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Rare earth-transition metal (RETM)-based ferrimagnets are known to exhibit strong bulk perpendicular magnetic anisotropy and bulk Dzyaloshinskii-Moriya interaction [1]. These properties make RETM ferrimagnets a model system to study exciting magnetic phenomena such as magnetic skyrmion [2,3], chiral domain wall [3], all-optical switching [4], spin-orbit torque switching [5] and canted magnetic moments. Here, we demonstrate a field-free spin-orbit torque-driven multistate switching of a nearly compensated GdCo ferrimagnet sandwiched between Ta and Pt. We show that our GdCo film exhibits a strong canting of magnetic moments, and the canted moments can be deterministically switched among three stable states using a current-driven spin-orbit torque, even in the absence of a magnetic field. We further show that the three states persist in the presence of an in-plane magnetic field and the levels of the three states can be tuned with the magnitude of the magnetic field. We consider various possible origins of the canting, including concentration gradient, Dzyaloshinskii - Moriya interaction, and balanced pair-correlations of unlike atoms versus like atoms in the growth direction, and discuss various methods to differentiate among these mechanisms. Furthermore, we discuss the possibility of domain formations to explain the observed multistate. Our results provide a new perspective to study the competing magnetic interaction in RETM-based ferrimagnetic alloys at the near-compensation point, and enable a new pathway to achieve multistate spin-orbit torque devices.

![](https://assets.underline.io/uploads/markdown_image/1/image/df0a749c720a6befff1af56d0b3f65bb.jpg)

Multistate switching of canted GdCo moments via spin-orbit torque with zero in-plane symmetry breaking field.


2022 Joint MMM-INTERMAG

Field-free Spin-orbit Torque-driven Multistate Switching of Canted GdCo Moments

The 15th Joint MMM-INTERMAG Conference (2022 Joint) is sponsored jointly by AIP Publishing and the IEEE Magnetics Society. Members of the international scientific and engineering communities interested in recent developments in fundamental and applied magnetism are invited to attend and contribute to the technical sessions. The technical program will include invited and contributed papers in oral and poster sessions, invited symposia, a plenary session, and an evening session, with about 1500 presentations overall. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

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This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

technical paper

The real-space Berry phase associated with conduction carriers has recently attracted much attention from the viewpoints of fundamental science and spin-electronics applications. The noncoplanar spin textures responsible for the Berry phase usually appear during the magnetization reversal, often occur in systems with Dzyaloshinskii-Moriya interactions (DMI) due to, broken inversion symmetry, and yield skyrmions in specific temperature and magnetic-field ranges [1, 2]. One key aim in skyrmion research is to realize small feature sizes, which lead to a pronounced topological Hall effect (THE), at high temperatures. Confined geometries such as nanoparticles or clusters are potential systems for this purpose because the competing exchange and magnetocrystalline anisotropy of nanoparticles are expected to cause substantially noncoplanar noncollinear spin structures even in the absence of DMI. Here, we use experiments and micromagnetic simulations to investigate spin textures in exchange-coupled Co nanoclusters produced by inert-gas condensation-type cluster deposition. The nanoclusters have an average size of 14 nm and exhibit a significant topological Hall effect (THE), as shown in the experimental Hall data of Fig. 1(a). The micromagnetic THE simulations, Fig. 1(b), predict the skyrmion number Q by integration over the skyrmion density and are in good agreement with the experimental data. THE is caused by the noncoplanar noncollinear spin structure of the Co nanoclusters, visualized in Fig. 1(c). A characteristic feature of both experimental THE and theoretical prediction (skyrmion number Q) is a drastic change over a relatively small field range, which we interpret as a topological phase transition analogous to the Lifshitz transition in metals. This work is supported by NSF-DMREF (No. 1729288), NSF-EQUATE (OIA-2044049), the NU Collaborative Initiative, and NCMN,

![](https://assets.underline.io/uploads/markdown_image/1/image/1dc29675931a0b1064caa936e9c420a1.jpg)

Fig. 1. Topological Hall effect (THE) in Co nanoclusters: (a) measured THE at 300 K and 10 K, (b) calculated Q as a function magnetic field and (c) simulated spin structure. The insets in (b) show the simulated spin textures at different fields. Red and blue colors represent spin-up and spin-down magnetization directions, respectively.

