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Non-interacting particles exhibiting Brownian motion have been observed in many occasions of sciences, including spin textures in magnetic materials. Skyrmions are particle-like topological spin textures stabilized by the Dzyaloshinskii-Moriya interaction (DMI), with their topological properties being governed by the skyrmion number Q, which can also be thermally activated and behave like Brownian particles. In the present report, the Brownian dynamics of skyrmion is firstly discussed through performing micromagnetic simulation based on stochastic Landau-Lifshitz-Gilbert equation. More interestingly, a topology-dependent gyromotion from being clockwise (Q = +1) to counterclockwise (Q = -1) can be identified, as shown in Figs. 1(a) and 1(b), respectively. We subsequently utilized a polar magneto-optic Kerr effect (MOKE) microscopy to experimentally examine the Brownian motion of a single isolated skyrmion in the Ta/CoFeB/TaOx multilayer. The diffusion coefficient of skyrmion is found to exhibit an exponential dependence on temperature, instead of simple linear temperature dependence as Einstein predicted, as shown in Fig.1(c). Further, a topology-dependent Brownian gyromotion is confirmed by revealing the clockwise and counterclockwise rotations for Q = +1 and Q = -1 skyrmions, as shown in Figs. 2(a) and 2(b), respectively. Average rotation angle 〈θsr〉 is systematically calculated and shown in Fig.2(c), in which a clear difference in the whole temperature range can be seen. The experimental results are consistent with the analytical calculations from the stochastic Thiele equation, suggesting the Brownian gyromotion of a single skyrmion is captured.References: [1] L. Zhao, Z. Wang, X. Zhang, Phys. Rev. Lett., (in press)

MMM 2020

Topology-Dependent Brownian Gyromotion of a Single Skyrmion

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

Magnetic multilayers can combine strong spin-orbit interaction with lacking inversion symmetry, which may give rise to the presence of topologically nontrivial spin textures, so-called magnetic skyrmions. Recent studies have indicated strongly enhanced propagation velocities of skyrmions in antiferromagnets and compensated ferrimagnets [1]. At the same time, it is unclear how magnetic compensation may affect dynamic excitations of magnetic skyrmions, such as breathing modes, which entail an oscillation of the skyrmion size at GHz frequencies [2]. Here, we present comprehensive micromagnetic simulations of these resonance modes in synthetic ferri- and antiferromagnets that are excited by either out-of-plane radiofrequency magnetic fields or spin torques. The observed features in the calculated power spectra exhibit a systematic dependence on the strength of the RKKY-like antiferromagnetic coupling between the individual magnetic layers and are related to pure in-phase and anti-phase breathing modes as well as to hybridizations of breathing and spin wave modes that are characteristic for the considered circular-shaped geometry [3]. As a simplified classical analog, the coupled skyrmion breathing modes can be viewed as two harmonic oscillators that are connected by a spring. The experimental detection of these resonant oscillation modes may provide a means for skyrmion sensing applications and for the general characterization of skyrmion states in multilayer stacks with antiferromagnetic interlayer exchange coupling. This work is supported by the Deutsche Forschungsgemeinschaft (DFG) through the research fellowship LO 2584/1-1.References: [1] L. Caretta, M. Mann, F. Büttner, K. Ueda, B. Pfau, C. M. Günther, P. Hessing, A. Churikova, C. Klose, M. Schneider, D. Engel, C. Marcus, D. Bono, K. Bagschik, S. Eisebitt, and G. S. D. Beach, Nat. Nanotechnol. 13, 1154-1160 (2018) [2] M. Garst, J. Waizner, and D. Grundler, J. Phys. D: Appl. Phys. 50, 293002 (2017) [3] M. Lonsky, and A. Hoffmann, arXiv:2006.11318 (2020)

