We report measurements of the thickness and temperature (T) dependencies of current-induced spin-orbit torques, especially the field-like (FL) component, in various heavy metal (HM)/normal metal (NM) spacer/ferromagnet (FM)/Oxide (MgO and HfOx/MgO) heterostructures. The FL torque in these samples originates from spin current generated by the spin Hall effect (SHE) in the HM. For a FM layer sufficiently thin that a substantial portion of this spin current can reach the FM/Oxide interface, T-dependent spin scattering there can yield a strong FL torque that is, in some cases, opposite in sign to that exerted at the NM/FM interface.
The manipulation of magnetization in a metallic ferromagnet by using optical helicity has been much attracted attention for future opto-spintronic devices. The optical helicity induced torques on the magnetization, {\it optical spin torque}, have been observed in ferromagnetic thin films recently. However, the interfacial effect of the optical spin torque in ferromagnet/nonmagnetic heavy metal heterostructures have not been addressed so far, which are widely utilized to efficiently control magnetization via electrical means. Here, we studied optical spin torque vectors in the ferromagnet/nonma…
High-entropy alloy (HEA) is a family of metallic materials with nearly equal partitions of five or more metals, which might possess mechanical and transport properties that are different from conventional binary or tertiary alloys. In this work, we demonstrate current-induced spin-orbit torque (SOT) magnetization switching in a Ta-Nb-Hf-Zr-Ti HEA-based magnetic heterostructure with perpendicular magnetic anisotropy (PMA). The maximum damping-like SOT efficiency from this particular HEA-based magnetic heterostructure is further determined to be $|ζ^{\operatorname{HEA}}_{DL}|\approx0.033$ by hys…
In the last few years, some ideas of electric manipulations in ferromagnetic heterostructures have been proposed for developing next generation spintronic devices. Among them, the magnetization switching driven by spin-orbit torque (SOT) is being intensely pursued. Especially, how to control the switching current density, which is expected to enrich device functionalities, has aroused much interest among researchers all over the world. In this paper, a novel method to adjust the switching current is proposed, and the BiFeO3 (BFO) based heterostructures with opposite spontaneous polarizations f…
Electrical currents in a magnetic insulator/heavy metal heterostructure can induce two simultaneous effects, namely, spin Hall magnetoresistance (SMR) on the heavy metal side and spin-orbit torques (SOTs) on the magnetic insulator side. Within the framework of the pure spin current model based on the bulk spin Hall effect (SHE), the ratio of the spin Hall-induced anomalous Hall effect (SH-AHE) to SMR should be equal to the ratio of the field-like torque (FLT) to damping-like torque (DLT). We perform a quantitative study of SMR, SH-AHE, and SOTs in a series of thulium iron garnet/platinum or Tm…
Spin-orbit torque facilitates efficient magnetization switching via an in-plane current in perpendicularly magnetized heavy metal/ferromagnet heterostructures. The efficiency of spin-orbit-torque-induced switching is determined by the charge-to-spin conversion arising from either bulk or interfacial spin-orbit interactions, or both. Here, we demonstrate that the spin-orbit torque and the resultant switching efficiency in Pt/CoFeB systems are significantly enhanced by an interfacial modification involving Ti insertion between the Pt and CoFeB layers. Spin pumping and X-ray magnetic circular dic…
The giant spin Hall effect in magnetic heterostructures along with low spin memory loss and high interfacial spin mixing conductance are prerequisites to realize energy efficient spin torque based logic devices. We report giant spin Hall angle (SHA) of 28.67 (5.09) for W (Ta) interfaced epi- Co60Fe40/TiN structures. The spin-orbit torque switching current density (J_Crit) is as low as 1.82 (8.21) MA/cm2 in W (Ta)/Co60Fe40(t_CoFe)/TiN structures whose origin lies in the epitaxial interfaces. These structures also exhibit very low spin memory loss and high spin mixing conductance. These extraord…