Hall Effect and Topological Phase Transition in Exchange-Coupled Nanomagnets

Magnetic skyrmions are a prime example of topologically non-trivial spin textures observed in a variety of magnetic materials. They emerge when the exchange and anisotropy energies promoting parallel alignment of spins in a ferromagnet enter in competition with energies favoring non-collinear alignment of spins such as the Dzyaloshinskii-Moriya interaction (DMI), the long-range dipolar interaction or higher-order exchange interactions. The orthodox theory of skyrmions in ultrathin ferromagnetic layers with interfacial DMI relies on a model that accounts for the dipolar interaction through an effective anisotropy term, neglecting long-range effects. At the same time, in single ferromagnetic layers with interfacial DMI, large chiral skyrmions, also called skyrmionic bubbles have been observed, suggesting a non-trivial interplay between DMI and long-range dipolar effects[1]. The competition between these two energies also leads to the formation of skyrmions exhibiting spin rotations with intermediate angles between Neel and Bloch, a phenomenon also present in domain walls. In addition, there is a growing body of theoretical evidence that points to a need to take into account the long-range dipolar energy in the models describing magnetic skyrmions. The above considerations put into question the validity of the commonly used assumption that the long-range contribution of the dipolar interaction is negligible. Here we use rigorous mathematical analysis to develop a skyrmion theory that takes into account the full dipolar energy in the thin film regime and provides analytical formulas for compact skyrmion radius, rotation angle and energy[2,3]. We demonstrate that the DMI threshold at which a compact skyrmion loses its Néel character is a factor of 3 higher than that for a single domain wall. A reorientation of the skyrmion rotation angle from Néel to intermediate Néel-Bloch angles is predicted as the layer thickness is increased in the low DMI regime, which is confirmed by micromagnetic simulations. We will also present an extension of our model which includes applied magnetic field.

Theory of Néel-Bloch transition for compact magnetic skyrmions

In nanomagnetism and spintronics, magnetic multilayers continue to thrive as pivotal structures to engineer complex non-trivial spin textures thanks to the tunability of their composition and their properties. Two-dimensional magnetic textures such as skyrmions or chiral domain walls were mostly under focus for the last decade, but recently interest has surged for more complex objects which display an inhomogeneous behavior over the vertical dimension [1,2]. Interesting examples include bobbers which could become remarkable assets for the development of logic devices [3] or the recently observed hopfions [4] or even different skyrmions phases [5]. Our own efforts to engineer and explore three-dimensional textures in Pt/Co based multilayers allows us to observe the signature of new textures, which we name skyrmionic cocoons. At low magnetic field, they resemble tubular skyrmions but upon an increase of the out-of-plane field, they shrink and disappear in the outer layers (Fig 1.b,c), becoming elongated ellipsoids. To observe such textures, we grew multilayers displaying variable thicknesses of a ferromagnetic material, thereby introducing a non-uniform effective anisotropy. By carefully tuning the thickness of each magnetic layer, it was possible to observe in a single sample two distinct types of objects, as shown by the strong difference in the Magnetic Force Microscopy (MFM) contrasts (Fig 1.a). With the support of micromagnetic simulations (Fig 1.b), we identify them as two vertically coupled cocoons (large contrast) and single cocoons only present in half of the layers (weak contrast). The existence and field-dependent behavior of such textures could represent interesting possibilities for potential applications.

![](https://assets.underline.io/uploads/markdown_image/1/image/e2c9cf21f889d9f4fd7c83a4aa3ac691.jpg)

Fig 1. a) MFM measurement at 265 mT on a multilayer with variable thickness of Co. b) Corresponding micromagnetic simulations at different fields displayed with isosurfaces, mz=0 (white) and mz=-0.8 (red), with plane cuts identified by the coloured lines. The yellow dotted ellipses evidence the two kinds of objects correlated with the MFM image: coupled cocoons (left) and single cocoons (right). c) Simulated vertical cuts showing the evolution of a cocoon at different out-of-plane magnetic fields.