Skyrmion Breathing Modes in Synthetic Ferri- and Antiferromagnets

Magnetic skyrmions are topologically protected whirling spin textures, which can be used as information carriers and have a potential application for spintronics, like skyrmion-based racetrack magnetic memory [1]. In thin films, skyrmions can be stabilized by the competition of different kind of interactions, like Heisenberg exchange interaction, magnetic anisotropy and Dzyaloshinskii-Moriya interaction (DMI). Recently, skyrmions have been generated by an electrical field applied on dielectric thin films [2-4]. But, to achieve a large gating effect, a high gate voltage must be applied. Ionic liquid gating using ionic liquids or ion gels has been demonstrated as a powerful method to effectively control the magnetic anisotropy with a low voltage since an ultra-high electric field is generated at the electric double layer interface between ions and electron conductors [5]. However, there is no evidence that shows skyrmions can be generated by ionic liquid gating. We have investigated the magnetic anisotropy and domain structures of MgO/Mn2CoAl/Pd ultra-thin films [6] at various gate voltages. This structure shows clear perpendicular magnetic anisotropy in its original state. By applying positive gate voltage VG = 1.5 V, the coercive field can be slightly increased. On the other hand, the coercive field significantly shrinks after applying negative field, as shown in Fig. 1. Domain structures at various electric field were captured by magneto-optical Kerr microscopy at ambient temperature, as shown in Fig. 2. For the original state, the magnetization is still saturated at -1 mT due to the magnetic hysteresis. After applying VG = -1.5 V, these uniformly ferromagnetic states are transformed to labyrinth domains. What’s more, skyrmions with ~ 900 nm size can be induced at VG = -2.5 V which can be ascribed to the voltage-induced reduction of effective perpendicular magnetic energy even though the DMI constant decreases as well.References: 1 A. Fert et al., Nature Reviews Materials 2, 17031 (2017). 2 M. Schott et al., Nano Letters, 17, 3006−3012 (2017). 3 T. Srivastava et al., Nano Letters, 18, 4871−4877 (2018). 4 C. Ma et al., Nano Letters, 19, 353−361 (2019). 5 C. N. Senent et al., APL Materials 7, 030701 (2019). 6 B. M. Ludbrook et al., Scientific Reports 7, 13620 (2017)

Skyrmion generation by ionic liquid gating in ultra-thin films

Thermally activated processes are intrinsic effects in every physical system and their understanding key to the underlaying dynamics of such systems. Using skyrmions, magnetic, topologically stabilized spin structures, we investigate the thermal diffusion dynamics in specifically tailored metal-multilayer. We find that for low pinning materials stacks, the thermal diffusion dominates the dynamics and allows for stable skyrmions at room temperature that move by thermal activation [1]. These stable Skyrmions allow for a wide range of possible applications in logic, data storage or Brownian token computing devices [2]. In Brownian circuits as well as other applications, the control of the skyrmion diffusion and the implementation of a certain control is necessary [3]. We show that by applying a magnetic in-plane field, the skyrmion diffusion becomes anisotropic with faster diffusion along the field direction and slower diffusion perpendicular to it [4]. We furthermore show that the absolute value of the applied field also controls the absolute values of the diffusion coefficients so that one can tune both the orientation of the diffusion and its strength. We can analytically and numerically explain the anisotropic diffusion due to an elliptical deformation of the skyrmions by the application of the in-plane field, which leads to a preferential diffusion axis [4].References: [1] J. Zázvorka et al., Nat. Nanotech. 14, 658–661(2019). [2] F. Peper et al., ACM J. Emerg. Technol. Comput. Syst. 9, 3 (2013). [3] T. Nozaki et al., Appl. Phys. Lett. 114, 012402 (2019). [4] N. Kerber et al., arXiv:2004.07976 (2020).

