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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)

MMM 2020

Skyrmion Breathing Modes in Synthetic Ferri- and Antiferromagnets

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

We present experimental evidence for coherent long-distance transport of angular momentum inside a non-magnetic dielectric via the coupling to circularly polarized sound waves that exceeds previous benchmarks set by magnon diffusion by orders of magnitude. Most of the spintronics devices rely on the delocalized electrons in metals to carry the spin information, which induces loss by Joule heating. It turns out that insulating magnetic materials, such as yttrium iron garnet (YIG), also allow the spin to propagate between localized magnetic moments via propagating spin-waves which transmit information from an atomic site to the other without any Joule effect. In principle, the induced angular momentum can also pass through a non-magnetic insulators by coupling to circular vibrations of the crystal lattice called chiral phonons. But the extent to which these phonons can mediate spin currents in a circuit remains to be demonstrated. In a recent experiment [1], a collaboration lead by researchers at Spintec used a microwave field to excite a current of chiral phonons through a half-millimeter thick layer of non-magnetic gadolinium gallium garnet sandwiched between two YIG films. By showing interference effects between the two magnetic layers, they demonstrated that circularly polarized acoustic phonons allow coherent transmission of spin information over millimeter distances. This work has since inspired theoretical work [2] showing the interest of using this discovery with an electric current which is more practical for powering spintronic devices.References: [1] K. An, A. N. Litvinenko, R. Kohno, et al. Phys. Rev. B 101, 060407(R) – Published 21 February 2020; [2] Rückriegel, A. & Duine, R. A. Physical Review Letters, American Physical Society (APS), 2020, 124

Coherent long-range transfer of angular momentum between magnon Kittel modes by circularly polarized phonons

Conversion of heat into spin current has recently drawn a lot of attention due to its potential usage on heat recovery via the spin Seebeck effect (SSE) [1] as well as fundamental interests including generation of spin super currents [2] and Bose-Einstein condensation of magnons [3]. The underlying mechansim for SSE is understood as a combination of interfacial and bulk (intrinsic) contriubtion. The interfacial SSE is driven by the tempearture drop at the interface between metal and magnetic layer while the bulk SSE is driven by diffusive thermal magnons. In the nonlocal spin transport measurements, the long range exponential decay of thermally generated spin signal was explained solely by the intrinsic SSE [4] while there are several studies showing that there is another decay mechanism in subhundred nanometer scale [5-7]. Here, we study the spatial decay of thermally excited magnon currents inside a thin magnetic insulator by focusing on the short-range behavior in the nonlocal geometry. We compare SSE signal on the same device before and after adding a nonmagnetic Al capping layer. The Al capping alters the thermal profile significantly near the heat source, which results in that the nonequilibrium thermal magnon profile deviates from an exponential decay and shows two sign reversals within 1 μm from the heat source. From simulated temperature profiles, we find the vertical temperature gradient also reverses twice within the same length scale in the Al deposited case. The correlation suggests that thermal magnons behave locally at this length scale. Using a phenomenological spin transport model, we calculate the spatial profile of nonequilibrium spin density. The observed short-range behavior can be accounted if the relavant decay length is on the order of subhundred nanometers. Our result shows the existance of the shorter decay length in the nonlocal magnon transport experiments. This suggests that the long-range SSE signal in previous measurements should be attributed to magnons with lower energy.References: [1] Boona, S. R., Myers, R. C., & Heremans, J. P. Energy & Environmental Science, 7(3), 885-910 (2014) [2] Bozhko, D. A., Serga, A. A., Clausen, P. et al., Nature Physics, 12(11), 1057-1062 (2016) [3] Tserkovnyak, Y., Bender, S. A., Duine, R. A. et al., Physical Review B, 93(10), 100402 (2016) [4] Cornelissen, L. J., Liu, J., Duine, R. A. et al., Nature Physics, 11(12), 1022-1026 (2015) [5] Kehlberger, A., Ritzmann, U., Hinzke, D. et al., Physical review letters, 115(9), 096602 (2015) [6] Prakash, A., Flebus, B., Brangham, J. et al., Physical Review B, 97(2), 020408 (2018) [7] Jamison, J. S., Yang, Z., Giles, B. L. et al., Physical Review B, 100(13), 134402 (2019)

