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Recently, two-dimensional van der Waals (vdW) systems with a ferromagnetic behavior were found [1], [2], [3], [4], representing exciting opportunities for magneto-optics and magneto-electric applications. In those materials, the long-range magnetic order exists despite the thermal fluctuations of the Mermin-Wagner theorem because of a strong magnetic anisotropy. The compound Fe3GeTe2 (FGT) stands as a promising candidate among the vdW structures due to the tunability of its ferromagnetism under an electric field, allowing to rise the Curie temperature above 300 K [5]. In recent experiments by Park et al. on non-oxidized multilayer of FGT [6], Bloch skyrmions were observed using Differential Phase Contrast Microscopy and Lorentz Transmission Electron Microscopy and their stability cannot be explained by the existence of a chiral interaction such as Dzyaloshinskii–Moriya interaction (DMI), forbidden by the centrosymmetric structure of FGT. In this work, we numerically study the magnetic textures hosted by FGT using the micromagnetic solver Mumax3 [7] and axisymmetric simulations [8] to apprehend the phenomena at play. We demonstrate the existence of small hybrid magnetic textures, composed of Bloch skyrmionic bubbles in the middle of the structure with Néel “caps” close to the interface. These bubbles are stable in FGT for a range of external magnetic field and take sizes in the range of 20 nm for perpendicular fields in the range of a few 10 of mT comparable with the experimental observations. We would like to acknowledge S.Woo, X. Yu, A. Hassan and M. Chsiev for fruitful discussions. The ANR grant TOPSky TOPSKY (ANR-17-CE24-0025), the FLAGERA 2019 SOgraphMEM and the EU grant SKYTOP (H2020 FET Proactive 824123) are acknowledged for their financial support.References: [1] Cheng Gong et al., Nature 546, no. 7657 (June 2017): 265–69. [2] Shengwei Jiang, Jie Shan, and Kin Fai Mak, Nature Materials 17, no. 5 (May 2018): 406–10. [3] Jie Liu et al., AIP Advances 8, no. 5 (May 2018): 055316. [4] Bevin Huang et al., Nature 546, no. 7657 (June 2017): 270–73. [5] Yujun Deng et al., Nature 563, no. 7729 (November 2018): 94–99. [6] Park, Tae-Eon, et al., arXiv preprint arXiv:1907.01425 (2019). [7] Arne Vansteenkiste et al., AIP Advances 4, no. 10 (October 2014): 107133. [8] William Legrand et al., Physical Review Applied 10, no. 6 (December 2018): 064042.

MMM 2020

Micromagnetic Simulations Of Skyrmionic Bubbles In The Van Der Waals Structure Fe3GeTe2

#### Welcome to the 67th Annual Conference on Magnetism and Magnetic Materials, MMM 2022!

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MMM 2022

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Non-destructive imaging for buried interfaces has been recently developed by decelerating electron-beam energy in scanning electron microscope (SEM) [1]. This imaging technique has proven to be very useful to identify the contaminations formed in a magnetic tunnel junctions (MTJs), which reduce their tunnelling magnetoresistance (TMR) ratios. For example, in a Heusler-alloy MTJ, residual resist has been found to react with Al during Al-O sputtering for the isolatation of the top and bottom electrodes. By reducing the Al-O sputtering power, the yield of the MTJs has been reported to be improved over 70% [2]. In order to further evaluate the resolution of this technique, we prepared a new set of samples with elevating capping layers in this study. The samples, consisting of Ta (5)/(Ru (5)/)W or Pt (0.5)/Ta (5~60) (thickness in nm), were deposited on Si substrates using a high target utilisation sputtering system. Here, the heavy metal layer of W or Pt were intrinsically dispersed as nano-particles. Their diameters were evaluated by imaging with the non-destructive technique, confirming the resolution. The penetration depth of the electron beam in SEM with different energy was estimated using CASINO programme [3]. The electron beam at 4.7 keV is found to reach the interface between Pt and Ta for the case of the 60 nm thick Ta capping layer and to generate back scattered electrons (BSE). The electron beam at 5.0 keV, on the other hand, is found to reach the bottom Pt (or W) interface and to generate BSE. By subtracting these images, the distribution of the Pt nano-particles can be assessed. The corresponding SEM image taken by the subtraction of these acceleration voltages can resolve the Pt nano-particles with 10 nm diameter. For the case of the 5 nm thick Ta capping layer, 2 nm resolution is achieved. Such resolution can be useful for the evaluation of buried MTJs with a few 10 nm diameter. We will further improve the resolution by optimising the imaging conditions, so that we will be able to image smaller MTJs. This work is partially supported by EPSRC-JSPS Core-to-Core programme (EP/M02458X/1) and JST CREST (JPMJCR17J5).References: [1] A. Hirohata et al., Nat. Commun. 7, 12701 (2016). [2] E. Jackson et al., Sci. Rep. 8, 7585 (2018). [3] D. Drouin et al., Scanning 29, 92 (2007).