Anisotropic skyrmion diffusion controlled by field-induced symmetry breaking

Skyrmion has, in the last decade, attracted considerable attention for its application to novel devices. To realize the futuristic devices that will be using the skyrmion circuit, the tracks which guide the motion of skyrmions are needed. The tracks patterned with differences in the magnetic-anisotropy energy are well-paved without a potential pocket, whereas the tracks carved out of magnetic films have the potential pockets at corners due to the demagnetizing field[1]. This work aims to identify the forces acting between skyrmions and anisotropy walls of the tracks as a first step studying the dynamics of skyrmions in the tracks. The static force on a skyrmion can be expressed as minus the gradient of the potential energy caused by the magnetic-anisotropy undulation[2]. We find that the forces from the wall Fwall depend not only on the distance from the wall X but also on the shape of skyrmions with their radii R and domain wall widths w in Fig. 1[3]. We have also performed micromagnetic simulations where the Magnus force and the force by the magnetic-anisotropy gradient are taken into account. When these forces are in balance with Fwall, the values of Fwall are determined. The simulation results show good agreement with those calculated from the modeled skyrmions as Fig. 2[4]. The force Fwall has a characteristic X-dependence where a peak locates at the skyrmion radius, since the force stems mostly from the transition part of the magnetization overlapping the potential jump at X=0. The force also acts on the skyrmions that have crossed over the wall to push back them to tracks. The property might be useful to stabilize the skyrmion circuits. Another helpful feature is that the magnetic anisotropy wall does not give rise to additional friction. This research and development work was supported by the Center for Spintronics Research Network (CSRN), the ULVAC. Inc., and the MIC.References: [1] Y. Jibiki et al., arXiv: 1909.10130 (2019) [2] A.A. Thiele, Phys. Rev. Lett. 30, 230 (1973) [3] X.S. Wang, et al., Commun. Phys. 1, 31 (2018) [4] E. Tamura, et al., arXiv: 2005.04860 (2020)

Skyrmion dynamics in tracks patterned with magnetic anisotropy: theory and simulations

Phases of matter are ubiquitous with everyday examples including solids and liquids. In reduced dimensions, particular phases, such as the two-dimensional (2D) hexatic phase and corresponding phase transitions occur (1-4). A particularly exciting example of 2D ordered systems are skyrmion lattices (5), where in contrast to previously studied 2D colloid systems (6), the skyrmion size and density can be tuned by temperature and magnetic field (7). In this work we use a skyrmion lattice to study phase transitions in 2D (8). We first show that we can drive the system from a liquid phase to a hexatic phase as deduced from the analysis of the hexatic order. The presence of a hexatic phase highlights the 2D nature of the system. Using coarse-grained molecular dynamics simulations of soft disks, we determine the skyrmion interaction potentials and we find that the simulations are able to reproduce the full two-dimensional phase behaviour. In particular by comparing the numerical simulations and the experimental results, we understand how the equilibration in the hexatic phase occurs on long timescales. This shows that not only the static behaviour of skyrmions is qualitatively well described in terms of a simple two-dimensional model system but skyrmion lattices are versatile two-dimensional model systems that allow for studying phases and phase transitions in reduced dimensions. Finally, as the next step, we investigate the effect of geometrical confinement and find a strong effect on the dynamics and ordering.References: 1. S. C. Kapfer, W. Krauth, Phys. Rev. Lett. 114, 035702 (2015). 2. Y. Nishikawa, K. Hukushima, W. Krauth, Phys. Rev. B 99, 064435 (2019). 3. M. Engel, J. Anderson, S. Glotzer, et al., Phys. Rev. E 87, 042134 (2013). 4. E. P. Bernard; W. Krauth, Phys. Rev. Lett. 107, 155704 (2011). 5. A. Fert, N. Reyren, V. Cros, Nat. Rev. Mater. 2, 17031 (2017). 6. K. Zahn, R. Lenke, G. Maret, Phys. Rev. Lett. 82, 2721–2724 (1999). 7. K. Everschor-Sitte, J. Masell, R. Reeve, M. Kläui, J. Appl. Phys. 124, 240901 (2018). 8. J. Zázvorka et al., arxiv:2004.09244

