United States

The manipulation of exchange interactions in two-dimensional magnets has fundamental research value and potential applications. Based on first-principles calculations, the exchange interactions in experimental controversial ferromagnetic 1T-VSe2 monolayer [1,2] are systematically studied. It is found that three shells of nearest-neighbor Heisenberg exchange interactions and higher-order interactions are crucial for an accurate description of the ferromagnetism in 1T-VSe2 monolayer. Based on the understanding of tuning the magnetic interactions and the magnetic ground state in 1T-VSe2 monolayer by external factors, two modulation methods, alkali metal Lithium adsorption and electride Ca2N substrate, are proposed. In both systems, the strongly frustrated Heisenberg exchange interactions compete with higher-order exchange interactions, Dzyaloshinskii-Moriya interaction and magnetocrystalline anisotropy, leading to complex magnetic ground states, such as antiferromagnetic spin spiral, periodical antiferromagnetic cycloidal state and double row-wise antiferromagnetic states. These results highlight the effective manipulation of exchange interactions in two-dimensional magnets.&lt;br&gt;
This work was supported by the National Natural Science Foundation of China (51871161 and 52071233).
**References**&lt;br&gt; [1] M. Bonilla, S. Kolekar, Y. Ma, et al. Nat. Nanotechnol. 13, 289 (2018).&lt;br&gt;
[2] P. K. J. Wong, W. Zhang, F. Bussolotti, et al. Adv. Mater. 31, 1901185 (2019).&lt;br&gt;
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MMM 2022

Tuning exchange interactions in 1T VSe2 monolayer by alkali metal adsorption and electride substrate

The manipulation of exchange interactions in two-dimensional magnets has fundamental research value and potential applications. Based on first-principles calculations, the exchange interactions in experimental controversial ferromagnetic 1T-VSe2 monolayer [1,2] are systematically studied. It is found that three shells of nearest-neighbor Heisenberg exchange interactions and higher-order interactions are crucial for an accurate description of the ferromagnetism in 1T-VSe2 monolayer. Based on the understanding of tuning the magnetic interactions and the magnetic ground state in 1T-VSe2 monolayer by external factors, two modulation methods, alkali metal Lithium adsorption and electride Ca2N substrate, are proposed. In both systems, the strongly frustrated Heisenberg exchange interactions compete with higher-order exchange interactions, Dzyaloshinskii-Moriya interaction and magnetocrystalline anisotropy, leading to complex magnetic ground states, such as antiferromagnetic spin spiral, periodical antiferromagnetic cycloidal state and double row-wise antiferromagnetic states. These results highlight the effective manipulation of exchange interactions in two-dimensional magnets. 
This work was supported by the National Natural Science Foundation of China (51871161 and 52071233).
**References** [1] M. Bonilla, S. Kolekar, Y. Ma, et al. Nat. Nanotechnol. 13, 289 (2018). 
[2] P. K. J. Wong, W. Zhang, F. Bussolotti, et al. Adv. Mater. 31, 1901185 (2019). 
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technical paper

#### Welcome to the 67th Annual Conference on Magnetism and Magnetic Materials, MMM 2022!

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Spin selectivity depends on the magnetism of substrate and the interaction between chiral molecules and substrate[1]. Measurements of the interfaces based on chiral molecules and ferromagnet by Kelvin probe show that the length of electron spin wave function entering chiral monolayer is chirality-dependent[2]. In this work, the electronic structure and magnetic properties of R,S-methylbenzylamine-PbI4/Fe interfaces are studied by first-principles calculations. The effects of stacking patterns and chirality on the interfaces are discussed. All four interfaces can exist at low temperature, among which the type-II is more stable. The existence of chiral organic molecules leads to the emergence of positive spatial spin polarization in the vacuum layer and the attenuation of positive spatial spin polarization in the substrate, indicating that the microstructures of interfaces will affect the spin injection efficiency. The four interfaces show negative spin polarization and perpendicular magnetic anisotropy. The effect of chiral molecules on the interfaces can be further studied by applying external electric field. 
This work was supported by the National Natural Science Foundation of China (51871161 and 52071233). 
**References** [1] K. Michaeli, N. Kantor-Uriel, R. Naaman and D. Waldeck, Chem. Soc. Rev. 45, 6478-6487 (2016) 
[2] Z. Huang, B. Bloom, X. Ni, Z. Georgieva, M. Marciesky, E. Vetter, F. Liu, D. Waldeck and D. Sun, ACS Nano 14, 10370-10375 (2020) 
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Spin Dependent Electronic Structure and Magnetic Properties of Fe/Chiral Methylbenzylamine PbI4 Spinterfaces