Resolution of Non-Destructive Imaging for Buried Interfaces

It is a matter of debate whether a pillar or a stepped structure better retains magnetic tunnel junctions’ (MTJs) performance while scaling down. In this work we use micromagnetic simulation to model the scaling effects on the free-layer’s stray-field (Hstray) for the two MTJ structures. The model was built on an MTJ containing a synthetic ferromagnetic (SyF) layer (free-layer/MgO/reference-layer) and a synthetic antiferromagnetic (SyAF) layer (reference-layer/Ru/hard-layer). Approximate Hstray strength is obtained in both structures with a free-layer of ~ 100nm. However, upon size reduction the Hstray raises significantly in the pillar structure, but it appears less responsive in the stepped structure. This trend is shared by experimental results with the MTJ reduced from 130 to 80 nm. We are suggested that the stepped structure is a more promising candidate on mitigating Hstray in pursuit of high density MRAM [1]. The combined effects of Hstray and Dzyaloshinskii–Moriya interaction (DMI) on switching current density (Jc) were also calculated for a 30 nm free-layer MTJ. The in-plane Hstray appears to interact with the DMI in a complementary or a competing manner, depending on the sign of the DMI and initial switching state (parallel or antiparallel) of the MTJ. The stepped structure is able to reduce Jc more effectively than the pillar case. This is due to strong mediation from the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction of the SyAF layer in the stepped structure.References: [1]. S. Bandiera, S. Bandiera, R. C. Sousa, et al., IEEE Magn. Lett. 1, 3000204 (2010).

Combined Effects of Stray Field and Dzyaloshinskii–Moriya interaction on Magnetic Tunnel Junction with Stepped and Pillar Structures

Surface acoustic wave (SAW) can induce ferromagnetic resonance (FMR) [1] in the magnetostrictive soft layer of a magnetic tunnel junction (MTJ) that can be leveraged for magnetization reversal with reduced STT current [2]. However, in realistic scenarios, the MTJ soft layer can have inhomogeneity in its lateral anisotropy due to the intrinsic anisotropy variation, edge modification, roughness and thickness variation [3]. Consequently, different regions of magnetizations precess non-uniformly under the excitation of SAW and this incoherent precession become more prominent in the presence of thermal noise (see Fig.1 for 1 ns and 0.92 ns snapshots at T=0 K and T=300 K respectively for inhomogeneous anisotropy distribution). Such incoherency is detrimental as it can reduce the net magnetization deflection to a much lower value and thereby prove ineffective in reducing the STT current needed to switch the magnetization. Remarkably, magnetization precessions in different regions are found to be in phase even though they are precessing in non-uniform cones and the resulting high net magnetization deflection contributes to decrease the STT current required for magnetization reversal. In addition, such magnetization reversal is attained with SAW induced stress amplitude that is much lower than the total anisotropic barrier. This work points to the energy efficiency of the SAW assisted STT scheme and the potential for scalability below lateral dimension ~ 50 nm, which is technologically significant for STT-RAM application. It also shows the robustness of the scheme in realistic scenarios with thermal noise and material inhomogeneity. Finally, we will present some experimental results to demonstrate the effect of ferromagnetic resonance on ~ 100 nm magnetostrictive nanomagnets driven to FMR by SAW where the lateral anisotropy variation would be inherently present due to lithography and fabrication imperfection. ACKNOWLEDGEMENT: NSF SHF grant 1815033 and VMEC Seed grant.References: [1]. M. Weiler, L. Dreher and C. Heeg, Phys. Rev. Lett. Vol. 106, p. 117601 (2011) [2]. A. Roe, D. Bhattacharya and J. Atulasimha, Appl. Phys. Lett. Vol. 115, p. 112405 (2019) [3]. W. A. Misba, M. M. Rajib and D. Bhattacharya, arXiv:2003.12903 (2020)

Investigation of Acoustic Wave Induced FMR Assisted Spin Toque Switching of MTJs with Lateral Anisotropy Variation

