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Current-induced spin-orbit torques (SOT) have attracted great attention for their unique ability to manipulate the magnetization of ferromagnets and antiferromagnets [1]. SOT-induced switching offers speed and reliability comparable to or better than spin transfer torque (STT) switching, as was shown in nanodots [2,3] and magnetic tunnel junctions (MTJ) [4,5]. However, whereas the STT-driven switching dynamics of MTJs has been extensively studied [6-8], less is known about the transient dynamics and actual speed of the magnetization reversal induced by SOT. In this study we investigate the reversal dynamics of SOT switching in 3-terminal MTJs and show how the interplay of voltage control of magnetic anisotropy (VCMA) and STT can be used to optimize the switching efficiency [9,10]. We report real-time measurements of in-field and field-free SOT switching and disentangle the combined impact of SOT, STT, and VCMA on the switching speed and efficiency. We show that the combination of these effects leads to reproducible sub-ns switching with an extremely narrow distribution of the switching times without the aid of an external field. Our 3-terminal devices are fabricated using a fully compatible CMOS process [11] and are based on CoFeB/MgO/CoFeB MTJs grown on a b-W SOT-injection line and patterned into 80 nm pillars (Fig. 1a). The field-free switching functionality is enabled by an in-plane magnet embedded into a hard-mask [12], which provides a symmetry-breaking magnetic field to the magnetization of the free layer (Fig. 1b). Our electrical setup combines after-pulse and real-time detection [13] allowing for the exploration of individual SOT switching events in the time domain as well as of their statistical distributions. The voltage time traces of individual switching events exhibit a finite incubation delay followed by a single-jump reversal, after which the magnetization remains quiescent in the final state (Fig. 1c,d) [13]. Whereas complete magnetization reversal occurs within ≈1 ns, the incubation delay can take a substantial part of the total switching time in close-to-critical conditions. This incubation time, which is not expected for the “instant-on” SOT in perpendicular MTJs, can be minimized by a moderate increase of the SOT current (compare Figs. 1c and 1d), resulting in a very narrow distribution of the switching latency (Fig. 1e) [14]. A similar effect is achieved by increasing the external magnetic field strength or by biasing the MTJ. We attribute the two-steps switching process to the nucleation of a reversed domain and propagation of a domain-wall across the free layer, as supported by micromagnetic simulations (Fig. 1f). The model reveals that a key element to the observed dynamics is the reduction of magnetic anisotropy of the free layer related to the current-induced temperature rise [13]. The results further evidence a significant dependence of the switching speed and reversal onset on the MTJ bias. In Fig. 1g, averaged time traces obtained for different bias conditions clearly show that the bias accelerates the switching process. Finally, from symmetry considerations, we show that the contributions of STT and VCMA can be separated, unraveling their distinct impact on the magnetization dynamics.References: [1] A. Manchon, J. Zelezný, I. M. Miron, et al. Rev. Mod. Phys. 91, 035004 (2019) | [2] K. Garello, C. O. Avci, I. M. Miron, et al. Appl. Phys Lett. 105, 212402 (2014) | [3] M. Baumgartner, K. Garello, J. Mendil, et al. Nat. Nanotech. 12, 980-986 (2017) | [4] S. V. Aradhya, G. E. Rowlands, J. Oh, et al. Nano Lett, 16, 5987-5992 (2016) | [5] M. Cubukcu, O. Boulle, N. Mikuszeit, et al. IEEE Trans. Magn. 54, 9300204 (2018) | [6] Y.-T. Cui, G. Finocchio, C. Wang, et al. Phys. Rev. Lett. 104, 097201 (2010) | [7] C. Hahn, G. Wolf, B. Kardasz, et al. Phys. Rev. B 94, 214432 (2016) | [8] T. Devolder, J.-V. Kim, F. Garcia-Sanchez, et al. Phys Rev. B 93, 024420 (2016) | [9] H. Yoda, H. Sugiyama, T. Inokuchi, et al. IEEE Int. Mem. Wkshp. (2017) | [10] A. van den Brink, S. Cosemans, S. Cornelissen, et al. Apply. Phys. Lett. 104, 012403 (2014) | [11] K. Garello, F. Yasin, S. Couet, et al. IEEE Symp. VLSI Circ., 81-82 (2018) | [12] K. Garello, F. Yasin, H. Hody, et al. IEEE Symp. VLSI Circ., T194-195 (2019) |[13] E. Grimaldi, V. Krizakova, G. Sala, et al. Nat. Nanotech. 15, 111-117 (2020) | [14] V. Krizakova, K. Garello, E. Grimaldi, et al. Appl. Phys. Lett. 116, 232406 (2020)

