United States

Synthetic antiferromagnets (SAFs) are of interest in a wide variety of spintronic applications owing to their net zero magnetisation and inherent tunability arising from control over complex stacking sequences [1]. They show very fast domain wall (DW) motion in response to spin torques [2].
Here we describe measurements of the current-driven DW motion in each of the separate magnetic sublattices of a SAF with structure Ta/[Ru/Pt/CoB/Ru/Pt/CoFeB]×5/Ru/Pt which displays both perpendicular magnetic anisotropy (PMA) and the Dzyaloshinskii-Moriya interaction (DMI). The thickness of the Ru layers is tuned to provide AF coupling between each pair of layers. The thicknesses of the alternating CoB and CoFeB layers are tuned to give net zero magnetisation (as measured by SQUID magnetometry) at a wide range of fields up to ~50 mT.
The magnetic films were grown on Si3N4 membranes and imaged with scanning transmission x-ray microscopy (STXM). They were patterned into 2 µm wide wires with Cu leads attached to each end. The distinct chemical composition of the two sublattices means that we could use the element specificity of STXM to observe the CoFeB separately by imaging at the Fe L3 edge, whilst contrast at the Co L3 edge is dominated by the other sublattice of CoB layers. Inverted domain structures observed at these two edges with XMCD-STXM are shown in Fig. 1, confirm the SAF ordering of the layers. Current pulses drive domain wall motion, as shown in Fig. 2, with average velocities up to ~ 40 m/s achieved at current densities as low as 3 × 1011 A/m2. These results demonstrate a low depinning current and fast motion compared to comparable FM multilayers we have previously studied, suggesting that domain walls in SAF heterostructures are superior to their ferromagnetic equivalents for low energy consumption racetrack technologies.&lt;br&gt;&lt;br&gt;
**References** &lt;br&gt;[1] R. A. Duine et al., Nature Phys. 14, 217 (2018)
[2] S.-H. Yang et al., Nature Nanotech. 10, 221 (2015)&lt;br&gt;&lt;br&gt;

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MMM 2022

Current Driven Domain Wall Motion in a Synthetic Antiferromagnet Multilayer

Synthetic antiferromagnets (SAFs) are of interest in a wide variety of spintronic applications owing to their net zero magnetisation and inherent tunability arising from control over complex stacking sequences [1]. They show very fast domain wall (DW) motion in response to spin torques [2].
Here we describe measurements of the current-driven DW motion in each of the separate magnetic sublattices of a SAF with structure Ta/[Ru/Pt/CoB/Ru/Pt/CoFeB]×5/Ru/Pt which displays both perpendicular magnetic anisotropy (PMA) and the Dzyaloshinskii-Moriya interaction (DMI). The thickness of the Ru layers is tuned to provide AF coupling between each pair of layers. The thicknesses of the alternating CoB and CoFeB layers are tuned to give net zero magnetisation (as measured by SQUID magnetometry) at a wide range of fields up to ~50 mT.
The magnetic films were grown on Si3N4 membranes and imaged with scanning transmission x-ray microscopy (STXM). They were patterned into 2 µm wide wires with Cu leads attached to each end. The distinct chemical composition of the two sublattices means that we could use the element specificity of STXM to observe the CoFeB separately by imaging at the Fe L3 edge, whilst contrast at the Co L3 edge is dominated by the other sublattice of CoB layers. Inverted domain structures observed at these two edges with XMCD-STXM are shown in Fig. 1, confirm the SAF ordering of the layers. Current pulses drive domain wall motion, as shown in Fig. 2, with average velocities up to ~ 40 m/s achieved at current densities as low as 3 × 1011 A/m2. These results demonstrate a low depinning current and fast motion compared to comparable FM multilayers we have previously studied, suggesting that domain walls in SAF heterostructures are superior to their ferromagnetic equivalents for low energy consumption racetrack technologies. 
**References** [1] R. A. Duine et al., Nature Phys. 14, 217 (2018)
[2] S.-H. Yang et al., Nature Nanotech. 10, 221 (2015) 

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poster

#### Welcome to the 67th Annual Conference on Magnetism and Magnetic Materials, MMM 2022!

The Conference was held from October 31 to November 4 and offers both in-person and on-demand content.