Non-Collinear Three-Dimensional Textures In Magnetic Multilayers: Hatching of Skyrmionic Cocoons

Antisymmetric exchange interactions are used to stabilize magnetic textures and lead to non-reciprocal spin-wave propagation [1-2]. As a result, left and right propagating waves at the same energy have different wavelengths. Thus, interference between counter-propagating spin waves does not lead to standing waves; instead, confined modes have a time-dependent phase, i.e., their phase is modulated at a rate determined by the Dzyaloshinskii–Moriya interactions (DMI) [3]. We report on a Brillouin light scattering (BLS) study of confined spin waves in Co/Pt nanowires with strong DMI, whose widths range from 100 to 400 nm [4]. Two different scattering geometries were used: a transverse geometry where the incident light is perpendicular to the nanowire, as illustrated in Fig. 1(a), and a longitudinal geometry, where the incident light is parallel to the nanowire. Fig. 1(b) shows a SEM image of a nanowire array. Fig. 2(a-d) show sample BLS spectra for both scattering geometries. Fig. 2(e) shows spin-wave quantization in narrow (&lt;200nm width) wires dramatically reduces the frequency shift between BLS Stokes and anti-Stokes lines in the transverse geometry. In contrast, the frequency shift associated with the longitudinal geometry is independent of nanowire width. A model that considers phase-modulated confined modes captures this physics and predicts a dramatic reduction in frequency shift of light scattered from higher energy spin waves in narrow wires, which is confirmed by our experiments. Our results show that, in contrast to the BLS frequency shift in the longitudinal scattering geometry, which enables direct determination of the DMI, the BLS frequency shift in the transverse scattering geometry is not directly related to the DMI.

![](https://assets.underline.io/uploads/markdown_image/1/image/bacdbe811474e59401429bb719b9e203.jpg)

Fig. 1 (a) Schematic of spin waves in a confined geometry with chiral magnetic interactions. (b) A SEM image of the nanowire array consisting of 100 nm width Co/Pt nanowires with 100 nm spacing.

![](https://assets.underline.io/uploads/markdown_image/1/image/385e357996864555747b01fc03369e04.jpg)

Fig. 2 (a)-(d) BLS spectra for Stokes and anti-Stokes processes for both positive and negative fields on nanowire arrays with different widths. (e) The absolute value of the frequency shift on nanowire arrays with different widths in the longitudinal (k∥L) and transverse (k⊥L) scattering geometries.

Brillouin Light Scattering from Quantized Spin Waves in Nanowires with Antisymmetric Exchange Interactions

Skyrmions exhibit topologically nontrivial spin textures [1] and can be motioned by comparably small spin-polarized currents [2]. This renders them promising for the use as information carriers in future magnetic data storage and processing technologies, referred to as Skyrmionics. To better understand the physics of Skyrmions, a detailed knowledge of the real space magnetic structure of these spin solitons is mandatory. We have therefore studied the 3D magnetic textures of Skyrmion tubes (SkTs) using in-line and off-axis electron holography (EH). While the orientation of the in-plane magnetic induction B obtained from a Fe0.95Co0.05Ge nanoplate using in-line EH shows the expected hexagonal vortex-like pattern (Fig. 1), a thorough quantitative analysis implies that the underlying 3D texture deviates from that of homogeneously extended Bloch Skyrmions [3]. Low temperature holographic vector field electron tomography (VFET [4]) in an external magnetic field was therefore used to quantitatively reconstruct the full 3D magnetic texture of SkTs in an FeGe needle [5]. The resulting high-resolution 3D magnetic images (Fig. 2) reveal various previously unseen details of the SkTs. Our findings include the occurrence of local deviations from a homogeneous Bloch character within the tubes. They highlight the collapse of the Skyrmion texture upon approaching the surfaces of the needle, provide evidence for the coexistence of longitudinal and transverse Skyrmion textures, and reveal an axial modulation of the SkTs that is found to be strongly correlated among neighboring tubes in the needle. Based on the quantitative 3D magnetic induction data, we have calculated spatially resolved energy density maps across the SkTs that provide experimental evidence for the energetic stabilization of these magnetic solitons through an energy gain due to the Dzyaloshinskii-Moryia interaction, which overcompensates the exchange energy in the tube centers.