Short-range Study of Thermal Magnon Transport in Magnetic Garnets

Usually negligible thermoelectric effects in superconductors can be increased using the simultaneous effects of spin splitting and spin filtering. These superconductor-ferromagnetic hybrids have been predicted to have thermal electric efficiencies (zT ~ 1.8) far exceeding any other cryogenic thermoelectric materials. Confirmation of these predictions requires controlled S-F interfaces, the generation of temperature gradients, and precise local cryogenic thermometry. S-F heterostructures have been fabricated using a combination of lithography, thermal evaporation, and magnetron sputtering, providing precise control over interfaces, materials, and geometries. Heaters and resistive thermometers, patterned via focused ion beam assisted platinum deposition have been calibrated and optimized for thermal transport measurements at cryogenic temperatures. Finally, the Seebeck coefficient of S-F heterostructures has been measured in the presence of a magnetic field. This measurement framework and measurement set the stage for additional studies of the effects of dimensionality, ferromagnet polarization, and interface quality.References: P. Machon, M. Eschrig, and W. Belzig, “Nonlocal thermoelectric effects and nonlocal onsager relations in a three-terminal proximity-coupled superconductor-ferromagnet device,” Phys. Rev. Lett., vol. 110, p. 47002, 2013. P. Machon, M. Eschrig, and W. Belzig, “Giant thermoelectric effects in a proximity couple superconductor- ferromagnet device,” New J. Phys., vol. 16, p. 073002, 2014.

Thermoelectric Effects of Superconductor-Ferromagnetic Hybrids

Interaction of two skyrmions stabilized by the ferromagnetic exchange, Dzyaloshinskii-Moriya interaction (DMI), and external magnetic field has been studied numerically on a 2D lattice of size large compared to the separation, $d$, between the skyrmions. We show that two skyrmions of the same chirality (determined by the symmetry of the crystal) repel. In accordance with earlier analytical results, their long-range pair interaction falls out with the separation as $\exp(-d/\delta_H)$, where $\delta_H$ is the magnetic screening length, independent of the DMI. The prefactor in this expression depends on the DMI that drives the repulsion. The latter results in the spiral motion of the two skyrmions around each other, with the separation between them growing logarithmically with time. When two skyrmions of the total topological charge $Q = 2$ are pushed close to each other, the discreteness of the atomic lattice makes them collapse into one skyrmion of charge $Q = 1$ below a critical separation. Experiment is proposed that would allow one to measure the interaction between two skyrmions by holding them in positions with two magnetic tips. Our findings should be of value for designing topologically protected magnetic memory based upon skyrmions.References: D Capic, DA Garanin and EM Chudnovsky, Skyrmion-skyrmion interaction in a magnetic film, Journal of Physics: Condensed Matter, https://doi.org/10.1088/1361-648X/ab9bc8 (2020). (Accepted Manuscript)