MMM 2022 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 tutorial, and several special sessions. 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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Europium (Eu) metal has a body centered cubic crystal structure which, upon a paramagnetic-to-helical magnetic transition, undergoes a body centered tetragonal distortion. The magnetic helix appears below Néel temperature (TN) of ~90 K, and the presence of a magnetic field gives rise to conical helimagnet [1,2]. We have prepared Eu metal thin films on Si (001) substrates using Eu metal as a target by pulsed laser deposition (PLD). The transport measurement shows the helical antiferromagnetic transition at 88 K, and a thermal hysteresis reveals the first-order nature of the phase transition. We present the magnetoresistance (MR) of Eu thin films when the magnetic field (B) is applied both out-of-plane and in-plane. We found, at temperatures below TN, the MR is positive whereas above TN the MR is negative. We also observed the hysteretic oscillation above 30 K and below the Néel temperature. The hysteretic oscillations observed in the MR is believed to be associated with the change in the distribution of the antiferromagnetic domains in Eu caused by the interplay of the applied magnetic field and the strain in the films.

This work was supported by NSF (DMR-1710512) and the USDOE (DE-SC0020074) 
**References** [1] C. E. Olsen, N. G. Nereson, and G. P. Arnold, J. Appl. Phys., 33, 1135 (1962).
[2] N.G. Nereson, C. E. Olsen, and G. P. Arnold, Phys. Rev. 135, A176, (1964).

Magnetoresistance in Helical Antiferromagnet Eu Metal Thin Films

Transition metal nitrides with ferrimagnetism have recently attracted attention because of their skyrmionic functionalities at room temperature [1,2], and the topological Hall effect (THE) was observed for Mn based transition metal nitrides such as Mn4N thin films [3,4]. The conventional spin texture for the film is collinear with perpendicular magnetic anistoropy, which is remarkably sensitive to the growing temperature as well as substrate-induced strain [5,6]. Therefore, these characterisitcs of the Mn4N warrants further study how the spin texture is modulated by the method of elemental doping, and it is our expectation that the turnability of spin textures of the films could allow us to realize possible skyrmionic devices that work under no external magnetic field. In this study, we investigated the THE for the sputter-deposited (111)- and (110)-oriented Mn4(N,B) films aiming the control of topological spin textures by elemental-doping of B [7].
Figures 1 shows the representative THE for the 111-oriented Mn4N film without B at 300K. The THE component was extracted from the total AHE component, suggesting the presence of non-coplanar spin texture for the films at room temperature. Figure 2 shows the measurement temperature (T) dependence of ρxyTHE/ρxyAHE ratio for the films with and without B. The ratio increased at lower T, suggesting the stabilization of non-coplanar spin textrue at lower T. In addition, supression of THE was observed by B for all T. These results show a dilution effect in the spin frustration state with topological spin texture by B. Conversely, slight increase of THE was observed by B in the case of 110-oriented films. Therefore, B in the antiperovskite systems such as Mn4N could acts as an efficient suppressor or booster of frustrated exchange interactions between Mn atoms. 
**References** [1] C. T. Ma, et al., APL. 119, 192406 (2021).
[2] T. Bayaraa, et al., PRL. 127, 217204 (2021).
[3] G. Wang, et al., APL. 113, 122403 (2018).
[4] M. Meng, et al., APL. 112, 132402 (2018).
[5] S. Isogami, et al., JMMM, in press (2022).
[6] T. Hirose, et al., AIP Adv. 10, 025117 (2020);
[7] S. Isogami, et al., JAP. 131, 073904 (2022).
 
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Tailored non collinear magnetic structure in 111

Antiferromagnetic materials opened up a new avenue of research with potential use in spintronic devices [1]. Compared to their ferromagnetic counterparts antiferromagnets exhibit faster dynamics, insensitivity to the external magnetic fields, and absence of stray fields promising higher integration density.
Some functionalities of the antiferromagnetic spintronic devices such as readout using anisotropic magnetoresistance or reorientation of magnetic axis using current-induced spin-orbit torque [2] are directly derived from their ferromagnetic counterparts whereas other functionalities are unique to the antiferromagnets. One of these is the Quenching of the antiferromagnet into high resistivity states using electrical and optical pulses which was recently discovered in epitaxially grown thin CuMnAs films [3]. This effect is based on the change of the magnetic structure of the antiferromagnet induced by the application of high energy pulse driving the system to the vicinity of Néel temperature and its subsequent fast cooling resulting in quenching of the highly resistive disordered magnetic state. The observed changes of resistivity reach tens of percent at room temperature and even 100 percent at low temperatures and exceed by two orders of magnitude the change of the resistivity based on anisotropic magnetoresistance induced by the reorientation of the spin axis [2].