MMM 2020

Real-Time Measurements of Field-Free Spin-Orbit Torque Switching in 3-Terminal Magnetic Tunnel Junctions INVITED

The 65th Annual Conference on Magnetism and Magnetic Materials (MMM 2020) was held in a virtual form. The COVID-19 pandemic, with its associated uncertainty about international travel and the ability to gather in large groups, meant that the Steering Committee decided to cancel the face-to-face meeting that had been planned in Palm Beach, Florida November 2-6, 2020.

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technical paper

Using first-principles calculations, we demonstrated that the perpendicular magnetic anisotropy (PMA) of NiI2 monolayer can be effectively enhanced by decreasing interlayer distance of graphene/NiI2 (Gr/NiI2) heterostructure. Furthermore, by analyzing atomic-resolved magnetocrystalline anisotropy energy (MAE), orbital-hybridization-resolved MAE and density of states, we clarify that the magnetic anisotropy enhancement originates from the electronic states of interfacial I atoms. At the same time, the NiI2 substrate induces magnetic proximity effects on graphene, which can lead to the quantum anomalous hall effect (QAHE). Our findings demonstrate the enhancement of PMA via tuning interlayer distance of vdW heterostructure and provides a possible vdW system for realizing QAHE.References: Q. Cui, J. Liang, B. Yang, Z. Wang, P. Li, P. Cui, and H. Yang, Phys. Rev. B 101, 214439 (2020)

Giant enhancement of perpendicular magnetic anisotropy and induced quantum anomalous Hall effect in the graphene/NiI2 heterostructure via tuning the van der Waals interlayer distance

Chemically-synthesized magnetic nanoparticles (MNPs) consisting of different combinations of spinel ferrites (γ-Fe2O3, Fe3O4, MnFe2O4, CoFe2O4) provide a platform for developing ensembles of nanostructures whose magnetic properties are distinct from their bulk counterparts. We report on studies of MNPs composed of high-anisotropy CoFe2O4 combined with relatively high-moment, low anisotropy Fe3O4. We examined two variations of MNPs: a CoFe2O4 core with a Fe3O4 shell and the inverted structure (Fe3O4 core / CoFe2O4 shell). Both variants had a core diameter of 3-3.5 nm and an overall diameter of ∼10 nm and we investigated their properties using magnetometry, small-angle neutron scattering (SANS), and Monte Carlo simulations. The magnetometry indicates that both MNP variants are superparamagnetic at room temperature with a considerable coercivity enhancement below the blocking temperature (~250 K) accompanied by a multi-step path towards magnetization reversal (Fig 1-b). Fully spin-polarized SANS measurements show that magnetic order perpendicular to the applied field direction is strong at remanence; this spin configuration is quenched upon application of a small field (Fig. 1-a). Spin alignment parallel to the field develops at higher fields. Monte Carlo simulations indicate that the emergence of dipolar-coupled long range order may be associated with the steps observed in the field hysteresis loops. Modelling of the SANS distributions, informed by the Monte Carlo simulations, to investigate the spin alignment in the core and shell, as demonstrated for metallic Fe core / Fe oxide shell MNPs [1], for both MNP variants is currently underway. The results demonstrate the value of combining modeling of fully-spin polarized SANS data with numerical simulations of ensembles of macrospins to illuminate the complex spin ordering across a range of length scales. The authors acknowledge the support of Univ. of South Florida Nexus Initiative (UNI) Award, US Department of Energy, Office of Basic Energy Sciences (Award DE-FG02-07ER46438) and the Knut and Alice Wallenberg Foundation (Grant 2018.0060). Access to spin filters on NG-7 SANS was provided by CHRNS, a partnership between NIST and the NSF (No. DMR-1508249).References: [1] C. Kons, D. A. Arena, et al., “Investigating spin coupling across a three-dimensional interface in core/shell magnetic nanoparticles,” Phys. Rev. Mater., 4 034408 (2020).