The emergence of spin-orbit torques as a promising approach to energy-efficient magnetic switching has generated large interest in material systems with easily and fully tunable spin-orbit torques. Here, current-induced spin-orbit torques in VO$_2$/NiFe heterostructures were investigated using spin-torque ferromagnetic resonance, where the VO$_2$ layer undergoes a prominent insulator-metal transition. A roughly two-fold increase in the Gilbert damping parameter, $α$, with temperature was attributed to the change in the VO$_2$/NiFe interface spin absorption across the VO$_2$ phase transition. M…
A large anti-damping spin-obit torque (SOT) efficiency in magnetic heterostructures is a prerequisite to realize energy efficient spin torque based magnetic memories and logic devices. The efficiency can be characterized in terms of the spin-orbit fields generated by anti-damping torques when an electric current is passed through the non-magnetic layer. We report a giant spin-orbit field of 48.96 (27.50) mT at an applied current density of 1 MAcm-2 in beta-W interfaced Co60Fe40 (Ni81Fe19)/TiN epitaxial structures due to an anti-damping like torque, which results in a magnetization auto-oscilla…
In spite of the absence of a macroscopic magnetic moment, an anti-ferromagnet is spin-polarized on an atomic scale. The electric current passing through a conducting anti-ferromagnet is polarized as well, leading to spin-transfer torques when the order parameter is textured, such as in anti-ferromagnetic non-collinear spin valves and domain walls. We report a first principles study on the electronic transport properties of anti-ferromagnetic systems. The current-induced spin torques acting on the magnetic moments are comparable with those in conventional ferromagnetic materials, leading to mea…
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 ex…
As electrical control of Néel order opens the door to reliable antiferromagnetic spintronic devices, understanding the microscopic mechanisms of antiferromagnetic switching is crucial. Spatially-resolved studies are necessary to distinguish multiple nonuniform switching mechanisms; however, progress has been hindered by the lack of tabletop techniques to image the Néel order. We demonstrate spin Seebeck microscopy as a sensitive, table-top method for imaging antiferromagnetic order in thin films, and apply this technique to study spin-torque switching in NiO/Pt and Pt/NiO/Pt heterostructures. …
The spin Hall effect (SHE) is found to be strong in heavy transition metals (HM), such as Ta and W, in their amorphous and/or high resistivity form. In this work, we show that by employing a Cu-Ta binary alloy as buffer layer in an amorphous Cu$_{100-x}$Ta$_{x}$-based magnetic heterostructure with perpendicular magnetic anisotropy (PMA), the SHE-induced damping-like spin-orbit torque (DL-SOT) efficiency $|ξ_{DL}|$ can be linearly tuned by adjusting the buffer layer resistivity. Current-induced SOT switching can also be achieved in these Cu$_{100-x}$Ta$_{x}$-based magnetic heterostructures, and…
We study the spin-orbit torque (SOT) effective fields in Cr/CoFeAl/MgO and Ru/CoFeAl/MgO magnetic heterostructures using the adiabatic harmonic Hall measurement. High-quality perpendicular-magnetic-anisotropy CoFeAl layers were grown on Cr and Ru layers. The magnitudes of the SOT effective fields were found to significantly depend on the underlayer material (Cr or Ru) as well as their thicknesses. The damping-like longitudinal effective field (ΔH_L) increases with increasing underlayer thickness for all heterostructures. In contrast, the field-like transverse effective field (ΔH_T) increases w…
The motion of magnetic domain walls in ultrathin magnetic heterostructures driven by current via the spin Hall torque is described. We show results from perpendicularly magnetized CoFeB|MgO heterostructures with various heavy metal underlayers. The domain wall moves along or against the current flow depending on the underlayer material. The direction to which the domain wall moves is associated with the chirality of the domain wall spiral formed in these heterostructures. The one-dimensional model is used to describe the experimental results and extract parameters such as the Dzyaloshinskii-Mo…
We demonstrate experimentally the electrical ballistic electron spin injection from a ferromagnetic metal / tunnel barrier contact into a semiconductor III-V heterostructure. We introduce the Oblique Hanle Effect technique for reliable optical measurement of the degree of injected spin polarization. In a CoFe / Al2O3 / GaAs / (Al,Ga)As heterostructure we observed injected spin polarization in excess of 8 % at 80K.