In this contribution, we provide an overview of detailed experimental characterization of quenching of CuMnAs using a single ultrashort laser pulse for excitation. We focus on the optimization of the electrical readout response of the Hall-bar devices with regard to the size and position (Fig.1) of the laser spot, pulse length, and fluency. It provides an overview of the response for CuMnAs films with varying thickness and substrate material. Lastly, this contribution evaluates the effects of permanent damage caused by laser pulse excitation with proposed damage mitigation techniques. 
**References** [1] Jungwirth, T., Marti, X., Wadley, P. et al. Antiferromagnetic spintronics. Nature Nanotech 11, 231–241 (2016). https://doi.org/10.1038/nnano.2016.18
[2] Wadley, P. et al. Electrical switching of an antiferromagnet. Science 351, 587–590 (2016). https://doi.org/10.1126/science.aab1031
[3] Kašpar, Z., Surýnek, M., Zubáč, J. et al. Quenching of an antiferromagnet into high resistivity states using electrical or ultrashort optical pulses. Nat Electron 4, 30–37 (2021). https://doi.org/10.1038/s41928-020-00506-4
 
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Characterization of laser pulse induced quenching of resistivity of antiferromagnetic CuMnAs

Room-temperature skyrmions have been presented as potential candidates for encoding information bits in several types of new spintronic devices [1]. There have been many recent progresses allowing to stabilize sub-100 nm skyrmions at room temperature in crystalline ferromagnetic thick layers or in (amorphous) thin magnetic multilayers (MML) [2]. In most case, at least in extended films or large structures, the application of relatively large perpendicular field (a few 10 mT) is needed which might be unfavorable for most of the anticipated skyrmion based devices. Hence, the stabilization of zero-field isolated skyrmions or skyrmion lattices is an important step towards application. There are recent works demonstrating isolated zero-field skyrmions stabilized due to interlayer exchange in polycrystalline [3], epitaxial [4] or exchange biased [5] trilayers. Here we demonstrate a new approach showing that room-temperature zero-field skyrmion lattices can be stabilized in MML. We develop a system in which perpendicular magnetic anisotropy, chiral order and bias field strength, through a non-magnetic spacer, can be adjusted simultaneously. Typical stacking sequence is schematically presented in Figure 1 (a). The samples have been characterized first by standard magnetometry (Fig. 1b). Relying on the interlayer electronic coupling to an adjacent bias magnetic layer with strong perpendicular magnetic anisotropy (uniform configuration), we demonstrate by Magnetic Force Microscopy that the remnant wormy-stripe “as-grown” domains (Fig. 1d) can be turned into skyrmion lattice phase (Fig. 1c). The skyrmion density and size can be modified by finely tuning the thicknesses of the layers allowing the control of the parameters related in the stabilization of the lattices. ANR TOPSKY (ANR-17-CE24-0025), DARPA TEE program (MIPR#HR0011831554) and EU SKYTOP (H2020 FET Proactive 824123) are acknowledged for financial support. 
**References** [1] A. Fert, N. Reyren, V. Cros, Nat. Rev. Mat. 2, 17031 (2017)
[2] C. Moreau-Luchaire et al., Nat. Nanotechnol. 11, 444 (2016)
[3] G. Chen et al., Appl. Phys. Lett. 106, 242404 (2015)
[4] R. Loconte et al., doi : 10.1021/acs.nanolett.0c00137
[5] K. G. Rana et al., Phys. Rev. Applied 13, 044079 (2020)
 
