Deformation of Topologically-Protected Supercooled Skyrmions in a

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Deformation of Topologically-Protected Supercooled Skyrmions in a Thin Plate of Chiral Magnet CoZnMn 8

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Daisuke Morikawa, Xiuzhen Yu, Kosuke Karube, Yusuke Tokunaga, Yasujiro Taguchi, Taka-hisa Arima, and Yoshinori Tokura Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.6b04821 • Publication Date (Web): 30 Jan 2017 Downloaded from http://pubs.acs.org on January 31, 2017

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Deformation of Topologically-Protected Supercooled Skyrmions in a Thin Plate of Chiral Magnet Co8Zn8Mn4 Daisuke Morikawa1*, Xiuzhen Yu1, Kosuke Karube1, Yusuke Tokunaga2, Yasujiro Taguchi1, Taka-hisa Arima1, 2, and Yoshinori Tokura1, 3

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RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan

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Department of Advanced Materials Science, University of Tokyo, Kashiwa 277-8561, Japan

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Department of Applied Physics and Quantum Phase Electronics Center (QPEC), University of

Tokyo, Tokyo 113-8656, Japan

KEYWORDS: Skyrmion, Lorentz transmission electron microscopy, Metastable state, Chiral magnet, Magnetic-field cooling, Topological protection

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Magnetic skyrmions in Co8Zn8Mn4 thin plates are observed to deform in a metastable state prepared in a magnetic-field-cooling process by way of the thermal-equilibrium skyrmion phase. In cooling, the disk-shape skyrmions change to bar- or L-shaped elongated form, while the skyrmion density is nearly conserved. The deformation of the skyrmions in the supercooled metastable phase is observed irrespective of the crystallographic orientation of the thin plate, while the elongation direction nearly aligns along the magnetic easy axis. It is proposed that the deformation should be induced by a large increase in magnetic modulation wave number with decreasing the temperature, while the topological protection of the skyrmions keeps the averaged skyrmion density constant.


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Magnetic skyrmions are spin vortices with topological nature characterized by an integer skyrmion number1-4. The magnetic skyrmions are topologically stable and can be driven by ultralow current density5-7, and hence have rich potentials for the application to new memory and storage devices. The skyrmions have been discovered in non-centrosymmetric magnets8-14, dipolar magnets15-17, and interfaces between ferromagnet and non-magnetic layers18-22. In chiral magnets, the pitch of the helix or cone as well as the spacing of skyrmions is determined by the ratio of ferromagnetic exchange (J) to chirality-induced antisymmetric exchange interaction (D). The direction of magnetic modulation wave vector (q) in zero magnetic-field helical phase is governed by the magnetocrystalline anisotropy. If the magnetic anisotropy is weak enough, the helical modulation vector tends to flop along the magnetic field to form a longitudinal cone phase, whereas three magnetic modulation vectors appear perpendicular to the magnetic field to form the triangular lattice of magnetic skyrmions. Hence, the stability of skyrmion phase is affected by the direction of magnetic field and magnetocrystalline anisotropy23. In the case of thin-plate, the phase diagram is modulated also by the shape magnetic anisotropy10. In chiral magnets, helical or conical magnetic phase appears in a low temperature and low magnetic field region, and the thermal-equilibrium skyrmions can be stabilized only just below the magnetic transition temperature in a bulk crystal. For applications, the skyrmionic phase in a wider temperature and magnetic field region is required. Moreover, the operation temperature is also required to extend to enough higher than room temperature. Recently, it was reported that βMn-type Co-Zn-Mn alloys with a chiral space group of P4132 or P4332 show skyrmion lattice even at room temperature13. With adjusting the composition, skyrmion phases can be created at temperatures higher than 400 K. As for the lower temperature boundary, metastable skyrmion lattice states were reported in Co8Zn8Mn424 recently. The skyrmion lattice phase can survive after