Magnetization switching of magnetic tunnel junctions (MTJs) via spin-orbit torque (SOT) is gaining interest in cache memory applications due to its benefits in lowering power consumption. Although SOT switching of perpendicular MTJs offers better scalability, in practice the requirement of an external magnetic field to assist SOT switching is a fundamental bottleneck. Meanwhile, in-plane (IP) MTJs, fabricated in the form of an ellipse, have been demonstrated to switch by SOT without an external field. Here, the easy axis of the elliptical MTJ is perpendicular to the charge flow in the spin-hall channel, and the magnetization trajectory is argued to undergo several precessions before magnetization flip similar to spin-transfer torque switching. [1] However, in this work we experimentally show that these IP-SOT MTJs, can in fact switch as fast as 400 ps, shorter than the precessional trajectory. The IP MTJs, which implements Pt/CoFeB/MgO as the free layer, are fabricated on a 200 mm wafer using stepper lithography and ion-beam etching. Interestingly, by applying asymmetric SOT pulse segments at substantially small voltage steps, we found that a significant number of MTJs demonstrated multilevel resistance states. While multilevel states have been reported in antiferromagnet/ferromagnet structures, the underlying mechanism arising from variation in exchange bias is not applicable in our case. [2] Using micromagnetic simulations, we formulate that the existence of meta-stable domain states inside the MTJ free-layer is a likely explanation in our case. In addition, we also probe the role of CoFeB thickness, aspect ratio, and switching probabilities of these devices. Multilevel resistance states in SOT devices could find potential in neuromorphic circuits.References: [1] S. Fukami et.al. Nat. Nanotechnol. 11, 621 (2016). [2] A. Kurenkov et.al. Appl. Phys. Lett. 110, 092410 (2017).

Multilevel magnetization switching of magnetic tunnel junctions induced by spin-orbit torque

Applying electric field to control magnetic properties would be a very convenient and energy-efficient way for spintronics devices. However, the control of magnetic characteristics by electric fields is not straightforward, due to the time-reversal symmetry of magnetism versus spatial inversion symmetry of electricity. Such fundamental difficulty makes it challenging to modify the topology of magnetic skyrmionic states with electric field. Here, we propose a novel mechanism that realizes the electric-field (E) switching of magnetic topological charge (Q) in a controllable and reversible fashion, through the mediation of electric polarization (P) and Dzyaloshinskii-Moriya interaction (D). Such mechanism is coined here EPDQ. Its validity is demonstrated in a multiferroic VOI2 monolayer, which is predicted to host magnetic bimerons. The change in magnetic anisotropy is found to play a crucial role in realizing EPDQ process and its microscopic origin is discussed. Our study thus provides a new approach toward the highly-desired electric-field control of magnetism.

Electric-Field Switching of Magnetic Topological Charge in Type-I Multiferroics

Magnetic skyrmions are topological spin textures holding great potential as nanoscale information carriers. Recently, skyrmions have been predicted in antiferromagnets, with key advantages over their ferromagnetic analogs [1,2]; they produce no dipolar fields, making them stable at the nanometer scale in zero external magnetic field; they are robust against perturbation due to magnetic fields, which is beneficial for data retention; they exhibit zero net topological charge [1,3], thus eliminating the unwanted transverse velocity related to the skyrmion Hall effect, [4,5], thereby ensuring a straight skyrmion trajectory with enhanced mobility [1]. Here we show that skyrmions can be stabilized at zero field and room temperature in an IrMn thin film exchange-coupled to a ferromagnetic layer. A Ta/Cu/IrMn(5)/Pt(0.5)/Co(0.3)/NiFe(0.9)/Al (nm) stack was deposited by magnetron sputtering on a Si substrate and annealed at 250°C for 30 minutes under a perpendicular magnetic field to achieve exchange bias (see Fig.1a). Using the high-spatial-resolution magnetic microscopy technique X-PEEM, we observe that exchange bias allows the stabilization of magnetic skyrmions at zero field and room temperature in the Co/NiFe (see Fig.1b, Fe edge). X-PEEM image of the uncompensated Mn spin at the IrMn interface show that these skyrmions are replicated within the IrMn layer (see Fig1c, Mn edge). This result opens up a path for logic and memory devices based on skyrmion manipulation in antiferromagnets.References: [1] J. Barker et al., Phys Rev Lett 116, 147203 (2016). [2] O. Gomonay et al., Nat. Phys. 14, 213 (2018). [3] L. Šmejkal et al., Nat. Phys. 14, 242 (2018). [4] W. Jiang et al., Nat. Phys. 13, 162 (2017). [5] R. Juge et al., Phys Rev Appl. 12, 44007 (2019).