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Zero field room

Magnetic skyrmions is a vortex like nanosized spin swirling texture with particle like property [1]. In the past decade, magnetic skyrmion has triggered great interest as component in futuristic magnetic memory devices due to its topological property, smaller size (few nm) and efficient current driven motion. The chiral cubic β-Mn type (Co0.5Zn0.5)20-xMnx (3 ≤ x ≤ 7) alloys are fascinating as they allow the fine tuning of size and stability of skyrmions in wide temperature range with composition [2]. Among (Co0.5Zn0.5)20-xMnx alloys, magnetic properties of the Co7Zn7Mn6 alloy are of renewed interest due to the detection of two independent skyrmion phases (SkX): (i) a conventional thermodynamically stable SkX below helimagnetic to paramagnetic transition temperature (TC ~ 213 K) and (ii) a disordered skyrmion phase above spin glass transition (Tg ~ 23 K) [3-4]. In spite of much progress made on the investigation of exotic magnetic field-temperature phase diagram of Co7Zn7Mn6 helimagnet, the nature of its underlying magnetic interactions still remains elusive. Thus an elaborate in-field critical behavior study of skyrmion hosting polycrystalline cubic β-Mn type Co7Zn7Mn6 chiral magnet based on magnetic isotherms measured in the vicinity of ordering temperature is presented. The critical exponents β, γ and δ for spontaneous magnetization, initial magnetic susceptibility and critical M-H isotherm, respectively are evaluated through the modified Arrott plot, Kouvel-Fisher method and critical isotherm analysis. The estimated critical exponents β = 0.382(1), γ = 1.386(2) and δ = 4.628(1) follow Widom equality and magnetic scaling equations of state. The values of these exponents corroborate that the critical behaviour of Co7Zn7Mn6 system is akin to that of three-dimensional (3D) isotropic nearest-neighbour Heisenberg ferromagnet in which the attractive extended type short-range interactions between spins decay with distance r as J(r) ~ r-4:94. 
**References** 1. S. Mühlbauer, B. Binz, F. Jonietz, Science 323, 915 (2009)
2. Y. Tokunaga, X. Yu, J. White, Nat. Commun. 6 (1) 1–7 (2015)
3. K. Karube, J. S. White, D. Morikawa, Sci. Adv. 4 (9) eaar7043 (2018)
4. V. Ukleev, K. Karube, P. Derlet, npj Quant. Mater. 6 (1) 1–8 (2021) 
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In field critical behaviour of β

We investigated the spin-orbit torque (SOT) switching of the single CoTb layer with or without the heavy metals (Pt and W) in different thicknesses to identify the self-torque effects generated in the CoTb layer. The generation of self-torque heavily depends on the thickness of CoTb. The SOT switching was not observed for a single CoTb layer with 3nm in thickness, suggesting self-torque may be quite weak in a very thin film. A deterministic SOT switching can be obtained for a single 9 nm CoTb layer. The amplitude of the self-torque generated in CoTb is comparable to the Pt/Co case with the same switching polarity as the Pt/Co one. When 3 nm CoTb has deposited on Pt or W underlayer, the Jc is smaller in W/CoTb than that of Pt/CoTb, which can be attributable to a high spin hall angle of W and negligible self-torque of CoTb. On the other hand, when the CoTb is increased to 9 nm, the Jc of W/CoTb is significantly increased and becomes higher than that of Pt/CoTb. The enhanced Jc of W/CoTb may result from the opposite sign of spin-orbit torque generated in W and CoTb. Since the self-torque generated in 9 nm CoTb becomes substantial, the competition of spin-orbit torque between W and CoTb occurs, leading to a high Jc. We define the switching efficiency η=(2Hk2-Hx2)1/2*Mst/Jc based on the macrospin model 1, in which Hk and Hx are anisotropy field and applied magnetic field along the x-direction. The variations of η with the layer structure are shown in Table 1. The addition of SOT from Pt and self-torque from CoTb leads to enhanced switching efficiency when the thickness of CoTb is increased. On the other hand, the competition of SOT from W and self-torque in TbCo of W/CoTb devices was revealed by increasing the thickness of CoTb. We further confirm this interplay by reversing the stack order, that is, CoTb/W, in which the efficiency is substantially enhanced. 
**References** 1 T. Taniguchi, S. Mitani, and M. Hayashi, Physical Review B., Vol.92, 024428 (2015).
 