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magnetic-field cooling down to the lowest temperature by way of the thermodynamically stable skyrmion lattice phase. The supercooled metastable skyrmion lattice phase is protected by a high potential barrier against the thermodynamically stable conical phase. The high potential barrier is closely related to the topological aspect of magnetic skyrmions. Therefore, it is anticipated that there should be a variety of metastable states resulting from the topological protection with the change of physical parameters. In this paper, we report the real space observation of a metastable state of Co8Zn8Mn4 in a thin-plate form, which is realized by the field-cooling procedure by way of the thermodynamical skyrmion-lattice phase, by using Lorentz transmission electron microscopy (TEM). In the bulk form of Co8Zn8Mn4, the lattice-structure transition of metastabilized skyrmions from triangular to square form was observed by small angle neutron scattering24, while the magnetic modulation wave number (q) shows strong temperature dependence. It has remained as a highly nontrivial issue how the topological stability of the skyrmion ensured by the conservation of skyrmion number is compatible with the lattice form change accompanying the large q-change. We anticipated that the real-space observation could give a clue to this problem. A Co8Zn8Mn4 ingot which contained several single-crystalline grains was grown in an evacuated quartz tube by Bridgman method, as described in Ref. 13. Thin plate samples with a typical thickness of 150 nm for TEM experiments were prepared by focused ion beam (FIB) of Ga with an acceleration voltage of 40 kV. Lorentz TEM observations were performed with transmission electron microscopes (JEM-2100F and JEM-2800) at an acceleration voltage of 200 kV. Liquid-helium and liquid-nitrogen cooling double-tilt holders were used to obtain Lorentz TEM images at low temperatures. A magnetic field was applied along the vertical direction to the thin-plate specimen by using an objective lens. The applied magnetic field was controlled


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with changing the electric current of the objective lens. The defocus values of Lorentz TEM images were set to 480 µm (Ref. 25). The lateral magnetization distribution was obtained by the transport-of-intensity equation (TIE) analysis of the over-focused and under-focused Lorentz TEM images26. For the TIE analysis, Lorentz TEM images with relatively smaller defocus values (±192 µm) were used. Figure 1 (a) shows a Lorentz TEM image of (001) plane at 280 K in a magnetic field of 70 mT after zero field cooling (ZFC). A triangular lattice of skyrmions was observed. The inset shows the Fourier-transformed pattern of a real space image for an area about four times larger than shown in the main panel, indicating the clear hexagon pattern. Higher-order signals may be an artifact due to the large defocus value. The distribution of the in-plane magnetic moments obtained by TIE analysis is shown with color wheel. The yellow circle points to a skyrmion. Swirling skyrmionic structures are clearly observed. The specimens with (110) and (111) planes were also prepared; we confirmed that both also showed a triangular lattice of skyrmions (not shown). Figures 1 (b)-(d) show Lorentz TEM images for three kinds of crystal planes obtained at 6 K in a magnetic field of 70 mT after a FC process. The FC process was started from room temperature. All the monochromatic real-space images and Fourier transformed patterns in Fig. 1 are displayed in the same magnification. Disk-shaped magnetic skyrmions are no more observed and deformed to bar- or L-shaped structures. Simultaneously, the translational symmetry of triangular lattice is broken to become an amorphous state. The q values of the magnetic pattern, typically measured from the helical structure in the zero-field cooled state, are almost twice as large as that for skyrmion triangular lattice at 280 K. Here it is noteworthy that q value shows up for the deformed structures as dominated by the average width of the bar- or L-shape but not by