![](https://assets.underline.io/uploads/markdown_image/1/image/95d4498ede230bdf211fb866fabb1ce2.jpg)

Orientation map of the projected in-plane component of the magnetic induction in the hexagonal Skyrmion lattice of a Fe0.95Co0.05Ge nanoplate.

![](https://assets.underline.io/uploads/markdown_image/1/image/a445af1acb5f54ffe8123e81a66772df.jpg)

Morphology of an FeGe needle (left) and direction of the 3D magnetic induction B (right) as determined from holographic VFET experiments.

Unravelling the details of the magnetic texture of skyrmion tubes in three dimensions

Focused ion beam (FIB) irradiation is a versatile means to tune magnetic thin films on the nanoscale [1]. Ion irradiation can create nucleation sites for Skyrmions [2] and even establish Skyrmion-tracks [3]. In this work, we present statistical data of Skyrmion motion driven by 50 ns long current pulses in a sputtered W/CoFeB/MgO trilayer. In this layers a Skyrmion phase can be stabilized by a an oop-field in the low single digit mT regime. Furthermore, we elaborate on how Skyrmion motion can be tuned and directed by non-destructive Ga+ Ion irradiation with ultra-low doses (&lt;1e13 Ions/cm2) and high dose resolution of &lt; 1e12 Ions/cm2. First, we will give an overview of how the magnetic properties of the thin film are affected by ion irradiation. Here we analyze the average domain size, film coercivity (Hc) and relative decrease of saturation magnetization (Ms) and effective magnetization (Meff), over different irradiation steps and compare this data to stepwise annealing of the samples. Next, we track the motion of at least 50 Skyrmions for various current densities in magnetic wires, utilizing widefield magneto-optical measurements, as depicted in Figure 1. Hereby half of the wire is treated with Ga+ ions. We show that ion irradiation can be used to adjust the motion of Skyrmions towards lower velocities. While the Skyrmion velocity is very similar in the pristine parts of the wires, the velocity in the irradiated region is heavily dependent on the ion dose (see Figure 2). This lower velocity is accompanied by a significantly reduced Skyrmion Hall angle in the irradiated part, which leads to a nearly straight motion in the direction of the current flow. Beyond that, also stochastical motion due to thermal effects is largely supressed in the irradiated parts.

![](https://assets.underline.io/uploads/markdown_image/1/image/bb1f0be62208fad403370b509e76634d.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/82950f12d80d3940195e22e18676c0c9.jpg)

Influence of Ga+ Ion Irradiation on Skyrmion Motion

Influence of Ga+ Ion Irradiation on Skyrmion Motion

Skyrmions are topologically protected chiral spin textures that have shown promise as data carriers in future spintronic applications. They can be stabilized by the interfacial Dzyaloshinskii-Moriya interaction (iDMI) in material systems with inversion asymmetry and spin-orbit coupling, such as Ir/Co/Pt multilayers [1]. The ability to locally (at the nanoscale) tune such interface interactions, and hence the skyrmion energy, could lead to novel ways to optimise the nucleation and control of skyrmions. In this contribution we investigate the local tuning of the iDMI and the perpendicular magnetic anisotropy (PMA) using Ga+ ion irradiation, as well as its effect on skyrmion nucleation. Ga+ ion irradiation affects the coordination of atoms at the interfaces (Fig. 1a), which is expected to decrease both PMA and iDMI [2]. From Fig. 1b, we find that the reduction in PMA and iDMI are correlated, suggesting that both effects depend similarly on the interface quality. This reduces the energy cost of domain walls but does not affect their chirality. Hence, we expect that this will also facilitate the nucleation of more complicated chiral textures, such as skyrmions. To confirm this, we studied for the first time the current driven nucleation of skyrmions [3] in identical devices with and without Ga+ ion irradiation. We find that the ion irradiation indeed affects skyrmion nucleation, see Fig. 2. The critical current density required for nucleation is reduced by almost 30% and the number of skyrmions is doubled by irradiation. Thus, we argue that ion irradiation can be used to facilitate and control the nucleation of skyrmions in novel devices.