Spin Ordering in Bi-Magnetic (Core / Shell) Nanoparticles With Varying Anisotropy

Thanks to advances in synthesis that enable control over size, structure, and properties, magnetic nanoparticles (NPs) present opportunities in data storage, cancer treatment, biomedical imaging, etc. While superparamagnetism (SP) dominates the properties of magnetic NPs, quantitative understanding of SP blocking in NP assemblies remains elusive. We address this here via comprehensive magnetic characterization and analysis of soft ferromagnetic Ni NP ensembles. NPs were synthesized by hot injection of a Ni-oleylamine (OAm) complex into trioctylphosphine (TOP), with size control achieved via TOP:OAm ratio, reaction time, and differential centrifugation.1 X-ray diffraction, transmission electron microscopy (TEM), and various spectroscopies reveal polycrystalline/twinned FCC Ni NPs with mean diameters <D> from 4 to 22 nm, dispersity down to 10%, and TOP/OAm ligands.1 SP blocking temperatures (TB) are carefully determined, quantitatively accounting for the substantial yet frequently ignored effects of dispersity, yielding mean TB (<TB>) from 5 to 300 K.1 Quantitative understanding of the size-dependent <TB> is achieved (Fig. 1), with no adjustable parameters, but only by accounting for the size distribution, effective ferromagnetic volume (Vmag), temperature-dependent magnetocrystalline anisotropy (MCA), and average shape anisotropy due to random deviations from spherical.1 The reduced saturation magnetization (Ms) and Vmag deduced from magnetometry were investigated by small-angle neutron scattering (SANS) (Fig. 2) and high-resolution TEM, evidencing a thin Ni-P shell arising from reactions with TOP. We thus achieve fully quantitative understanding of SP blocking in model NP assemblies. Work supported by 3M and DOE Center for Quantum Materials.References: [1] J.T. Batley, M. Nguyen, I. Kamboj, C. Korostynski, E.S. Aydil and C. Leighton, submitted (2020).

Quantitative understanding of superparamagnetism in Ni nanoparticle assemblies

Magnetic nanoparticles are increasingly used in biomedical applications such as drug-delivery, gene delivery, hyperthermia, or contrast agents for MRI. Magnetite (Fe3O4) nanoparticles are good candidates for these applications due to their non-toxicity and long-life in the bloodstream. While the structural and magnetic properties of bulk Fe3O4 has been widely studied [1], knowledge is still lacking regarding the magnetic behaviour of collections of Fe3O4 nanoparticles. In particular, when the particles are small and the assembly is superparamagnetic, it is useful to understand the nature of the magnetic correlations within the assemblies. Here we show how inter-particle magnetic correlations can be probed at the nanoscale via x-ray resonant magnetic scattering (XRMS) [2] as illustrated in Figure 1. By tuning the energy of the x-rays to resonant edges of Fe and comparing opposite polarization helicities, we extract information about the local inter-particle magnetic orders within the nanoparticle assemblies. We show the dependence on particle size, varying from 5 to 11 nm, suggesting an enhancement of magnetic couplings for bigger particles. [3] Additionally, we show a model based on chains of nanoparticles, which we use to fit the XRMS data. The data fitting suggests the occurrence of ferromagnetic ordering when an external magnetic field is applied, but when the external field is brought to zero (remanence), the fit suggest a mix of antiferromagnetic ordering and randomness. [4]References: [1] Verwey, Nature 144, 327 (1939); Fleet, Acta Cryst. B 37, 919-929 (1981) [2] Kortright et al., Phys. Rev. B 71, 012402 (2005) [3] Chesnel et al., Magnetochemistry 4, 42-58 (2018) [4] J. Rackham et al, AIP Advances 9, 035033 (2019)