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the length of those structures. The orientations of the L-shaped structures are affected by the magnetic anisotropy. The magnetic easy axes of Mn non-doped Co10Zn10 are known to be 27, and it was reported that the preferred orientation of q of Co8Zn8Mn4 in bulk form is also 24. In the (001) plane, the edges of the deformed structures are approximately aligned to either a or b-axis. The Fourier transform pattern shows broadened peaks in the aligned directions. The four-fold Fourier pattern is also observed in the (110)-plane case, while the contrast is lower. On the other hand, a ring-like Fourier transform pattern appears for the (111) plate. This suggests random orientations of the deformed structures. This can be ascribed to the weaker crystal magnetic anisotropy in the (111) plane than in the (001) or (110) plane. The deformation of magnetic skyrmions in the (111) plane suggests that the magnetocrystalline anisotropy should not be crucial for the deformation. While large anisotropic deformation of skyrmion lattice was reported for FeGe under tensile strain28 due to a strain modulation of antisymmetric exchange interaction, the present results are obviously not the case of straininduced skyrmion deformation. Figure 1 (e) shows the temperature dependence of the q values measured in a warming process with a rate of about 0.2 K / s29. The q value steeply increases as the temperature decreases in accord with the behavior of the bulk Co8Zn8Mn4 crystal, in which the same temperature dependence was observed for increasing and decreasing of temperature24. An error for the measured temperature is estimated to be within 10 K. There is no significant dependence of the q value on crystal orientation. Such large temperature dependence of the q value is rather exceptional among chiral magnets like many B20 compounds hosting magnetic skyrmions. Another example is MnGe where the q value shows similarly large temperature dependence30. Since the q value is approximately determined by the ratio between J and D, the strong


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temperature dependence of q may arise from the temperature dependence of J or more likely of D; the D value in a metallic chiral magnet is proven to be very sensitive to the distribution of the band-crossing Weyl points in the spin-polarized band in momentum space31-33, which may change to a large extent in itinerant magnets with varying spin polarization as a function temperature. Another possible origin for the large change in q is the strong temperature dependence of magnetocrystalline anisotropy (MCA) as evidenced by the lattice-structure transition of skyrmions itself; theoretically it is pointed out that the increase of MCA tends to increase the period of skyrmion lattice (and hence the q-value) even at the constant D value34. Figure 2 (a) shows the evolution of the skyrmion shape in a warming process after FC. Elongated skyrmions continuously change back to the disk shape with increasing the temperature. These images obtained for the same specimen area with the same TEM condition indicate that the density of skyrmions is kept unchanged in the warming process. Figure 2 (b) shows the temperature dependence of the skyrmion density investigated for a wider area of 4 µm2. The data include errors of about 10 % because a strong diffraction contrast prevented from an accurate counting. The skyrmion density little changes with temperature and is kept nearly constant, in contrast to the q-value, which should be associated with the topological protection of skyrmions. In other words, magnetic textures cannot keep their original disk shape upon cooling and must be deformed to bar- or L-shape when the magnetic modulation wave number q increases under the condition such that the density of skyrmions is conserved. Next we discuss the metastable nature of distorted skyrmions. We have investigated the change in the magnetic structure with sweeping the external magnetic field, as shown in Fig. 3 (a). Barand L-shape deformed skyrmions are observed in the (001) plane after cooling from room temperature to 6 K in a magnetic field of 70 mT, i.e. by way of the thermodynamic skyrmion-


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lattice phase region, as shown in the top panel of Fig. 3 (b). With increasing the magnetic field, elongated-shape skyrmions gradually change to disk shape. In this process, however, disk shape skyrmions remain still more or less disordered at their positions and do not form a triangular lattice. In higher magnetic fields, each skyrmion shrinks and finally disappears, similarly to the conventional magnetic bubbles. When magnetic field is turned off (0 T) after the application of the saturation magnetic field, the helical magnetic structure with an in-plane modulation is not observed at 6 K. There appear some weak and complicated magnetic contrasts, while the origin is not clear. Nonetheless, it is clear that the observed deformed skyrmions can appear only in a supercooled metastable state. We also investigated the magnetic field dependence of ZFC state at 6 K (Fig. 3(c)). The helical magnetic structure with rather short correlation lengths is observed at 6 K with zero magnetic field. The direction of q vector is almost fixed to the a or b-axis. No magnetic skyrmion is observed when a magnetic field of 70 mT is applied after ZFC. With increasing the magnetic field, disk-shape skyrmions appear sparsely in an isolated manner. In a higher magnetic field, those skyrmions shrink and finally disappear. The magnetic field for the saturation is the same as in the case of FC state. After the application of a magnetic field high enough to saturate the magnetization, the helical magnetic structure is not recovered even at H = 0. The observed deformed skyrmion state at 6 K after FC shows high stability against a sweep of the applied magnetic field between 0 and 70 mT. The magnetic textures are not affected by the change of magnetic field in this range. The metastable skyrmions are observed in a very wide temperature range even in case of a zero-field warming process after FC with H = 70 mT (not shown). Elongated skyrmions gradually change to disk shape with increasing temperature. Upon