Skyrmion Lattice Phases in Thin Film Multilayers

Magnetic skyrmions are localized chiral whirling of magnetization that hold great promise as nanoscale information carrier. Skyrmion racetrack memory and logic devices have recently been proposed where trains of skyrmions in tracks are manipulated by electrical current [1]. These devices require the controlled nucleation and current driven motion of skyrmions in narrow tracks. In particular, the skyrmion Hall effect (i.e. the skyrmion motion towards the track edge), is a critical issue as it can lead to the skyrmion annilation [2–5]. Here, we report on the controlled nucleation and current induced guiding of magnetic skyrmions along tracks defined by local He+ ion irradiation on an ultrathin sputtered magnetic film at room temperature. A He+ focused ion beam was used to define 150 nm wide tracks (red areas, Fig.1a) within a sputtered ultrathin Pt/Co/MgO film patterned into 3-µm-wide tracks [5,6]. Magnetometry and Brillouin Light Scattering measurements show that the He+ ion irradiation results in a decrease of the perpendicular magnetic anisotropy as well as the Dzyaloshinskii-Moriya interaction. Under a small perpendicular magnetic field, this leads to the nucleation of skyrmion racetrack (Fig.1b), whose size and density can be tuned by the field amplitude. Experiments of current induced skyrmion motion, show that the skyrmions move along the He+ ion defined tracks. Thus, the track acts as a local potential well that guides the skyrmion trajectory, which allows to suppress the skyrmion Hall effect. Our results are well substantiated by micromagnetic simulations using experimentally derived magnetic and transport parameters. These results open a new path to nucleate and guide skyrmions in racetrack memory and logic devices.References: [1] A. Fert et al., Nat. Nanotechnol. 8, 152 (2013). [2] J. Sampaio et al., Nat. Nanotechnol. 8, 839 (2013). [3] W. Jiang et al., Nat. Phys. 13, 162 (2017). [4] S. Woo et al., Nat. Mater. 15, 501 (2016). [5] R. Juge et al., Phys. Rev. Appl. 12, 044007 (2019). [6] O. Boulle et al., Nat. Nanotechnol. 11, 449 (2016).

Skyrmion racetracks defined by light-ion irradiation and current induced skyrmion guiding at room temperature

When applied to C2V ferromagnetic/heavy metal interfaces, Moriya’s rules do not deterministically predict the orientation of interatomic DM vectors. Low-symmetry magnetic systems can exhibit both Rashba (DR) and Dresselhaus (DD) forms of the Dzyaloshinskii-Moryia interaction (DMI), as both spin-orbit couplings are generally present [1]. We assert that the spatial variation of the DM vectors—and thus that of the strength and direction of the effective DMI field—is determined by the DMI’s character (i.e., ||DD||/||DR||), as well as the unit cell’s aspect ratio [2]. Overall, the DMI is thus nominally anisotropic and hybridized—potentially stabilizing antiskyrmions and Bloch-Néel (i.e. mixed) skyrmions [2-3]. Ascertaining the existence and tunability of [anti]skyrmions in such systems is of technological interest and would elucidate the nature of DMI [2]. Employing the Wulff construction [3], ξ-vector formalism [4], and an augmented wall energy that accounts for DMI character, this work models the equilibrium shape and wall magnetization profile of bubble domains and skyrmions in thin films with C2v symmetry. We show that for sufficiently large DMI, square-shaped antiskyrmions are stable for certain DM vector orientations while lens- and oval-shaped mixed skyrmions are favored otherwise. A symmetry-breaking applied in-plane field stabilizes domain shapes resembling ovals and Reuleaux triangles. The impact of the unit cell’s aspect ratio, the DM vector’s orientation, and other material parameters on the shape of bubble domains and skyrmions are discussed. Moreover, our results reveal unusual relationships between faceting behavior and wall stiffness under rather reasonable conditions. Elucidating the interplay between the different effective fields present, we explore the validity of these results based on pedal plots, discontinuities in the magnetization profiles, and local extrema in the wall energy.References: U. Güngördü et al., Physical Review B., 93, 064428 (2016) M. Hoffman et al., Nature Communications., 8, 308 (2017) J. P. Pellegren, D. Lau, and V. Sokalski, Physical Review Letters., 119, 027203 (2017) A. A. Wheeler, Journal of Statistical Physics., 95, 1245–1280 (1999)

Energetics, equilibrium shape, and vorticity of skyrmions and antiskyrmions stabilized by the anisotropic Dzyaloshinskii-Moriya interaction in thin films with C2v symmetry