The anomalous Hall effect is an ubiquitous phenomenon in magnetic materials but it vanishes in time reversal systems. Nevertheless, Sodemann and Fu [1] suggested that a second order response in the electric field is allowed in time reversal invariant materials without inversion symmetry, as a consequence of the shift in the Fermi distribution function when the electrons go out of equilibrium. This nonlinear Hall effect is driven by the curvature dipole (BCD), which motivated several experiments [2,3] and encouraged the exploration of numerous platforms to enhance the resulting Hall current. In this context, topological materials such as Weyl semimetals (WSM) are excellent candidates to exhibit large values of nonlinear Hall effect due to monopoles of Berry curvature. In addition, the Fermi arcs that connect Weyl nodes of opposite chirality have a known impact on the anomalous Hall effect, but an extended analysis of the surface states is still missed at the level of the nonlinear Hall effect, especially in the regime when there is an important tilting of the Weyl cones. In this work [4], we reveal the contribution of the surface states to the BCD in WSM. Starting from a two-band model [5,6] and applying a slab construction method [7], we deduce that the topological nature of the surface states does not play a crucial role on the BCD. Besides, the transition between type I and type II WSM uncovers a strong impact of the Fermi pockets' projections because of a higher number of states at the surface rather than at the bulk. In contrast, after comparing to the bulk instance we notice that track states' projections does not show a profound effect on the BCD. We extend our study to the realistic case of WTe2 thin film using a Wannier-projected tight-binding representation, confirming that there is a notorious thickness dependence on the BCD subjected to the slab under consideration. 
**References** [1] I.Sodemann and L.Fu. Physical Review Letters 115, 216806 (2015).
[2] K.Kang, T.Li, E.Sohn. Nature Materials 18, p. 324-328 (2019).
[3] Q.Ma, S.Xu, H.Shen. Nature 565, p. 337-342 (2019).
[4] D.García Ovalle, A.Pezo and A.Manchon. Arxiv 2206.08681 (2022).
[5] T. Mc Cormick, I.Kimchi and N.Trivedi. Physical Review B 95, 075133 (2017).
[6] C.Zeng, S.Nandy and S.Tewari. Physical Review B 103, 245119 (2021).
[7] G. Manchon, S. Ghosh, C. Barreteau. Physical Review B 101, 174423 (2020). 
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Influence of the surface states on the nonlinear Hall effect in Weyl semimetals

Orthoferrites (REFeO3) containing rare-earth (RE) elements are 3D antiferromagnets (AFM) that exhibit characteristic weak ferromagnetism originating due to slight canting of the spin moments and display a rich variety of spin reorientation transitions in the magnetic field (H)-temperature (T) parameter space (1, 2). We present spin Hall magnetoresistance (SMR) studies (3) on a b-plate (ac-plane) of crystalline Ho0.5Dy0.5FeO3│Pt hybrid at various T in the range, 11 to 300 K. In the room temperature Γ4(Gx, Ay, Fz) phase, the switching between two degenerate domains, Γ4(+Gx, +Fz) and Γ4(-Gx, -Fz) occurs at fields above a critical value, Hc ≈ 713 Oe. Under H > Hc, the angular dependence of SMR (α-scan) in the Γ4(Gx, Ay, Fz) phase yielded a highly skewed curve with a sharp change (sign-reversal) along with a rotational hysteresis around a-axis. This hysteresis decreases with an increase in H (Fig.1). Notably, at H < Hc, the α-scan measurements on the single domain, Γ4(± Gx, ± Fz) exhibited an anomalous sinusoidal signal of periodicity 360 deg. Low-T SMR curves (H = 2.4 kOe), showed a systematic narrowing of the hysteresis (down to 150 K) and a gradual reduction in the skewness (150 to 52 K), suggesting weakening of the anisotropy possibly due to the T-evolution of Fe-RE exchange coupling. Below 25 K, the SMR modulation showed an abrupt change around the c-axis, marking the presence of Γ2(Fx,Cy,Gz) phase. We have employed a simple Hamiltonian and computed SMR to examine the observed skewed SMR modulation. In summary, SMR is found to be an effective tool to probe magnetic anisotropy as well as a spin reorientation in Ho0.5Dy0.5FeO3. Our spin-transport study highlights the potential of Ho0.5Dy0.5FeO3 for future AFM spintronic devices. 