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warming, metastable skyrmion structures are destroyed and turned into the thermal-equilibrium helical magnetic structure at about 280 K. Recently, it was reported that rearrangement of skyrmion lattice from triangular to square occurs with lowering temperature for the FC metastable state in the same material of bulk form24. This thermal transition of the metastable skyrmion-lattice form appears to correspond to the strong skyrmion distortion and lattice amorphization in the present thin-plate sample. We consider here the origin of different aggregation forms of low-temperature metastable skyrmions dependent on the sample form, i.e. thin plate (present study) versus bulk single crystal (Ref. 24). In common to the thin-plane and bulk forms, the q value shows a significant increase with decreasing temperature toward zero temperature, almost twice from the room-temperature value. In the thin plate the skyrmion density remains unchanged, while they are strongly deformed so as to be tiled over the space with the tendency of the edge of the bar- or L-shape skyrmion aligning along the magnetic easy axis. In the case of the bulk crystal as investigated by small angle neutron scattering24, on the other hand, the conservation of the total skyrmion number against the steep temperature-dependent change in q vectors is anticipated to be ensured by the relative volume change of the metastable skyrmion square-lattice state and the thermodynamically-stable conical states. In this context, in the thin (~100 nm) plate the direction of q vectors of spin helix is favored to be confined within the plate, leading to the suppression of the conical phase with the q vector along the applied magnetic field, i.e. normal to the plate. Furthermore, the TEM specimen may have more abundant pinning sites due to Ga ions or damaged layer arising from FIB fabrication procedure. The pinning sites may also prevent from the phase separation as claimed in the case of bulk24 and realize the deformed skyrmion state as observed in this work.


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In conclusion, we have observed the strong deformation of metastabilized skyrmions to the bar- or L-shape form as well as their random tiling in a thin-plate form of chiral magnet Co8Zn8Mn4. This is triggered by the large change of the magnetic modulation period from the thermal-equilibrium hexagonal skyrmion-lattice and perhaps also by the enhancement of the magnetocrystalline anisotropy. The observed features exemplify the topological protection of the skyrmion, not only the conservation of the total skyrmion number but also the skyrmion density over the coarse-grained area on a scale of (µm)2.

Figure 1. (a) Lorentz transmission electron microscopy (TEM) image of hexagonal skyrmion lattice obtained in thermal-equilibrium skyrmion phase with (001) plane at 280 K and the result of transport-of-intensity (TIE) analysis. Enclosed area by a yellow line corresponds to the one of skyrmions. Inserted figure shows the Fourier-transform pattern. Field-cooled (FC) state as


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prepared by way of the thermodynamic skyrmion phase (e.g. at 280 K and 70 mT) observed in (b) (001), (c) (110), and (d) (111) planes at 6 K, respectively. Each skyrmion shows elongated structure. In (001) and (110) planes, the direction of elongation is almost fixed to the one of the crystal axes. (e) Temperature dependence of the magnitude of q vector measured from Fourier transformed patterns of Lorentz TEM images29.