Layers structuring is one of the effective methods of regulating the exchange interaction of heterogeneous magnetic layers, which, in turn, sets the specifics of the magnetization reversal of multilayered films, including the presence and the magnitude of the so-called exchange bias [1, 2]. This work is devoted to studying the features of the formation of interlayer interaction in the (Fe-Ni)/Ti/(R-Co) (R = Gd, Dy) film structures, where Fe-Ni is a polycrystalline ferromagnetic layer, R-Co is a structurally amorphous ferrimagnetic layer, and Ti is a paramagnetic spacer of variable thickness. The film samples were obtained on glass substrates by high-frequency ion-plasma sputtering of homogeneous (Fe-Ni, Ti) and mosaic (Gd-Co or Dy-Co) targets at the presence of an external magnetic field of 170 Oe. The nominal thicknesses of the Fe-Ni and R-Co layers were 50 and 110 nm, respectively. The thickness of the Ti spacer varied within L = 0–1.3 nm. The iron content in the ferromagnetic layers corresponded to 10 at.%. The concentration of rare-earth metal in the ferrimagnetic layers was 26–30 at.%. To analyze the magnetic properties, we used the measurements of hysteresis loops performed on a LakeShore 7407 VSM vibrating magnetometer. Figures 1 and 2 show the hysteresis loops m(H) demonstrating the features of the magnetization reversal of individual layers in the considered film structures. It was found that at L < 0.8 nm, the joint magnetization reversal of the interacting layers, which is the result of a strong interlayer exchange coupling, takes place (Fig. 1(a), 2(a)). With an increase in L, the interlayer interaction weakens and the described peculiarity of the magnetization reversal process disappears (Fig. 1(b), 2(b)), however, for samples with Dy-Co, an exchange bias of the hysteresis loops of the Fe-Ni ferromagnetic layer begins to be observed. The work has been financially supported by the RSF grant, project no. 18-72-10044.References: 1. W. H. Meiklejohn and C. P. Bean, Phys. Rev. 102, 1413–1414 (1956). 2. F. Radu and H. Zabel, Springer Tracts in Modern Physics 227 (Springer, Berlin Heidelberg, 2008), pp. 97–184.

Features of Magnetization Reversal of Fe10Ni90/Ti/(R-Co) (R = Gd, Dy) Films

Since the discovery of single-layer graphene in 2004, two-dimensional (2D) van der Waals (vdW) materials represented by it have demonstrated excellent electrical, magnetic, mechanical and optical physical properties under the structure of one or several layers of atomic thickness1. Based on these superior properties, 2D-layered vdW ferromagnetic materials have become the basis for constructing low-dimensional spintronics devices2, in which Fe3GeTe2 (FGT)3, Cr2Ge2Te64 and CrI35 as the main representative materials exhibit strong perpendicular magnetic anisotropy and other important characteristics in single layer. However, the Curie temperature (Tc) of above materials has not reached room temperature yet, which has greatly hinderer the subsequent development for device application. Therefore, recently researchers have been committed to explore 2D vdW ferromagnetic materials for room-temperature Tc in both theory and experiment. Here, we report that the interfacial engineering effect could effectively increase the Tc of the 2D vdW ferromagnetic material FGT from 230 K to 400 K, through heteroepitaxy with topological insulator of Bi2Te3. A theoretical calculation was further carried out to describe the magnetic properties by using first-principles calculations and the self-consistent Hubbard U approach (DFT+Uscf) together with the Monte Carlo (MC) simulations. After combination with Bi2Te3, the intralayer interactions in FGT was calculated to dramatically increase compared to that in pure FGT, well explaining the Tc enhancement. Our results may open up a new door to benefit the magnetic order in the 2D limit and realize spintronic devices based on 2D-layered vdW ferromagnetic materials with room temperature performances towards industrialization.References: 1. Geim, A. K.; Novoselov, K. S. The Rise of Graphene. Nat. Mater. 2007, 6 (3), 183–191. 2. Lin, X.; Yang, W.; Wang, K. L.; Zhao, W. Two-Dimensional Spintronics for Low-Power Electronics. Nat. Electron. 2019, 2 (7), 274–283. 3. Liu, S.; Yuan, X.; Zou, Y.; Sheng, Y.; Huang, C.; Zhang, E.; Ling, J.; Liu, Y.; Wang, W.; Zhang, C.; Zou, J.; Wang, K.; Xiu, F. Wafer-Scale Two-Dimensional Ferromagnetic Fe3GeTe2 Thin Films Grown by Molecular Beam Epitaxy. npj 2D Mater. Appl. 2017, 1 (1), 30. 4. Gong, C.; Li, L.; Li, Z.; Ji, H.; Stern, A.; Xia, Y.; Cao, T.; Bao, W.; Wang, C.; Wang, Y.; Qiu, Z. Q.; Cava, R. J.; Louie, S. G.; Xia, J.; Zhang, X. Discovery of Intrinsic Ferromagnetism in Two-Dimensional van Der Waals Crystals. Nature 2017, 546 (7657), 265–269. 5. Huang, B.; Clark, G.; Navarro-Moratalla, E.; Klein, D. R.; Cheng, R.; Seyler, K. L.; Zhong, D.; Schmidgall, E.; McGuire, M. A.; Cobden, D. H.; Yao, W.; Xiao, D.; Jarillo-Herrero, P.; Xu, X. Layer-Dependent Ferromagnetism in a van Der Waals Crystal down to the Monolayer Limit. Nature 2017, 546 (7657), 270–273.