It has been shown that W in its resistive form possesses the largest spin-Hall ratio among all heavy transition metals, which makes it a good candidate for generating efficient dampinglike spin-orbit torque (DL-SOT) acting upon adjacent ferromagnetic or ferrimagnetic (FM) layer. Here we provide a systematic study on the spin transport properties of W/FM magnetic heterostructures with the FM layer being ferromagnetic Co$_{20}$Fe$_{60}$B$_{20}$ or ferrimagnetic Co$_{63}$Tb$_{37}$ with perpendicular magnetic anisotropy. The DL-SOT efficiency $|ξ_{DL}|$, which is characterized by a current-induced…
The ability to switch magnetic elements by spin-orbit-induced torques has recently attracted much attention for a path towards high-performance, non-volatile memories with low power consumption. Realizing efficient spin-orbit-based switching requires harnessing both new materials and novel physics to obtain high charge-to-spin conversion efficiencies, thus making the choice of spin source crucial. Here we report the observation of spin-orbit torque switching in bilayers consisting of a semimetallic film of 1T'-MoTe2 adjacent to permalloy. Deterministic switching is achieved without external ma…
We report on the resonant tunneling effect and the increase of tunneling magnetoresistance (TMR) induced by it in ferromagnetic-semiconductor GaMnAs quantum-well heterostructures. The observed quantum levels of the GaMnAs quantum well were successfully explained by the valence-band kp model with the p-d exchange interaction. It was also found that the Fermi level of the electrode injecting carriers is important to observe resonant tunneling in this system.
Spin-orbit torque (SOT) provides an efficient way to achieve charge-to-spin conversion and can switch perpendicular magnetization, which is essential for designing novel energy-efficient spintronic devices. An out-of-plane SOT could directly switch perpendicular magnetization. Encouragingly, field-free perpendicular magnetization switching of a two-dimensional (2D) material WTe2/ferromagnet (FM) bilayer has been reported recently, but the working temperature (200 K) is below room temperature. Here, we report the field-free perpendicular magnetization switching carried out at room temperature o…
Substantial understanding of spin-orbit interactions in heavy-metal (HM)/ferromagnet (FM) heterostructures is crucial in developing spin-orbit torque (SOT) spintronics devices utilizing spin Hall and Rashba effects. Though the study of SOT effective fields dependence on the out-of-plane magnetization angle has been relatively extensive, the understanding of in-plane magnetization angle dependence remains unknown. Here, we analytically propose a method to compute the SOT effective fields as a function of the in-plane magnetization angle using harmonic Hall technique in perpendicular magnetic an…
The experimental observation of quantum anomalous Hall effect (QAHE) in magnetic topological insulators has stimulated enormous interest in condensed-matter physics and materials science. For the purpose of realizing high-temperature QAHE, several material candidates have been proposed, among which the interface states in the CdO/ferromagnetic insulator heterostructures are particularly interesting and favorable for technological applications. Here, we report the experimental observation of the interfacial ferromagnetism and anomalous Hall effect in the Fe3O4/CdO/Fe3O4 heterostructures grown v…
We demonstrate the spin valve effect by ballistic transport in fully epitaxial MnAs ferromagnetic metal / GaAs semiconductor / GaAs:MnAs granular hybrid heterostructures. The GaAs:MnAs material contains ferromagnetic MnAs nanoparticles in a GaAs matrix, and acts as a spin injector and a spin detector. Although the barrier height of the GaAs/MnAs interface was found to be very small, relatively large magnetoresistance was observed. This result shows that by using ballistic transport, we can realize a large spin valve effect without inserting a high tunnel barrier at the ferromagnetic metal / se…
Spin-orbit torque manifested as an accumulated spin-polarized moment at nonmagnetic normal metal, and ferromagnet interfaces is a promising magnetization switching mechanism for spintronic devices. To fully exploit this in practice, materials with a high spin Hall angle, i.e., a charge-to-spin conversion efficiency, are indispensable. To date, very few approaches have been made to devise new nonmagnetic metal alloys. Moreover, new materials need to be compatible with semiconductor processing. Here we introduce W-Ta and W-V alloys and deploy them at the interface between $β$-W/CoFeB layers. Fir…
We investigate the spin-dependent tunneling properties in a three-terminal III-V-based ferromagnetic-semiconductor heterostructure with a 2.5-nm-thick GaMnAs quantum well (QW) and double barriers. We successfully control the quantum levels and modulate the spin-dependent current with varying the voltage of the electrode connected to the GaMnAs QW. Our results will open up a new possibility for realizing three-terminal spin resonant-tunneling devices.