Figure 2. (a) Deformation of skyrmions with increasing temperature. Elongated shapes gradually change to the disk shape. All images were obtained under the same TEM condition and at the same specimen area. Dashed lines serve as a guide to the eyes. (b) Temperature dependence of


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the skyrmion density. The numbers of skyrmions are counted for the same specimen area of 4 µm2. The number of skyrmions and the density are nearly kept for whole temperature range.

Figure 3. (a) Diagram for the experimental condition. In the field-cooling (FC) process, the magnetic field (70 mT) is applied at room temperature. The specimen temperature is lowered


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down to 6 K with FC with 70 mT or zero-field-cooling (ZFC) with 0 T. (b) Magnetic field dependence of magnetic configuration after the FC process. Elongated skyrmions gradually change to disk shape with increasing the magnetic field. Each skyrmion shrinks and finally disappears, indicating the change to forced ferromagnetic state (forced FM). At zero magnetic field after the application of saturation magnetic field, no helical magnetic structure with in-plane q vector is observed. (c) Magnetic field dependence after ZFC. The helical magnetic structure as the thermal-equilibrium state is observed. With increasing the magnetic field, some parts show isolated skyrmions. The saturation magnetic field, above which no in-plane magnetic texture is discerned, is the same as the result obtained by FC process.


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AUTHOR INFORMATION Corresponding Author *Daisuke Morikawa E-mail: [email protected] Author Contributions Y. Tokura, T. A, and Y. Taguchi jointly conceived the project. D. M and X. Y designed the experiments, performed LTEM observations, and analyzed LTEM data. K. K. and Y. Tokunaga synthesized the bulk Co8Zn8Mn4. D. M., T. A., and Y. Tokura wrote the draft. All authors discussed the data and commented on the manuscript. Funding Sources This study was supported by the JSPS Grant-in-Aid for Scientific Research, (No.24224009). Notes The authors declare no competing financial interest. ACKNOWLEDGMENT The authors would like to thank Material Characterization Team, RIKEN for careful maintenance of TEM, and A. Kikkawa, T. Nakajima, K. Shibata, Y. Okamura, H. Oike, and F. Kagawa for fruitful discussions.


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(12). Kanazawa, N.; Kim, J. –H.; Inosov, D. S.; White, J. S.; Egetenmeyer, N.; Gavilano, J. L.; Ishiwata, S.; Onose, Y.; Arima, T.; Keimer, B.; Tokura, Y.; Phys. Rev. B 2012, 86, 134425. (13). Tokunaga, Y.; Yu, X. Z.; White, J. S.; Rønnow, H. M.; Morikawa, D.; Taguchi, Y.; Tokura, Y.; Nat. Commun. 2015, 6, 7638. (14). Kézsmárki, I.; Bordács, S.; Milde, P.; Neuber, E.; Eng, L. M.; White, J. S.; Rønnow, H. M.; Dewhurst, C. D.; Mochizuki, M.; Yanai, K.; Nakamura, H.; Ehlers, D.; Tsurkan, V.; Loidl, A.; Nat. Mater. 2015, 14, 1116-1122. (15). Yu, X. Z.; Mostovoy, M.; Tokunaga, Y.; Zhang, W.; Kimoto, K.; Matsui, Y.; Kaneko, Y.; Nagaosa, N.; Tokura, Y.; Proc. Natl. Acad. Sci. 2012, 109, 8856-8860. (16). Nagao, M., So, Y.; Yoshida, H.; Isobe, M.; Hara, T.; Ishizuka, K.; Kimoto, K.; Nat. Nanotech. 2013, 8, 325. (17). Finazzi, M.; Savoini, M.; Khorsand, A. R.; Tsukamoto, A.; Itoh, A.; Duὸ, L.; Kirilyuk, A.; Rasing, Th.; Ezawa, M.; Phys. Rev. Lett. 2013, 110, 177205. (18). Heinze, S.; Bergmann, K.; Menzel, M.; Brede, J.; Kubetzka, A.; Wiesendanger, R.; Bihlmayer, G.; Blügel, S.; Nat. Phys. 2011, 7, 713-718. (19). Romming, N.; Hanneken, C.; Menzel, M.; Bickel, J. E.; Wolter, B.; Bergmann, K.; Kubetzka, A.; Wiesendanger, R.; Science 2013, 341, 636-639. (20). Sampaio, J.; Cros, V.; Rohart, S.; Thiaville, A.; Fert, A.; Nat. Nanotech. 2013, 8, 839844.