![](https://assets.underline.io/uploads/markdown_image/1/image/3e984d72283a4626aa9f30b40e9bb2d9.jpg)

Fig. 1 a) Illustration: Ion irradiation causes intermixing at interfaces (left to right). b) Plot of the strength of the iDMI Ds against the strength of the interface PMA Ks, both Ds and Ks decrease when the Ga+ dose is increased, as indicated by the arrow.


![](https://assets.underline.io/uploads/markdown_image/1/image/920cf7b2d1c34d1c6fbb082d4a8f6f88.jpg)

Fig. 2 Number of skyrmions nucleated in our devices after applying 1000 50 ns pulses with current density J. In an irradiated device the number of skyrmions is increased and the current density required for nucleation is lowered. Black lines are fits to the data with the error function. Top: MFM scans of the devices.

Facilitating Skyrmion Nucleation in Ir/Co/Pt Multilayers With Ga+ Ion Irradiation

Anisotropic magnetoresistance (AMR) is a ubiquitous and versatile probe of magnetic order in contemporary spintronics research [1]. It arises from the dependence of the resistance of a magnetically ordered solid on the relative angle between the applied electric field and the magnetization vector independent of their polarity. The origins of the AMR are usually ascribed to extrinsic effects (i.e. spin-dependent electron scattering), whereas intrinsic (i.e. scattering-independent) contributions are neglected [2]. Here, we perform a broadband measurement of the AMR of prototypical ferromagnets such as Co, Ni or NiFe alloys in a frequency range from DC to 28 THz [3]. The large bandwidth covers the regimes of both diffusive and ballistic intraband electron transport and, thus, allows us to separate extrinsic and intrinsic AMR components. Analysis of the THz response based on Boltzmann transport theory reveals that the AMR of the Ni and NiFe alloys is of predominantly extrinsic nature. However, the Co thin film exhibits a sizeable intrinsic, frequency-independent AMR contribution, which amounts to more than 2/3 of the DC AMR contrast of 1%. These features are attributed to the lower symmetry of the hexagonal structure of Co crystallites which allows for larger anisotropies in their bandstructure. The new insight into the nature of AMR is not only relevant for the fundamental understanding of the magnetotransport but might also advance the ultrafast probing techniques in spintronic devices.

![](https://assets.underline.io/uploads/markdown_image/1/image/b939fa383f615a86b5ac200134a15b4d.jpg)

Fig. 1. THz detection of the AMR. The incident THz pulse applies transient electric field in the direction of polarization, in which, as a consequence of the AMR, the electrical resistance and the transmission of the THz pulse depend on the angle of the magnetization. Variations in transmitted amplitude allow us to calculate the AMR contrast.


![](https://assets.underline.io/uploads/markdown_image/1/image/584dca932356943c776e64e9fc76bbd6.jpg)

Fig. 2. Spectral composition of the AMR in different metals. (a) The absolute value of the AMR contrast in permalloy versus frequency is well described within the Drude formalism (curve) assuming only magnetization-dependent electron scattering rates. (b) The same measurement for a cobalt sample shows a scalable frequency-independent offset which witnesses the intrinsic contribution to the AMR.

Broadband terahertz spectroscopy of anisotropic magnetoresistance reveals intrinsic contributions

Spin torque ferromagnetic resonance (ST-FMR)1 has widely been used for evaluation of the spin Hall effect (SHE) of the nonmagnetic metal (NM) in an NM/ferromagnetic metal (FM) bilayer structure. Figure 1 shows a schematic of the measurement setup of the ST-FMR. DC voltage, VDC, is monitored under a microwave irradiation with sweeping the external magnetic field, Bext. VDC-Bext curve in the ST-FMR measurement is composed of symmetric and anti-symmetric Lorentzian functions. In the simplest case, efficiency of the SHE, which is especially called spin Hall angle (SHA), can be estimated by taking the amplitude ratio between two Lorentzian functions. However, unwanted effects such as the spin pumping, the anomalous Nernst effect, and non-uniform flow of the charge current impede a precise estimation of SHA. Therefore, a cross-check of the obtained SHA by using another methodology is desired. In this study, we found an additional signal related to the SHA in the ST-FMR spectrum2. Figure 2 shows the ST-FMR spectrum of a tantalum (Ta)/cobalt (Co) sample, where the microwave frequency, f, was 12 GHz and the microwave power, P, was 5 dBm. l, w, and q defined as shown in Fig. 1 were 5 μm, 5 μm, and 45°, respectively. In addition to the conventional Lorentzian functions which correspond to the ST-FMR, a magnetization-dependent background (BG) signal was also observed. From the Bext, P, f , temperature and NM material dependences, we conclude that the BG signal is mainly generated by the spin-dependent unidirectional spin Hall magnetoresistance (SD-USMR)3, the origin of which is the spin-dependent electron mobility in the FM. From the magnitude of the BG signal, SHA of Ta was estimated to be -0.042±0.006, which is consistent with the previous works. The ST-FMR spectrum is produced by the spin orbit torque, whereas the BG signal is produced by the spin accumulation. Therefore, our finding provides an effective cross-check of the SHA, which are obtained from two different physical origins by using only one ST-FMR spectrum.