Self-induced spin-orbit torques (SI-SOTs) in ferromagnetic (FM) layers have been overlooked when estimating the spin Hall angle (SHA) of adjacent nonmagnetic (NM) layers. In this work, we observe anomalous sign inversion of the total SOT in the spin-torque ferromagnetic resonance due to the enhanced SI-SOT, and successfully rationalize the sign inversion through a theoretical calculation considering the SHE in both the NM and FM layers. The findings show that using an FM layer whose SHA sign is the same as that of the NM achieves efficient SOT-magnetization switching with the assistance of the…
We investigate the influence of the domain wall ferromagnetic resonance frequency on the spin transfer torque in a ferromagnetic nanowire. By employing micromagnetic simulations with the spin transfer torque, we find that the domain wall resonance frequency decreases with increasing spin polarized current density, when there is no change in the resonance frequency of the domain itself. Surprisingly, the variation of the resonance frequency is remarkable (> 1.6 GHz) with the spin transfer torque even though the domain wall is pinned. Since the presented domain wall ferromagnetic resonance study…
The flow of in-plane current through ultrathin magnetic heterostructures can cause magnetization switching or domain wall nucleation owing to bulk and interfacial effects. Within the magnetic layer, the current can create magnetic instabilities via spin transfer torques (STT). At interface(s), spin current generated from the spin Hall effect in a neighboring layer can exert torques, referred to as the spin Hall torques, on the magnetic moments. Here, we study current induced magnetization switching in perpendicularly magnetized CoFeB/MgO heterostructures with a heavy metal (HM) underlayer. Dep…
We describe a systematic study of the exchange coupling between a magnetically hard metallic ferromagnet (MnAs) and a magnetically soft ferromagnetic semiconductor (GaMnAs) in bilayer and trilayer heterostructures. An exchange spring model of MnAs/GaMnAs bilayers accounts for the variation of the exchange bias field with layer thickness and composition. We also present evidence for hole-mediated interlayer exchange coupling in MnAs/p-GaAs/\GaMnAs trilayers and study the dependence of the exchange bias field on the thickness of the spacer layer.
This paper reports the development of a methodology combining microstrip ferromagnetic resonance (MS-FMR) and digital image correlation (DIC) in order to silmuteanously measure the voltage-induced strains and the magnetic resonance in artificial magnetoelectric heterostructures (magnetic films/piezoelectric substrate? or magnetic films/flexible substrate/piezoelectric actuator ?). The overall principle of the technique and the related analytical modelling are described. It is powerful to estimate the magnetostriction coefficient of ferromagnetic thin films and can be used to determine the effe…
Topological insulators have emerged as an important material class for efficient spin-charge interconversion. Most topological insulators considered to date are binary or ternary compounds, with the exception of $α$-Sn. Here we report a comprehensive characterization of the growth, magnetotransport properties, and current-induced spin-orbit torques of $α$-Sn and $β$-Sn-based ferromagnetic heterostructures. We show that $α$-Sn grown with a Bi surfactant on CdTe(001) promotes large spin-orbit torques in a ferromagnetic FeCo layer at room temperature, comparable to Pt, whereas $α$-Sn grown withou…
We use a combination of analytic calculations and numerical simulations to demonstrate that electrical current flowing through a magnetic bilayer induces dynamical coupling between the layers. The coupling originates from the dependence of the spin transfer torque exerted on the layers on the relative orientations of their magnetic moments. We demonstrate that such coupling modifies the behaviors of both layers, significantly affecting the the stability of the current-induced dynamical regimes and the efficiency of current-induced magnetic reversal.