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Effects of self torque in rare earth

Magnetic multilayers are material systems that offer a high degree of tunability with respect to their magnetic and electronic properties. These are essential for today’s spintronics and magnonics-based magnetic applications [1], [2]. The Dzyaloshinskii-Moriya interaction (DMI) [3] is one of the interesting phenomena in such multilayers that give rise to the presence of magnetic skyrmions under certain conditions even at room temperature. Pt/Co is one of the most promising classes of the multilayers that contributes to a significant DMI due to the different characters of Pt/Co and Co/Pt interfaces [4]. The performance of the films may vary depending on the substrates, deposition temperature, layer thickness, and other factors in the Pt/Co multilayers. The thermal stability can be significantly increased and the magnetic anisotropy of Pt/Co multilayers can be controlled by adding spacer layers between two Co layers [5].
In our study, we investigate magnetic bubbles in Pt/Co-based multilayer thin films. The bubbles have been expanded using an external magnetic field both in-plane and out-of-plane. In presence of the in-plane field, bubbles expand asymmetrically as observed in Fig.1(a). The in-plane field-dependent velocities of two opposite chiral domain walls are measured as shown in Fig. 1(b). The asymmetry of bubble expansion is found to be influenced by the thickness of Co which gives us information about the intrinsic chiral properties of the system. Mumax simulations are performed to understand underlying behavior. The study is important for race track memory applications. 
**References** [1]. R. E. Camley, and R. L. Stamps, “Magnetic multilayers: spin configurations, excitations, and giant magnetoresistance,” Journal of Physics: Condensed Matter, vol. 5, no. 23, 1993.
[2]. E. Y. Vedmedenko, R. K. Kawakami, D. D. Sheka, P. Gambardella, A. Kirilyukand, A. Hirohata, C. Binek, O. Chubykalo-Fesenko, S. Sanvito, and B. J. Kirby, “The 2020 magnetism roadmap,” Journal of Physics D: Applied Physics, vol. 53, no. 45, 2020.
[3]. T. Moriya, “Anisotropic Superexchange Interaction and Weak Ferromagnetism,” Phys. Rev, 1960.
[4]. A. W. J. Wells, P. M. Shepley, C. H. Marrows, and T. A. Moore, “Effect of interfacial intermixing on the Dzyaloshinskii-Moriya interaction in Pt/Co/Pt,” Phys. Rev. B, vol. 95, 2017.
[5]. S. Eimer, H. Cheng, J. Li, and X. Zhang, “Perpendicular magnetic anisotropy based spintronics devices in Pt/Co stacks under different hard and flexible substrates,” Science China. Information Sciences, 2021. 
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Asymmetric Pt/Co magnetic multilayers bubble expansion under in plane and out

Magnetic skyrmion, as one of the topologically protected spin textures stabilized in the materials with perpendicular magnetic anisotropy (PMA) and interfacial Dzyaloshinskii-Moriya interaction (iDMI), are quite small in the nanometer size and can be driven by spin torque with lower current density, which provide a reliable technique for use in next-generation racetrack memory, logical devices, spin transfer nano-oscillator, etc. Magnetic skyrmion in the above applications are mainly based on the controllable motion of skyrmions in the confined geometrics. Furthermore, a controllable, reproducible, and realized skyrmion nucleation is another most important elements in such skyrmion-based devices. Several researchers have proposed and demonstrated skyrmion nucleation schemes, such as, patterning the magnetic structures with notches or defects, domain wall transfer or chopping to skyrmions. However, all these methods include significant structural or even geometrical modifications of the magnetic racetrack which increasing the devices design complexity. Recently works have shown that sputtering process can control magnetic properties, such as PMA and DMI, at the nanoscale. In this work, we adopted a nanoregion without PMA as a skyrmion nucleation core and demonstrate a current driven highly efficient, in-line and on-demand skyrmion nucleation schematic. Fig. 1(a) shows an illustration of skyrmion nucleation devices considered here. One key factor for realizing this is that the vanishing of the PMA and the existing of the DMI induced magnetization tilt and create a chiral perpendicular stripe domain wall at left edges. This stripe domain wall that allows spin torque to efficiently controlled and ejected from the modified region and propelled into the nanowire to form a skyrmion. As shown in Fig. 1(b), this device integrated both skyrmion nucleation and control function is more advantages in simply the devices with two terminals. This working mode could be controlled by the selective current pulse sequence with one for nucleation and another one for shifting which is important to skyrmion-based racetrack memory applications. 
**References** 
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Magnetic skyrmion nucleation via current injection in confined nanowire with modified perpendicular anisotropy region