Magnetic correlations and time fluctuations in assemblies of Fe3O4 nanoparticles

Magnetization states in conducting nanostructures have attracted renewed attention because they give rise to a Berry phase and to an anomalous Hall contribution commonly known as topological Hall effect (THE). The effect requires spin configurations that are not only noncollinear but also noncoplanar, while spins in small spherical Stoner-Wohlfarth particles are parallel and the THE is therefore zero. However, metallic nanoparticles are never perfectly spherical, which creates magnetization inhomogeneities. Examples are stray-field effects near corners and edges, such as the flower state in cubes [1] and the spin configuration shown in Fig. 1(a). When the particles form in conducting thin films or granular nanostructures, then these inhomogeneities yield skyrmionic magnetization features [2] and THE contributions [3]. Our focus is on nanoparticles whose radius R is smaller than the coherence radius Rcoh above which a reverse magnetic field causes magnetization curling. We estimate the Berry curvature Φ by considering the triple product M1.(M2 × M3), which describes the degree of noncoplanarity. When the three vectors are symmetrically arranged and form an angle θ with the symmetry axis, then the triple product is equal to (27/4)1/2 sin2 θcosθ Ms3. The angle θ depends on the radius of the nanoparticles and on the external magnetic field. In very small nanoparticles, the exchange energy ~ A/R2 dominates, and θ approaches zero. Figure 1(b) shows the zero-field Berry curvature as a function of R. An external magnetic field reduces Φ, and the THE is obtained by areal integration. For very small nanoparticles, Φ decreases as R4. This research is supported by DOE BES (DE-FG02-04ER46152).References: [1] E. Pinilla-Cienfuegos, S. Mannas-Valero, A. Forment-Aliaga, and E. Coronado, ACS Nano 10, 1764 (2016). [2] B. Das, B. Balasubramanian, R. Skomski, P. Mukherjee, S. R. Valloppilly, G. C. Hadjipanayis, and D. J. Sellmyer, Nanoscale 10, 9504 (2018). [3] W. Zhang, B. Balasubramanian, A. Ullah, R. Pahari, X. Li, L. Yue, S. R. Valloppilly, A. Sokolov, R. Skomski, and D. J. Sellmyer, Appl. Phys. Lett. 115, 172404 (2019).

Berry Curvature and Topological Hall Effect in Quasi-Coherent Nanoparticles

In applications that utilize films of nanoparticles, there is a need to develop methods to fabricate stable thick films to improve materials for energy storage, sensing, or flexible electronics. [1-3]. This work seeks to increase film thickness and stability by increasing film-substrate interactions by functionalizing conductive substrates with various chelating agents. These nanoparticles are deposited via electrophoretic deposition (EPD), a method that deposits charged particles in colloidal suspensions via electrophoresis. Here, we will demonstrate the efficacy of this approach by depositing iron oxide nanoparticles onto conductive substrates functionalized with three chelating agents with different functional moieties and therefore differing chelating strengths [4]. We show that increasing chelating strength can increase film-substrate interactions, resulting in thicker films when compared to traditional EPD. Results will also be presented on how the effect of the chelating strength relates to film formation as a function of deposition conditions. Yield for EPD is influenced by deposition conditions including applied electric field, particle concentration, and deposition time. Substrates functionalized with chelating agents were used with three different sets of deposition parameters, varying the applied electric field and particle concentration. This work shows that the functionalization of substrates with chelating agents that coordinate strongly with nanoparticles used for deposition overcome parameters that traditionally hinder the deposition of thicker and more stable films. Further, films that suffer instability and low quality from high applied electric field and high particle concentration were more stable when deposited on substrates functionalized with phosphonic acid and dopamine.References: [1] C. Mahender, T. Sumangala, R. Ade, Ceram. Int., Vol. 45, p. 4316-4321 (2019) [2] E. Cao, Z. Chu, H. Wang, Ceram. Int., Vol. 44, p. 7180-7185 (2018) [3] L. Ming, H. Yang, W. Zhang, J. Mater. Chem., Vol. 2, p. 4566-4573 (2014) [4] A. Walter, A. Garofalo, A. Parat, Nanotechnol. Rev., Vol. 4, p. 581-593 (2015)

Fabrication of Thick and Stable Nanoparticle Films via Electrophoretic Deposition on Substrates Functionalized with Chelating Agents