We study laser-induced torques in bcc Fe, hcp Co and $L1_0$ FePt based on first-principles electronic structure calculations and the Keldysh nonequilibrium formalism. We find that the torques have two contributions, one from the inverse Faraday effect (IFE) and one from the optical spin-transfer torque (OSTT). Depending on the ferromagnet at hand and on the quasiparticle broadening the two contributions may be of similar magnitude or one contribution may dominate over the other. Additionally, we determine the nonequilibrium spin polarization in order to investigate its relation to the torque. …
We measure spin-orbit torque generated by exfoliated layers of the low-symmetry semi-metal ZrTe$_3$ using the spin-torque ferromagnetic resonance (ST-FMR) technique. When the ZrTe$_3$ has a thickness greater than about 10 nm, artifacts due to spin pumping and/or resonant heating can cause the standard ST-FMR analysis to overestimate the true magnitude of the torque efficiency by as much as a factor of 30, and to indicate incorrectly that the spin-orbit torque depends strongly on the ZrTe$_3$ layer thickness. Artifact-free measurements can still be achieved over a substantial thickness range by…
Harmonic measurements of the longitudinal and transverse voltages in Bi-Sb/Co bilayers are presented. A large second harmonic voltage signal due to the ordinary Nernst effect is observed. In experiments where a magnetic field is rotated in the film plane, the ordinary Nernst effect shows the same angular dependence in the transverse voltage as the damping-like spin-orbit torque and in the longitudinal voltage as the unidirectional spin-Hall magneto-resistance respectively. Therefore, the ordinary Nernst effect can be a spurious signal in spin-orbit torque measurements, leading to an overestima…
Magnetic heterostructure Mo/CoFeB/MgO has strong perpendicular magnetic anisotropy and thermal stability. Through current-induced hysteresis loop shift measurements, we show that the dampinglike spin-orbit torque (SOT) efficiency of Mo/CoFeB/MgO heterostructure is $ξ_{DL}\approx -0.003\pm 0.001$ and fairly independent of the annealing temperature from 300$^\circ$C to 400$^\circ$C. Though $|ξ_{DL}|$ is small while compare to those from Ta or W-based heterostructures, reversible current-induced SOT switching of a thermally-stable Mo/CoFeB/MgO heterostruture can still be achieved. Furthermore, we…
We investigate magnetic domain wall (MDW) dynamics induced by applied electric fields in ferromagnetic-ferroelectric thin-film heterostructures. In contrast to conventional driving mechanisms where MDW motion is induced directly by magnetic fields or electric currents, MDW motion arises here as a result of strong pinning of MDWs onto ferroelectric domain walls (FDWs) via local strain coupling. By performing extensive micromagnetic simulations, we find several dynamical regimes, including instabilities such as spin wave emission and complex transformations of the MDW structure. In all cases, th…
Spin injection using ferromagnetic semiconductors at room temperature is a building block for the realization of spin-functional semiconductor devices. Nevertheless, this has been very challenging due to the lack of reliable room-temperature ferromagnetism in well-known group IV and III-V based semiconductors. Here, we demonstrate room-temperature spin injection by using spin pumping in a (Ga,Fe)Sb / BiSb heterostructure, where (Ga,Fe)Sb is a ferromagnetic semiconductor (FMS) with high Curie temperature (TC) and BiSb is a topological insulator (TI). Despite the very small magnetization of (Ga,…
Spin-orbit torque can drive electrical switching of magnetic layers. Here, we report that at least for micrometer-sized samples there is no simple correlation between the efficiency of dampinglike spin-orbit torque (ξ_DL^j) and the critical switching current density of perpendicularly magnetized spin-current generator/ferromagnet heterostructures. We find that the values of ξ_DL^j based on switching current densities can either under- or over-estimated ξ_DL^j by up to tens of times in a domain-wall depinning analysis, while in the macrospin analysis based on the switching current density ξ_DL^…
It has been shown that the spin Hall effect from heavy transition metals can generate sufficient spin-orbit torque and further produce current-induced magnetization switching in the adjacent ferromagnetic layer. However, if the ferromagnetic layer has in-plane magnetic anisotropy, probing such switching phenomenon typically relies on tunneling magnetoresistance measurement of nano-sized magnetic tunnel junctions, differential planar Hall voltage measurement, or Kerr imaging approaches. We show that in magnetic heterostructures with spin Hall metals, there exist current-induced in-plane spin Ha…