Above room-temperature ferromagnetism in wafer-scale two-dimensional van der Waals Fe3GeTe2 tailored by topological insulator

Perpendicular magnetic anisotropy [PMA] in multilayers [1] plays a key role in various spintronic applications and is widely utilized in magnetic tunnel junctions [2] for high density applications. Recent studies suggest that the heavy metal (HM) having large spin-orbit coupling strength (SOC) can promote perpendicular magnetic anisotropy in the HM/FM/Oxide structures due to the interfacial magnetic anisotropy [3]. From the recent theoretical calculation, the origin of PMA in FM/Oxide heterostructures is attributed to the overlap between O-2p orbitals and transition metal 3d orbitals [4]. Hence, the ferromagnetic content is expected to play a crucial role in determining the PMA. Here, we studied the strength of PMA in Ta/CoxFe80-xB20/MgO heterostructures with varying Fe content for x=20 and 40. We use DC and RF magnetron sputtering for the deposition of Ta, CoFeB and MgO layers on the Silicon substrate. Here we have use the Ta(5)/CoxFe80-xB20(1.2)/MgO (2.5)/Ta (3) multilayers (nominal thickness in nm) with varying Fe content of x=20 and x=40. After deposition, the multilayers were annealed under high vacuum conditions at 300for one hour to enhance the perpendicular magnetic anisotropy [5]. The PMA properties can be investigated using out-of-plane M-H measurements, polar-magneto-optical Kerr effect (p-MOKE) measurements and anomalous Hall effect (AHE) measurement. Here, we have used p-MOKE and the AHE measurements for the study of PMA strength in our samples. The Hall effect in the ferromagnets consists of two terms, one is the ordinary Hall effect and another is the AHE. As shown in Fig. 1, the AHE measurement shows that the magnetization of the CoFeB (1.2 nm) layer stabilizes along the out-of-plane direction. We have found a squared shape of out-of-plane AHE hysteresis loops for Fe content x=40, which confirm the presence of larger PMA strength for x=40 compared to x=20 (as shown in Fig.1). This study provides a pathway to tune the PMA strength by varying FM content, which is useful for the storage devices.References: [1] P.F. Carcia, et al, Appl. Phys. Lett., 47,178(1985) [2] S. Ikeda, et al. Nature Mater 9, 721–724 (2010). [3] M T Johnson. et al. Rep. Prog.59, 1409-1458, (1996) [4] H.X. Yang, et al., Phys. Rev.B 84, 054401 (2011). [5] Gweon, et al. Sci Rep 8, 1266 (2018)

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Topology-Dependent Brownian Gyromotion of a Single Skyrmion

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Skyrmion Breathing Modes in Synthetic Ferri- and Antiferromagnets

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