**References:** 
(1) T. Yamaguchi, J. Phys. Chem. Solids, Vol. 35, p.479 (1974) 
(2) T. Chakraborty and S. Elizabeth, J. Magn. Magn. Mater., vol. 462, p. 78 (2018) 
(3) Y.-T. Chen, S. Takahashi, H. Nakayama, Phys. Rev. B, vol. 87, p. 144411 (2013) 

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Probing magnetic anisotropy and spin reorientation transition in 3D antiferromagnet, Ho0.5Dy0.5FeO3 │Pt using spin Hall magnetoresistance

Spin Hall antiferromagnetic oscillators (AFMO) (1) are a promising candidate for a CMOS-compatible THz-range frequency source. The output power of a nano-scale AFMO is relatively low, and mutual synchronization of AFMOs may be used to increase the power and to reduce the generation linewidth. The first step in understanding AFMO synchronization is to investigate the injection locking of a single oscillator, i.e., synchronization to an external driving signal.
Here, we numerically study the injection locking of AFMOs using the model derived in (1). In contrast with previous studies (2, 3), we study injection locking in a wide range of AFMO frequencies and assume that the driving signal is mixed with the DC bias current, i.e., that the bias and locking spin currents have the same spin polarization, which is more suitable for practical realization.
Figure 1 shows a dependence of the driven AFMO frequency f on the injected frequency fs. Straight segment near the AFMO free-running frequency f0 = 0.23 THz corresponds to the injection locking at the fundamental signal harmonic. The huge locking bandwidth Δf1≈100 GHz is due to strong influence of AFMO nonlinearity related to anisotropy of the antiferromagnet (1). An additional signature of a strongly nonlinear regime is the appearance of higher-order locking bands f=2fs and f=3fs. Synchronization at higher harmonics may be important in practical applications, since it allows one to synchronize THz-range AFMO by a driving signal of a lower frequency.
The synchronization bandwidth Δf1 drastically reduces with the increase of AFMO free-running frequency f0 (Fig. 2). This effect is caused by reduction of AFMO nonlinearity and may be a serious obstacle for practical use of AFMOs in the frequency range f > 1 THz. Therefore, alternative methods of AFMO injection locking should be studied, such as locking to a microwave magnetic field or to a spin current with different spin polarization (2). 

**References:** 
(1) R. Khymyn, et al., “Antiferromagnetic THz-frequency Josephson-like oscillator driven by spin current”, Sci. Rep. 7, 43705 (2017). 
(2) O. Gomonay, T. Jungwirth, and J. Sinova, “Narrow-band tunable terahertz detector in antiferromagnets via staggered-field and antidamping torques”, Phys. Rev. B 98, 104430 (2018). 
(3) R. Khymyn, et al., “Injection-locking of a nonlinear sub-THz antiferromagnetic spin-Hall oscillator”, DE-08, Abstracts of the International Magnetics Conference INTERMAG-18, Singapore, Singapore, April 2018. 

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Injection Locking of Antiferromagnetic Oscillators