Spin-orbit torques in ferromagnetic (FM)/non-magnetic (NM) heterostructures offer more energy-efficient means to realize spin-logic devices; however, their strengths are determined by the heterostructure interface. This work examines crystal orientation impact on the spin-orbit torque efficiency in different Fe/Pd bilayer systems. Spin torque ferromagnetic 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 decr…
We report that by measuring current-induced hysteresis loop shift versus in-plane bias magnetic field, the spin Hall effect (SHE) contribution of the current-induced effective field per current density, $χ_{SHE}$, can be estimated for Pt and Ta-based magnetic heterostructures with perpendicular magnetic anisotropy (PMA). We apply this technique to a Pt-based sample with its ferromagnetic (FM) layer being wedged-deposited and discover an extra effective field contribution, $χ_{Wedged}$, due to the asymmetric nature of the deposited FM layer. We confirm the correlation between $χ_{Wedged}$ and t…
The spin-orbit torques (SOTs) generated from topological insulators (TIs) have gained increasing attention in recent years. These TIs, which are typically formed by epitaxially grown chalcogenides, possess extremely high SOT efficiencies and have great potential to be employed in the next-generation spintronics devices. However, epitaxy of these chalcogenides is required to ensure the existence of topologically-protected surface state (TSS), which limits the feasibility of using these materials in industry. In this work, we show that non-epitaxial Bi$_{x}$Te$_{1-x}$/ferromagnet heterostructure…
Dominant spin Hall torque and negligible orbital Hall torque in α-W/ferromagnet heterostructures with artifacts-free angular momentum detectors
State Key Laboratory of Semiconductor Physics and Chip Technologies, Institute of Semiconductors, Chinese Academy of Sciences（中国科学院半导体研究所半导体物理与芯片技术国家重点实验室）；Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences（中国科学院大学材料科学与光电工程技术研究中心）；College of Physics and Information Technology, Shaanxi Normal University（陕西师范大学物理学与信息技术学院）
We investigate a spin-electricity conversion effect in a topological insulator/ferromagnet heterostructure. In the spin-momentum-locked surface state, an electric current generates nonequilibrium spin accumulation, which causes a spin-orbit torque that acts on the ferromagnet. When spins in the ferromagnet are completely parallel to the accumulated spin, this spin-orbit torque is zero. In the presence of spin excitations, however, a coupling between magnons and electrons enables us to obtain a nonvanishing torque. In this paper, we consider a model of the heterostructure in which a three-dimen…
Topological insulators (TIs) with spin momentum locked topological surface states (TSS) are expected to exhibit a giant spin-orbit torque (SOT) in the TI/ferromagnet systems. To date, the TI SOT driven magnetization switching is solely reported in a Cr doped TI at 1.9 K. Here, we directly show giant SOT driven magnetization switching in a Bi2Se3/NiFe heterostructure at room temperature captured using a magneto-optic Kerr effect microscope. We identify a large charge to spin conversion efficiency of ~1-1.75 in the thin TI films, where the TSS is dominant. In addition, we find the current densit…
We present an {\it ab initio}-based theoretical framework which elucidates the origin of the spin-orbit torque (SOT) in Normal-Metal(NM)/Ferromagnet(FM) heterostructures. The SOT is decomposed into two contributions, namely, {\it spin-Hall} and the {\it spin-orbital} components. We find that {\it (i)} the Field-Like (FL) SOT is dominated by the spin-orbital component and {\it (ii)} both components contribute to the damping-like torque with comparable magnitude in the limit of thick Pt film. The contribution of the spin-orbital component to the DL-SOT is present only for NMs with strong SOC cou…
Spin current and spin torque generation through the spin-orbit interactions in solids, of bulk or interfacial origin, is at the heart of spintronics research. The realization of spin-orbit torque (SOT) driven magnetic dynamics and switching in diverse magnetic heterostructures also pave the way for developing SOT magnetoresistive random access memory and other novel SOT memory and logic devices. Of scientific and technological importance are accurate and efficient SOT quantification techniques, which have been abundantly developed in the last decade. In this article, we summarize popular techn…
In ferromagnetic trilayers, a spin-orbit-induced spin current can have a spin polarization of which direction is deviated from that for the spin Hall effect. Recently, magnetization switching in ferromagnetic trilayers has been proposed and confirmed by the experiments. In this work, we theoretically and numerically investigate the switching current required for perpendicular magnetization switching in ferromagnetic trilayers. We confirm that the tilted spin polarization enables field-free deterministic switching at a lower current than conventional spin-orbit torque or spin-transfer torque sw…