Skyrmion-skyrmion interaction in a magnetic film

Since the discovery, the experimental observation of skyrmions in thin films has raised its demand among researchers.[1, 3, 4] So far, their applicability has been investigated for logic devices, nanooscillators, memory devices, stochastic computation, neuromorphic computation[5, 6] and many more. This work is focused on study of dynamics of skyrmionic structures to produce consequences for neuromorphic computation. When a complex chiral structure is allowed to pass through narrow channels, unzipping of the structure generates number of codes at the terminal depending upon the spin-polarized current. The dynamics is studied in single layer as well as on synthetic antiferromagnet and is observed to be almost similar in both isotropic and anisotropic DMI systems. This functional device can be realized analogous to biological synapse. Subsequently, another nanodevice is proposed to demonstrate how the antiskyrmionic codes in a ferromagnetic layout can be used to store memory of stimuli by recycling of codes and send reaction pulses to the reaction spot. Apart from that, it requires external circuitry along with MTJ sensors to monitor the device operation. However, we focus on micromagnetic simulations using OOMMF.[2] The potentiation and depression processes that take place in a biological synapse could be realized in the reaction centre. The conversion of long-term memory into short-term memory under stress can be realized like that happens in biological system. This device encounters no memory loss in its complete operation since all the codes generated are conserved in the system by PMA barriers at the edges. Hence, the proposed model may contribute in development of highly integrated and energy efficient neuromorphic computing systems for adaptive learning.References: [1] A. Fert, V. Cros, and J. Sampaio. Skyrmions on the track. Nat. Nanotechnol. 8, 152–156 (2013). [2] M. J. Donahue, and D. G. Porter, OOMMF User’s Guide, Version 1.0, Interagency Report. NO.NISTIR 6376, 158 (1999). [3] A. N. Bogdanov, and U. K. Rößler, Chiral symmetry breaking in magnetic thin films and multilayers. Phys. Rev. Lett. 87, 037203 (2001). [4] T. H. R. Skyrme et al Proc. Royal Soc. A 260, 127–138 (1961). [5] Huang et al 2017. Web. doi:10.1103/PhysRevB.96.144412. [6] S. Li et al 2017 Nanotechnology 28 31LT01.

Artificial Neural Network using Skyrmionics

Applications of skyrmions in spintronics have been largely discussed and their advantages compared to early magnetic devices such as magnetic bubbles have been pointed out in a recent review by W. Kang et al. [1]. Among the most important applications of skyrmions, let us mention skyrmion-based racetrack memory [2], skyrmion-based logic gates [3, 4], skyrmion-based transistor and skyrmion-based artificial synapse and neuron devices [5]. In this work we have studied the phase transition and ground state configurations in antiferromagnetic/ferroelectric bilayer formed by magnetic layer between ferroelectric layers by the use of Monte Carlo simulation and the steepest descent method. Antiferromagnetic film and ferroelectric films in this work were modeled as films of triangular lattice with respectively Heisenberg spins and polarizations. All interactions are limited to nearest neighbors (NN). We found the formation of a stable skyrmions in the ground state of bilayers with the triangular lattice at zero applied magnetic field in a region of interface magnetoelectric interaction (-1.0,-0.65) (meV). Very strong magnetoelectric interactions at the interface leads to the disappearance of the magnetic phase transition, unlike the case of simple cubic lattice where we observed very strong first-order phase transitions at large values of the interface magnetoelectric interaction. The existence of skyrmions at the magneto-ferroelectric interface in the ground state at zero magnetic field is very interesting and may have practical applications in digital technologies and spintronics. We found the formation of a perfect skyrmions lattice at acceptable values of magnetoelectric interaction. The skyrmions structure is stable in a large region of the external magnetic field. With a moderate increase in the magnetoelectric interaction parameter, the stability of the skyrmion lattice with respect to the magnitude of the applied magnetic field increases.References: 1. W.Kang , Y. Huang, X. Zhang, Y. Zhou and W. Zhao, Proceedings of the IEEE, Vol. 104, p. 2040 (2016) 2. S. S. P. Parkin, M. Hayashi and L. Thomas, Science, Vol. 320, p. 190 (2008) 3. X. Zhang, M. Ezawa and Y. Zhou, Scientific Reports, Vol. 5, p. 9400 (2015) 4. Y. Zhou, M.Ezawa, Nature communications, Vol. 5, p. 1 (2014) 5. S.Li, W. Kang, Y. Huang, X. Zhang X, Y. Zhou and W. Zhao, Nanotechnology, Vol. 28, p. 31LT01 (2017)

Magnetic Skyrmions and Phase Transitions in a Antiferromagnetic/Ferroelectric bilayers

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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