![](https://assets.underline.io/uploads/markdown_image/1/image/a0a14efb8444390cd598c3d1052c95a2.jpg)

A schematic of the device and the electrical circuit used in the ST-FMR measurement


![](https://assets.underline.io/uploads/markdown_image/1/image/d505d560f88dbba485e85162b710bd64.jpg)

ST-FMR spectra with the BG signal originating from the SD-USMR for Ta/Co.

DC voltage generated by the unidirectional spin Hall magnetoresistance in the spin torque ferromagnetic resonance spectrum

Pure spin currents produced by the spin Hall effect(SHE) in a nonmagnetic heavy metal has the potential to drive ultra-fast, energy-efficient spintronic devices such as spin Hall nano-oscillators(SHNOs)[1-3], spin-orbit torque based magnetic random access memory(SOT-MRAM), and spin logic devices[4,5]. One key challenge in such emerging devices remains to reduce their high current densities(Jc) and energy consumption to drive magnetization switching and auto oscillations in the adjacent ferromagnets. Efforts have been made to increase the SOT efficiency(ζSOT) by choosing suitable material combinations and/or use oxygen incorporation[6]. However, the increased ζSOT is observed at the expense of an equivalent increase in the longitudinal resistivity(ρ), which essentially cancels out any reduction in the power consumption. A more successful direction is instead to alloy elements, which are in themselves already good SOT material[7]. Here, we demonstrate such alloying of W with Ta to obtain a simultaneous increase of both the ζSOT and the spin Hall conductivity(σSH), which in turn substantially reduces the Jc in W100-xTax(5nm)/CoFeB(tCFB=1.4 to 2 nm)/MgO(2nm) SHNOs. First, we performed STFMR measurements on microbars (6 ×18 µm2, 6 ×12 µm2) to determine their magnetodynamical properties such as current induced ζSOT and σSH. The ζSOT varies from maximum ~ -0.57(x=10%) to ~-0.18(x = 50%) as compared to pure β-W, ~-0.36(x=0). Thanks to a reduced resistivity of W100-xTax, the increased ζSOT is accompanied with a significant increase of the σSH of about ~140% as compared to pure β-W. Finally, we investigated the alloying effect on the auto-oscillation threshold current(Ith) densities by fabricating SHNOs of different widths varying from 10nm to 150nm on a 4 × 14 µm2 mesa[1] and observed about 40% reduction in Ith (at x=12%) as compared to pure β-W measured. The trade-off between ζSOT, ρ, and σSH demonstrates the promising aspects of a W-Ta alloying approach for energy-efficient operation of emerging spintronic devices

![](https://assets.underline.io/uploads/markdown_image/1/image/5e590e6a057e20864ec79b7e0c117dad.jpg)

Fig.1: (a) Variation of ρ(blue) and σSH(red) vs. W100-xTax alloy composition. (b-c) Power spectral densities showing a 40% reduction in the SHNO Ith for two SHNOs with identical constriction width of 50nm.

Field-free Spin-orbit Torque-driven Multistate Switching of Canted GdCo Moments

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Field-free Spin-orbit Torque-driven Multistate Switching of Canted GdCo Moments

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Hall Effect and Topological Phase Transition in Exchange-Coupled Nanomagnets

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Local and Non-local Curvature-induced Chiral Effects in Nanomagnetism

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