Spin-orbit torques (SOTs) originating from a ferromagnetic spin source have attracted much attention for spintronics devices because they offer field-free switching of perpendicular magnetization [1]. Cobalt-based Heusler alloy Co2MnAl (CMA) is attractive for the ferromagnetic spin source because it is theoretically predicted to be a magnetic Weyl semimetal with strong spin-orbit interaction [2]. In this work, we demonstrated SOT-induced magnetization switching for a perpendicularly magnetized CoFeB (CFB) under zero magnetic field by using an in-plane magnetized CMA spin source. We also measured modulation of coercive field by the SOTs and investigated the effective perpendicular magnetic field Heff induced by them.
A heterostructure consisting of, from the substrate side, MgO(10)/CMA(5)/Ti(3)/CoFeB(1.2)/MgO(3)/Ta(1) was deposited on an MgO(100) substrate (numbers in parentheses are nominal thickness in nm). Then, the stack was processed into Hall-bar devices with a 5-μm-wide channel. From measurements on transverse resistance Ryx reflecting the anomalous Hall effect (AHE), the CFB layer showed a clear perpendicular magnetic easy axis, whereas the CMA had an in-plane magnetic easy axis. After aligning magnetization of CMA, MCMA, to parallel or antiparallel to the channel direction, we studied SOT-induced magnetization switching of CFB layer by applying current pulses Ipulse to the channel in the absence of magnetic field. Clear field-free switching of CFB magnetization was observed in both cases. The polarity of SOT-induced magnetization switching with respect to Ipulse was reversed depending on the relative direction of MCMA to Ipulse (Fig. 1). Furthermore, we investigated Heff induced by SOTs with Heff = [Hc(+I) - Hc(-I)]/2, where Hc(I) is a coercive field determined from AHE measurements, and I is a channel current. We observed sizable effective field of μ0Heff = 1 mT at I = 3 mA. Importantly, the sign of Heff was also reversed depending on the relative direction of MCMA to I. These results suggest that the possible origin of the SOTs is spin-orbit precession [1]. 
**References** [1] S. C. Baek et al., Nat. Mater., Vol. 17, p.509 (2018)
[2] J. Kübler, C. Felser, EPL, Vol. 114, 47005 (2016)
 

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Field free switching of perpendicular magnetization by spin

Recently, transition metal oxide thin films with strong bulk or interfacial spin-orbit coupling have demonstrated to exhibit exceptionally large spin Hall angle, which can potentially enable energy-efficient spin-orbit torque devices. To characterize the spin Hall efficiency, spin-torque ferromagnetic resonance (ST-FMR) or spin pumping measurements that operate at microwave frequencies have been widely used in oxide epitaxial thin films on various oxide substrates. At high frequency, the dielectric loss of those oxide substrates could significantly influence the resonance spin torque signals. However it has not been well considered when evaluating the spin Hall efficiency. Here we report that some insulating oxide substrates could generate significant spurious symmetric voltage signals on ST-FMR measurements, leading to serious overestimation of spin-Hall angle. We investigate the spurious signals in five widely used insulating oxide substrates SrTiO3, KTiO3, DySrO3, LSAT, and Al2O3 by performing ST-FMR measurements in oxide substrate/ferromagnetic bars. We find that all the devices present considerable resonance voltage signals even with the absence of spin source layer, see Fig.1. Among which, STO, KTO, DSO show significant symmetric voltage signals, while Al2O3 presents S/A smaller than other oxides due to its large A signal. In contrast, the low frequency second harmonic Hall measurements give no signals for all the devices, indicating that the extra resonance signals on ST-FMR are not originated from spin Hall effect. Our work reveals significant influence of oxide insulator substrates on ST-FMR measurement that should be taken into account on study of spin Hall angle. 
**References** 
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Spurious symmetric voltage signals on the spin torque ferromagnetic resonance measurement induced by oxide substrates

Bismuth-substituted yttrium iron garnets (Bi:YIG) have attracted recent interest due to the possibility of having coexisting perpendicular magnetic anisotropy (PMA) and
ultralow Gilbert damping (~10-4) [1–3]. The existence of ultralow damping, however, has so far been accompanied by the presence of substantial inhomogeneous broadening (~10–100 Oe). The relevant parameter for applications is the total ferromagnetic resonance (FMR) linewidth, and so it is of interest to minimize the inhomogeneous broadening as well as the damping. Here we demonstrate the presence of both ultralow damping (≤ 5 × 10-4) and low inhomogeneous broadening (≈ 10 Oe) in a series of epitaxial PLD-grown Bi:YIG/GSGG(111)films. However, achieving these low linewidths requires the magnetization to be approximately parallel to the [100] crystallographic direction (roughly 55 degrees relative to the film normal), as seen in the figure. It is extremely unusual to observe a minimum linewidth for intermediate angles—typically a sharp maximum is observed where the angle of the magnetization is most sensitive to changes in the angle of the applied field [4]. We show that for a film grown on a GGG(100) substrate, the perpendicular FMR linewidth at 20 GHz (≈ 30 Oe) is much smaller than for the films grown on (111) substrates (≥ 60 Oe). Furthermore, the minimum in the linewidth as a function of angle is not nearly as sharp and occurs at approximately 35 degrees relative to the film normal. For applications, it is crucial for the FMR linewidth to be small for perpendicular magnetization. We discuss potential causes for the anomalous angular dependence of the FMR linewidth and how to minimize it for perpendicular magnetization. This work was supported by SMART, a center funded by nCORE, a Semiconductor Research Corporation program sponsored by NIST.
**References** 
[1] Soumah et al., Nat. Comm. 9, 3355 (2018).
[2] Lin et al., JMMM 496, 165886 (2020).
[3] Caretta et al., Science 370, 1438 (2020).
[4] Woltersdorf and Heinrich, Phys. Rev. B 69, 184417 (2004). 