Magnetic transition-metal silicides and germanides, crystallizing in the B20 cubic structure with broken inversion symmetry, have attracted much attention in the context of Dzyaloshinskii-Moriya interactions, helical spin structures, and magnetic skyrmions [1, 2]. Finding skyrmions in confined geometries such as nanoparticles and nanowires is particularly intriguing from the viewpoints of fundamental science and practical applications [3]. Such low-dimensional structures also often show size-induced magnetic properties as compared to corresponding bulk alloys [4]. We have used density-functional-theory (DFT) calculations and cluster-deposition experiments to investigate the size dependence of magnetic properties in equiatomic CoSi; the average particle size d of the clusters varies from about 0.6 nm to 11.6 nm. In sharp contrast to bulk CoSi, which is nonmagnetic down to liquid helium temperature, the nanoclusters order magnetically with a net low-temperature magnetic moment from 0.69 to 0.21 μB/Co as d varies from 0.6 to 11.6 nm. The fast Fourier transform (FFT) of the HRTEM image (Fig. 1a) and x-ray diffraction pattern (not shown here) of the sample having d = 11.6 nm confirm the cubic B20 structure. The corresponding DC susceptibility curves display anomalies in limited field (about 20 – 200 Oe) and temperature (100 K – 300 K) ranges (Fig. 1b), which are similar to the signature of helical or skyrmion-like spin structures. DC susceptibility and anomalous Hall resistivity data are used to determine a field-temperature magnetic phase diagram that includes a skyrmionic region and to discuss the confinement effect on skyrmions within the small diameter of CoSi nanoclusters.This research is supported by the US DOE/BES (DE-FG02-04ER46152) and performed in part in the Nebraska Nanoscale Facility and the NCMN, which are supported by the U.S. NSF (NNCI -1542182), and the Nebraska Research Initiative (NRI).References: [1] N. Nagaosa and Y. Tokura, Nature Nanotech. 8, 899 (2013). [2] B. Balasubramanian, P. Manchanda, R. Pahari, Z. Chen, W. Zhang, S.R. Valloppilly, X. Li, A. Sarella, L. Yue, A. Ullah, P. Dev, D. A. Muller, R. Skomski, G. C. Hadjipanayis, and D.J. Sellmyer, Phys. Rev. Lett. 124, 057201 (2020). [3] B. Das, B. Balasubramanian, R. Skomski, P. Mukherjee, S.R. Valloppilly, G.C. Hadjipanayis, and D.J. Sellmyer, Nanoscale. 10, 9504 (2018). [4] B. Balasubramanian, M. Sakurai, C.-Z. Wang, X. Xu, K.-M. Ho, J. R. Chelikowsky and D. J. Sellmyer, Mol. Syst. Des. Eng. DOI: 10.1039/d0me00050g (2020).

Size-Dependent Magnetism and Skyrmionic Properties in CoSi Nanoclusters

This work shows that Co-rich microwires (MWs) with nearly zero magnetostriction have colossal heating efficiency under radiofrequency fields.[1] MWs of 31 µm diameter and 5 mm length show a specific loss power (SLP) of 3000 W/g at 36 Oe and 625 kHz. The SLP varies with the MWs length and number. The role of length lies on the magnetic domains that change from radial to axial when the length is reduced, as deduced from the hysteresis curve shapes, and makes SLP to decrease by a factor of 10 when the length switch from 5 to 15 mm, see Fig. 1. The number of MWs sets side by side determine the magnetostatic interactions which affect to the remanence (Mr) and susceptibility: Mr = 80% for 2 to 6 MWs and then decreases to Mr = 50% for 10 MWs, suggesting the formation of closure domains that diminish the magnetostatic energy. This change of the hysteresis loop shapes also influences the SLP. In this work, it is assumed that this colossal heating efficiency is dominated by the eddy-currents, although a small contribution from hysteresis losses cannot be ruled out. The eddy currents are generated by electromagnetic induction and lead to Joule heating of the material. The eddy–currents in Co-rich MWs are enhanced by the magnetization reversal and, thus, the magnetic susceptibility becomes a key factor for the heating efficiency. This magnetic susceptibility is given by the change of the magnetic domain with the length, with the circumferential domains playing probable the main role at high frequency. Therefore, short MWs with nearly zero magnetostriction are key candidates to show colossal heating efficiencyReferences: [1] I. Morales, D. Archilla, P. de la Presa, et al., Sc. Report 10, 602 (2020).

Colossal heating efficiency for nearly zero magnetostrictive amorphous microwires via eddy currents at radiofrequency fields.