Spin state of currents and magnets offers a unique ability to store, transport and process information in vector boolean states leading to extreme density of memory and logic [1]. We propose and demonstrate basic vector logic manipulation with six state magnetic and spin currents utilizing spin orbit effect in a reservoir gate. Recently investigated bulk spin orbit coupling (SOC) effects [2,3,4] hold a special solution to this complex logic problem due to the vector phenemenology of spin orbit interaction. We propose three critical gates for GF-n state logic [5, 6], known as inversion gate, and rotation gates (rotation around X axis, Y-axis and Z-axis) using the combination of spin torque switching and spin orbit switching. 6-state memory can increase magnetic memory density of an n-bit word by 3^n, leading to extreme density of memory and logic for future AI and high-performance applications. For example, an 8-bit, 1GB MRAM can be converted into a 6.5TB MRAM with the use of six state signal manipulation. When utilised the complete informaton density of six-state logic can extend the Moore's law for many generations by improving coding [7] and information density [8,9] without needing extreme lithography and materials scaling.
**References** [1] Manipatruni, S.,et al 2018. Beyond CMOS computing with spin and polarization. Nature Physics, 14(4), pp.338-343.
[2] Witczak-Krempa, W., et al 2013. Correlated quantum phenomena in the strong spin-orbit regime. arXiv preprint arXiv:1305.2193.
Vancouver
[3] Everhardt, A.S., et al 2019. Tunable charge to spin conversion in strontium iridate thin films. Physical Review Materials, 3(5), p.051201.
[4] Zhu, L., et al 2021. Unveiling the Mechanism of Bulk Spin Orbit Torques within Chemically Disordered FePt Single Layers. Advanced Functional Materials, 31(36), p.2103898.
[5] Ellison, J.T., 1972. Universal function theory and Galois logic studies. SPERRY RAND CORP ST PAUL MN UNIVAC DEFENSE SYSTEMS DIV. AD0740849.pdf (dtic.mil)
[6] Jain, S.K., Song, L. and Parhi, K.K., 1998. Efficient semisystolic architectures for finite-field arithmetic. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 6(1), pp.101-113.
[7] Benvenuto, C.J., 2012. Galois field in cryptography. University of Washington, 1(1), pp.1-11.
[8] Lloyd, S., 2000. Ultimate physical limits to computation. Nature, 406(6799), pp.1047-1054.
[9] Krauss, L.M. et al 2004. Universal limits on computation. arXiv preprint astro-ph/0404510.
 
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Rotator Gates for Six state Boolean Spin Logic

Chirality is one of important research topics in the diverse field because it leads interesting phenomena.[1] Since the chirality by the inversion symmetry breaking has been observed in magnetic ordered system,[2] researches on asymmetric exchange coupling was actively investigated.[3] Here, the chirality is known as affecting to the dynamic and static phenomena, so it can be one approach that influence on the magnetization state as well. But for understanding the role of chirality deeply, it is necessary to control the chirality as a unique variable while keeping other materials parameters. However, controlling only the chirality is limited because it is determined from the materials and structural origins in general, affecting other parameters simultaneously. Therefore, more consideration is still required for revealing the role of chirality deeply.
For understanding the chirality precisely, we prepared the lateral perpendicular magnetic anisotropy (PMA) symmetry breaking system. In this system, magnetizations of each PMA react differently by the SOT, which results in in-homogeneous spin configuration (i-hSC). Here, notable point is that i-hSC can induce different system energy when it is combined with interfacial Dzyaloshinskii-Moriya interaction (DMI) as seen in Fig. 1.
The effect of i-hSC can be confirmed experimentally by measuring magnetization switching because the chirality reversal also occurs simultaneously (clockwise (CW) ↔ counter-clockwise (CCW)). Here, because more (less) energy should be required for switching the stabilized (destabilized) i-hSC, opposite directional shift of hysteresis loop is shown as seen in Fig. 2. The resultant degree of shift is directly related with the system energy variation, and our experimental analysis suggests the possibility of the chirality as one method determining the magnetization state. 
**References** F. Evers, A. Aharony, N. Bar-Gill, Advanced Materials, Vol.34, p.2106629 (2022)
M. Bode, M. Heide, K. von Bergmann, Nature, Vol.447, p.190-193 (2007)
S.-H. Yang, R. Naaman, Y. Paltiel, Nature Reviews Physics, Vol.3, p.328-343 (2021) 
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