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Full-width-at-half-maximum FMR linewidth as a function of magnetization angle θ relative to the film normal for a 70 nm Bi:YIG/GSGG(111) film. Angles corresponding to [111] and [100] crystallographic directions are indicated

Anomalous angular dependence of ferromagnetic resonance linewidths in perpendicular Bi:YIG films with ultralow damping

Inspired by the success of FETs in electronics, voltage controlled magnetic anisotropy (VCMA) induced magnetization dynamics has emerged as an important integrant in low-power spintronic devices. In this talk, I will discuss our recent demonstration of VCMA induced parametric resonance excitation for generating magnons with exchange-interaction wavelengths [1]. Earlier, we had shown that the growth-induced magnetocrystalline anisotropy can be used for giving rise to a direction-specific magnon scattering [2]. This was shown
using epitaxy dependent anisotropic damping in (111), (110) and (100) YIG/GGG thin films. However, metallic ferromagnets grown on Si have a better compatibility with CMOS
processes. Therefore, we choose CoFeB/MgO junctions, that have emerged to be technologically relevant owing to its high perpendicular magnetic anisotropy, low damping, and high
TMR ratios.
Following an introduction to our earlier work on YIG, I will focus on the excitation of VCMA induced magnetization dynamics for in-plane magnetized CoFeB/MgO junctions (Fig. 1a), a
long-standing limitation of VCMA. This is done using VCMA of interfacial in-plane anisotropy [1], that is induced by magnetic annealing [3]. At high powers, VCMA induced parametric
resonance is observed (Fig. 1b). The wavelengths of corresponding magnons are estimated to be tuned down to the exchange-interaction length scales using magnetic field, power and
frequency of excitation (Fig. 1c). Power dependent parametric pumping amplitudes reveal unique trends at different dynamical excitation regimes (Fig. 1d). The crucial role of excitation
frequency in distinguishing VCMA induced magnetization dynamics will be discussed. Finally in Fig 1(e-f), using angular dependent measurements, we prove the presence of electric-field
torque from VCMA in both linear and non-linear magnetization dynamics [1].
**References** [1] A. Deka et al., Phys. Rev. Research 4, 023139 (2022).
[2] R.M.*, A. Deka* et al., Appl. Phys. Lett. 119, 162403 (2021). (*Equal first author)
[3] A. Deka et al., Phys. Rev. B 101 (17), 174405 (2020). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/be5352b95a3d88e4f47b7b677c539406.png) 
Fig. 1 (a) Illustration of VCMA excitation. (b) Power dependent inverse spin Hall effect voltage VISHE. (c) Calculated frequency and magnetic field Hex dependence on wavength of
magnons. (d) Power dependence of VISHE at different wavelengths. In-plane angle dependence of VISHE amplitudes at (e) uniform and (f) parametric resonances. Lines are fits to equations
in Ref. 1.

Generation of Magnons with Nanoscale Wavelengths using Voltage Controlled Parametric Resonance