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(21). Jiang, W.; Upadhyaya, P.; Zhang, W.; Yu, G.; Jungfleisch, M. B.; Fradin, F. Y.; Pearson, J. E.; Tserkovnyak, Y.; Wang, K. I.; Heinonen, O.; Velthuis, S. G. E.; Hoffmann, A.; Science 2015, 349, 283-286. (22). Woo, S.; Litzius, K.; Krüger, B.; Im, M-Y.; Caretta, L.; Richter, K.; Mann, M.; Krone, A.; Reeve, R. M.; Weigand, M.; Agrawal, P.; Lemesh, I.; Mawass, M-A.; Fischer, P.; Kläui, M.; Beach, G. S. D.; Nat. Mater. 2016, 15, 501-506. (23). Yi, S. D.; Onoda, S.; Nagaosa, N.; Han, J. H.; Phys. Rev. B 2009, 80, 054416. (24). Karube, K.; White, J. S.; Reynolds, N.; Gavilano, J. L.; Oike, H.; Kikkawa, A.; Kagawa, F.; Tokunaga, Y.; Rønnow, H. M.; Tokura, Y.; Taguchi, Y.; Nat. Mater. 2016, 15, 12371242. (25). The defocus values of Lorentz TEM images were set to +480 µm (over-focus) and -480 µm (under-focus) for JEM-2100F and JEM-2800, respectively, because of the opposite magnetic-field direction for each TEM. (26). Ishizuka, K.; Allman, B.; J. Electron Microsc. 2005, 54. 191-197. (27). Xie, W.; Thimmaiah, S.; Lamsal, J.; Liu, J.; Heitmann, T. W.; Quirinale, D.; Goldman, A. I.; Pecharsky, V.; Miller, G. J.; Inorg. Chem. 2013, 52, 9399-9408. (28). Shibata, K.; Iwasaki, J.; Kanazawa, N.; Aizawa, S.; Tanigaki, T.; Shirai, M.; Nakajima, T.; Kubota, M.; Kawasaki, M.; Park, H. S.; Shindo, D.; Nagaosa, N.; Tokura, Y.; Nat. Nanotech. 2015, 10, 589-592. (29). For the accurate determination of the magnitudes of q vector, the Lorentz TEM images were calibrated by using a standard specimen of carbon grating for the same experimental


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condition. The measurements were conducted by using Gaussian fitting on the Fourier transformed pattern with averaging over azimuth angle. The temperature dependence of q value was obtained with warming process with typical warming rate at 0.2 K / s. (30). Kanazawa, N.; Kim, J.-H.; Inosov, D. S.; White, J. S.; Egetenmeyer, N.; Gavilano, J. L.; Ishiwata, S.; Onose, Y.; Arima, T.; Keimer, B.; Tokura, Y.; Phys. Rev. B 2012, 86, 134425. (31). Freimuth, F.; Blügel, S.; Mokrousov, Y.; J. Phys Condens. Matter 2014, 26, 104202. (32). Koretsune, T.; Nagaosa, N.; Arita, R.; Sci. Rep. 2015, 5, 13302. (33). Kikuchi, T.; Koretsune, T.; Arita, R.; Tatara, G.; Phys. Rev. Lett. 2016, 116, 247201. (34). Kiselev, N. S.; Bogdanov, A. N.; Schäfer, R; Rößler, U. K.; J. Phys. D: Appl. Phys. 2011, 44, 392001.


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Deformation of Topologically-Protected Supercooled Skyrmions in a

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