Fe3O4 (FeF), MnxFe3-xO4 (Mn1, Mn3, Mn5 for x = 0.1, 0.3, 0.5) and CoxFe3-xO4 (Co1, Co3, Co5 for x = 0.1, 0.3, 0.5) nanoparticles (NPs) were synthesized using co-precipitation technique to study the effect of factors that influence the effective specific absorption rate (ESAR). The samples were characterized using XRD, TEM, VSM, TMA and ESR. The heating efficiency was probed employing infrared thermography at ac field of 4 kA/m and frequency 500 kHz [1, 2]. The particle sizes are in the range of 10-13 nm, except Co5 which is 40 nm. The saturation magnetization (Ms) of the samples at 300 K is between 55-66 emu/g. The coercivity (Hc) of the Mn-doped samples is below 33 Oe where it increased up to 548 Oe with Co-doping. The low-temperature (15 K) hysteresis show a decrease in Hc with Mn-doping and enhancement with Co from 326 to 180 and 4345 Oe, respectively. Fig. 1 shows the ESR spectra from which the effective magnetic anisotropy (Keff) was computed. While the values are between 15.3-16.5 kJ/m3 for the Mn-doped samples, an increase in Keff of 20.9 (Co1) and 31.3 kJ/m3 (Co3) is observed with Co-doping reflecting the effect of particle size and doping. ESAR vs. magnetic anisotropy energy (KeffV) was theoretically and experimentally estimated (Fig. 2), where V is the volume of the particle. The highest and lowest ESAR (theoretical) of 1124 and 89 × 10-9 Wg-1Oe-2Hz-1 was obtained for Mn5 and Mn3, respectively. In contrast, the experimental ESAR (right axis) was the highest for Mn3 with a value of 21 × 10-9 Wg-1Oe-2Hz-1 and decreased with KeffV. The ESAR of FeF is 20 × 10-9 Wg-1Oe-2Hz-1. The deviation in the experimental from the theoretical values of the Mn-doped samples is mainly due to the distribution in particle sizes, whereas the decrease in ESAR with Co-doping from 20 to 18 × 10-9 Wg-1Oe-2Hz1 was as per the linear response theory (LRT) [3]. Our superparamagnetic NPs produce heat in accordance with LRT. The decreasing trend in ESAR with Co-doping in Fe3O4 is correlated with anisotropy, whereas with Mn-doping, particle size distribution plays a significant role rather than anisotropy.References: [1] J.S. Anandhi, G.A. Jacob and R.J. Joseyphus, Mater. Res. Express, 6, 015045 (2019) [2] J.S. Anandhi, G.A. Jacob and R.J. Joseyphus, J. Magn. Magn. Mater., 512, 166992 (2020) [3] J. Carrey, B. Mehdaoui and M. Respaud, J. Appl. Phys., 109, 083921 (2011)

Insights on the Heating Characteristics of Mn and Co-doped Fe3O4

Performing magnetization studies on individual nanoparticles is a highly demanding task, especially when measurements need to be carried out under large sweeping magnetic fields or variable temperature. Yet, characterization under varying ambient conditions is paramount in order to fully understand the magnetic behavior of these objects, e.g., the formation of non-uniform states, the mechanisms leading to magnetization reversal, thermal stability or damping processes. This, in turn, is necessary for the integration of magnetic nanoparticles and nanowires into useful devices, e.g., spin-valves, racetrack memories or magnetic tip probes. Here we show that YBa2Cu3O7 nano Superconducting QUantum Interference Devices (YBCO nanoSQUIDs, see Fig.) are particularly well suited for this task. We have successfully characterized a number of individual nanoparticles of soft magnetic materials with different shapes (nanodots, nanodiscs and nanowires, see Figure). Samples are transported to the surface of the sensor with nanometric resolution, achieving sufficiently strong particle-SQUID coupling. Magnetization measurements (see Figure) performed under sweeping magnetic fields (up to ~ 500 mT) and variable temperature (1.4 - 80 K) underscore the intrinsic differences between samples owing to their shape and the presence (or absence) of magnetocrystalline anisotropy. Our measurements also allow us to distinguish the mechanisms leading to magnetization reversal mediated by, i.e., nucleation/propagation of domain walls or nucleation/annihilation of magnetic vortices. These studies serve to shed light on the nature and magnitude of the energy barriers separating different magnetic states, nucleation/annihilation fields and switching times.

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Real-Time Measurements of Field-Free Spin-Orbit Torque Switching in 3-Terminal Magnetic Tunnel Junctions INVITED

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Giant enhancement of perpendicular magnetic anisotropy and induced quantum anomalous Hall effect in the graphene/NiI2 heterostructure via tuning the van der Waals interlayer distance

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