The domain wall (DW) magnetic tunnel junction (MTJ) is a promising component of next-generation neuromorphic, in-memory, and logical computing hardware due to features including non-volatility, multiple analog resistive states, low power, and ultrafast read-write operation [1-3]. Predicting the DW motion along a magnetic track involves complicated and time-consuming micromagnetic simulations, which greatly impede the development of computing systems designed with interconnected DW-MTJ devices [4]. The neural ordinary differential equations (ODE) is a recently conceptualized deep learning framework that can predict the behavior of dynamic systems [5]. In this approach, the ODE that defines the time derivative of the system output is expressed as a deep neural network; when provided with initial conditions, an ODE solver determines the system response at future times. Chen et al. [6] extended this approach by expressing hidden variables that are difficult to probe with higher-order derivatives of the output, which are then replaced with mathematically equivalent time-delayed versions. External inputs can be applied to the network in a similar time-delayed fashion. In this work, DW motion by spin-transfer torque excitation is modeled utilizing the neural ODE framework. Temporal DW position data along a magnetic track excited by a set of random sinusoidal current inputs are generated by mumax3 [7] and are used to train a neural ODE in a supervised fashion through backpropagation. For a different set of random sinusoidal current inputs, the DW position forecasted by the trained network matches with the results generated by mumax3 with very high accuracy (Fig. 2) while reducing the simulation time by a factor greater than 200x, thereby opening the path to efficiently design integrated systems interconnecting a large number of DWMTJs. 

**References** [1] M. Alamdar, T. Leonard, C. Cui et al., Appl. Phys. Lett., vol. 118, no. 11, p. 112401 (2021).
[2] N. Hassan, X. Hu, L. Jiang-Wei et al., Jour. Appl. Phys., vol. 124, no. 15, p. 152127 (2018).
[3] W. H. Brigner, N. Hassan, L. Jiang-Wei et al., IEEE Trans. Electron Devices, vol. 66, no. 11, pp. 4970-4975 (2019).
[4] X. Hu, A. Timm, W. H. Brigner et al., IEEE Trans. Electron Devices, vol. 66, no. 6, pp. 2817-2821 (2019).
[5] R. T. Q. Chen, Y. Rubanova, J. Bettencourtet al., Proceedings of NeurIPS, 31 (2018).
[6] X. Chen, F. A. Araujo, M. Riou et al, Nat. Comm., vol. 12, no. 1016 (2022).
[7] A. Vansteenkiste, J. Leliaert, M. Dvornik et al., AIP Advances, vol. 4, no. 10, p. 107133 (2014). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/01364715490ab753cd3ac85dcf7e5cc1.png) 
Up (blue) and down (red) polarized magnetic domains along a track separated by a DW (yellow). Current inputs control the position of the DW by applying spin-transfer torque. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/9e4b8c52f3c00844a1d6aa3d22edfa85.png) 

DW position forecasted by a trained neural ODE in comparison with mumax3 simulation.

Modeling Magnetic Domain Wall Motion with Neural Ordinary Differential Equations

Self-spin-orbit torque (SOT) that arises from within the ferromagnetic layer itself, such as FePt [1] and CoPt [2] systems, offers new design possibilities for the SOT devices. Unlike FePtâ€™s self-SOT that relies on chemical ordering and apparent global symmetry breaking, CoPt was found to possess rather robust self-SOT with A1-disorder phase. This kind of bulk-SOT which does not rely on the apparent symmetry-breaking attracted our attention. A question arises as to whether the bulk-SOT generated by the structural disorder is comparable to that generated by apparent symmetry-breaking such as composition gradient and interface cutting? This study investigates the microstructural ordering effects on the CoPtâ€™s self-SOT phenomena using orientation-resolved synchrotron x-ray diffraction. Three samples, (i)Ta/CoPt (20nm)/Ta (denoted as baseline-CuPt); (ii) Ta/[Co(0.5nm)/Pt(0.5nm)]20/Ta (denoted as superlattice-CoPt); (iii) Ta/Cu(2nm)/CoPt(20nm)/Cu(2nm)/Ta (denoted as Cu-CoPt), were investigated. All three samples were determined to possess the A1 phase with close Ïxx (â‰ˆ 55 Î¼Î©â—cm) under the Hall device structure. The baseline-sample possessed a (111)-textured A1-phase microstructure, and it yielded a damping-like torque efficiency ÎµDT=0.174Â±0.037. This value is close to that reported in the representative literature of CoPt self-SOT [2]. A similar microstructure, while with an enhanced ÎµDT=0.636Â±0.0333, was obtained in the superlattice sample due to the multi-interface symmetry-breaking effects. However, we found that the microstructure appeared to contain randomly-oriented grains in the Cu-CoPt sample, and this resulted in ÎµDT=0.502Â±0.089. The results imply that the short-range symmetry-breaking could contribute to the SOT in a level close to that achieved by the apparent symmetry-breaking.

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Tuning exchange interactions in 1T VSe2 monolayer by alkali metal adsorption and electride substrate

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