utilizing a customized four-point probe in a rhombus geometry, harmonic Hall measurement was performed on continuous films of a Pt/Co/Ti structure to characterize the spin–orbit torque efficiency. A correction factor, which is due to the non-uniform current distribution across the continuous film, was experimentally evaluated by taking the ratio of the measured damping-like field of the continuous film to that of a fabricated Hall device. Additionally, this correction factor is analytically derived and experimentally shown to be determined by the configuration of the probes and is independent of the structure material. Our measurement reveals that by performing a single calibration process for the particular set of probes, the same correction factor was validated on a second ferromagnetic heterostructure, Ti/Pt/Co/Ta; hence, it can be applied to other SOT films' stack measurements. Our four-probe harmonic Hall technique provides an alternative and swift way for SOT investigations by eliminating multiple lithography processes necessary in conventional approaches.

Generation and Detection of Dresselhaus‐Like Spin Current in a Single‐Crystal Ferromagnetic Metal

AbstractDistinct from the existing spin–orbit torque devices to only generate Rashba‐like spin current, it is proposed to generate Dresselhaus‐like spin current based on a single‐crystal ferromagnetic metal. By employing the second harmonic Hall measurement, it is found that the second harmonic Hall signal in single‐crystal ferromagnet exhibits an antisymmetric angular dependence induced by Dresselhaus‐like spin current, opposite to the reported symmetric angular dependence induced by Rashba‐like spin current. Such anomalous Dresselhaus‐like spin current is further confirmed by the current‐induced shift of the hysteresis loop when the magnetic field is swept along the current direction. However, when the ferromagnetic metal exhibits amorphous crystal structure or polycrystal structure, the Dresselhaus‐like spin current is absent. This result complements the missing type of spin currents due to charge‐to‐spin conversion and benefits the formulation of comprehensive spin–orbit coupling mechanism, by considering additional broken symmetry caused by ferromagnetic order and the structure symmetry of the crystalline lattice.

Room-Temperature Nonreciprocal Charge Transport in an InAs-Based Rashba Channel

Nonreciprocal charge transport is observed in a non-centrosymmetric system without a ferromagnetic layer. To observe the nonreciprocity of the Rashba system, an InAs-based two-dimensional electron gas channel is utilized and the angular dependent harmonic Hall measurement is performed. From the amplitude of the curve, a nonreciprocal coefficient of 1.36 A−1T−1 is extracted at 1.9 K. While the extracted value of the nonreciprocal coefficient decreases down to 0.44 A−1T−1 at 300 K, we can clearly observe the nonreciprocal charge transport at room temperature. In addition, the independent transport measurements clarify that the amplitude of nonreciprocal coefficient is closely connected with the strength of the Rashba effect.

Enhanced Spin-Orbit Torque and Low Critical Current Density in Pt100-xRux/[CoNi]/Ru Multilayer for Spintronic Devices.

Using a heavy-metal (HM) alloy layer in spin-orbit torque (SOT)-based devices is an effective method for obtaining a high current-spin conversion efficiency θSH. In this work, SOT-based spintronic devices with a Pt100-xRux-alloyed HM layer are studied by applying harmonic Hall measurements and magneto-optical Kerr effect microscopy to detect the θSH and to observe the process of current-induced magnetization switching. Both the highest θSH of 0.132 and the lowest critical current density (Jc) of 8 × 105 A/cm2 are realized in a device with x = 20, which satisfies the high SOT efficiency and low energy consumption simultaneously. The interfacial Dzyaloshinskii-Moriya interaction can be overcome by increasing the in-plane assist field. Meanwhile, the minimum in-plane field required for current-induced complete switching can be reduced to ±60 Oe. Our study reveals that using the Pt-Ru alloyed HM layer is an effective route for SOT application with enhanced performance.

Direct spin accumulation quantification in ferromagnetic heterostructures using DC bias harmonic Hall measurement

A technique for spin accumulation quantification, specifically in the ferromagnetic layer of spin-orbit torque inducing heterostructures has been elusive. Here, we demonstrate an easy-to-implement technique to achieve this quantification by applying an additional DC bias during the harmonic Hall measurement in Si/${\mathrm{SiO}}_{2}$/Ta/Co/Pt. The spin accumulation arising from the DC bias generates an amplitude offset detectable in the first harmonic Hall magnetoresistance. By performing the first harmonic Hall magnetoresistance measurement under a fixed DC bias for two oppositely magnetized states, spin accumulation polarity set by the DC bias enhances the magnetoresistance if it aligns with the magnetization, and vice versa. Thus, the difference in the magnetoresistance amplitude provides the quantitative magnitude of spin accumulation relative to the ferromagnet's saturation magnetization, measured to be up to 0.29% in Si/${\mathrm{SiO}}_{2}$/Ta/Co/Pt. The strength of both spin accumulation and dampinglike efficiency increased with Ta thickness, further verifying our experimental technique.

Spin–orbit torque magnetization switching in a perpendicularly magnetized full Heusler alloy Co2FeSi

To optimize the writing and reading performance of magnetic random-access memory (MRAM) devices, achieving current-induced spin–orbit torque (SOT) magnetization switching in perpendicularly magnetized full Heusler alloys is vitally important. For conventional SOT-metal bilayer systems, heavy metals (HMs) with a large spin Hall angle (θSH) are generally used for generating a spin current, which is injected into the adjacent ferromagnet (FM) layer and exerts a torque on the magnetization to switch it. However, the large resistivity of generally used HMs such as β-Ta and β-W can increase the Ohmic loss. In this article, we achieve full SOT switching in Heusler alloy Co2FeSi using low-resistivity Pd as a spin current generation source. The critical switching current density is found to be 3.7 × 107 A cm−2, which is in the same order of magnitude as that required for conventional HM/FM systems even though Pd has a smaller θSH than that of generally used HMs. Using harmonic Hall measurements, the damping-like and field-like effective fields per unit current density are estimated to be 56.9 (10−7 Oe A−1 cm2) and 39.8 (10−7 Oe A−1 cm2), respectively. This high efficiency can be attributed to the excellent lattice matching between Co2FeSi and Pd (only 2% mismatch), to a slight Pd diffusion, and possibly to the additional SOTs induced by the in-plane spin component generated in the Co2FeSi layer. Our finding will advance the development of SOT-MRAM devices with both better reading and writing performance.