Stabilisation of skyrmions in an antiferromagnet at room temperature using exchange bias

When the crystalline symmetries that protect a higher-order topological phase are not preserved at the boundaries of the sample, gapless hinge modes or in-gap corner states cannot be stabilized. Therefore, careful engineering of the sample termination is required. Similarly, magnetic textures, whose quantum fluctuations determine the supported magnonic excitations, tend to relax to new configurations that may also break crystalline symmetries when boundaries are introduced. Here we uncover that antiskyrmion crystals provide an experimentally accessible platform to realize a magnonic quadrupole topological insulator, whose hallmark signatures are robust magnonic corner states. Furthermore, we show that tuning an applied magnetic field can trigger the self-assembly of antiskyrmions carrying a fractional topological charge along the sample edges. Crucially, these fractional antiskyrmions restore the symmetries needed to enforce the emergence of the magnonic corner states. Using the machinery of nested Wilson loops, adapted to magnonic systems supported by noncollinear magnetic textures, we demonstrate the quantization of the bulk quadrupole moment, edge dipole moments, and corner charges.References: [1] T. Hirosawa, S. A. Díaz, J. Klinovaja, and D. Loss, arXiv:2005.05884

Magnonic Quadrupole Topological Insulator in Antiskyrmion Crystals

Magnetic skyrmions [1,2], topologically protected magnetic quasi-particles, are at the core of many recently proposed spintronic devices. Most of the materials systems shown hosting magnetic skyrmions at room temperature [3-5] are characterized by [heavy metals]\ferromagnet interfaces to generate a strong Dzyaloshinskii-Moriya interaction (DMI) and need an external magnetic field to stabilize the skyrmions. From an application point of view, both the use of heavy metals and the need for an external magnetic field are limitations. The former are usually rare, which makes them expensive; the latter is not compatible with nanoelectronics due to scalability issues. Accordingly, it is highly desirable to have a robust and tunable protocol to build systems made only with light metals which can host magnetic skyrmions in zero external magnetic field. Here we report [6] the observation of isolated magnetic skyrmions at room temperature and zero magnetic field, stabilized through interlayer exchange coupling [7,8] between a reference magnet and a free magnet (Fig. 1). In our stack, both magnets and the non-magnetic spacer in between are made out of 3d transition metals, and by carefully changing the thickness of the spacer we can tune the size of the observed skyrmions, whose 3D spin-texture is directly imaged by spin-polarized low energy electron microscopy. In addition, via density functional theory calculations we gain a deeper understanding on the origin of the DMI in such systems, allowing us to extract the strength of the DMI, which compares well with experimental results. Our findings open up the possibility to develop cheap skyrmion-based spintronic devices suitable for general-use applications which go beyond modern nanoelectronics.References: [1] A. Bogdanov and A. Hubert, J. Magn. Magn. Mater. 138, 255 (1994). [2] N. Romming et al., Science 341, 636 (2013). [3] C. Moreau-Luchaire et al., Nat. Nanotechnol. 11, 444 (2016). [4] S. Woo et al., Nat. Mater. 15, 501 (2016). [5] A. Soumyanarayanan et al., Nat. Mater. 16, 898 (2017). [6] R. Lo Conte et al., Nano Lett. (2020), https://pubs.acs.org/doi/10.1021/acs.nanolett.0c00137. [7] G. Chen et al., Appl. Phys. Lett. 106, 242404 (2015). [8] A. K. Nandy et al., Phys. Rev. Lett. 116, 177202 (2016).

Tuning zero-field magnetic skyrmions in all-light-metals multilayers

Magnetic skyrmions and antiskyrmions are topologically protected non-collinear spin textures. They have opposite topological charges of +1 and – 1 owing the differently winding of the in-plane spin component about a fixed direction of the core1. The existence of them in a material system mostly depends on the symmetry of the underlying crystal structure. For example, cubic B20 compounds host Bloch skyrmion of isotropic spin texture2, whereas D2d symmetry compounds have anisotropic spin texture named 'antiskyrmion'3,4. Antiskyrmions comprise of alternating chiral boundaries of helicoids and cycloids. They found in two varieties of shape, namely round and square-shaped antiskyrmion5. Here for the first time, using the Lorentz microscopy technique, we have discovered elliptical shape skyrmions in the same material which comprises of Bloch walls only 5. We named them as "elliptical Bloch skyrmions". The elliptical skyrmion's major axis is oriented along the helical propagation directions, [100] and [010], and have opposite chiralities. They are found as spare and lattice states. Interestingly, both topological structure phases can also be stabilized in zero biased fields and below, over wide temperature ranges. It is found that in D2d long-range dipole-dipole interactions play a significant rule for the stabilization of those different opposite topological spin textures. Micromagnetic simulations also confirms these nano-objects. Antiskyrmions are mostly found in room temperature and above, and in lower temperatures, elliptical Bloch skyrmion is observed. At a critical temperature of 268 K, both these nano-objects are stabilized. We also performed experiment at room temperature on the nano-stripes. The transformation and density variation of antiskyrmions and elliptical Bloch skyrmions occur here that depend on the degree of tilting6. Notably, those nano-objects in the nano-tracks produce as a single chain form in the middle of the track even without giving an in-plane field that was indeed needed in the broad width lamellae. The novel and unanticipated finding of opposite topological charges of 1in one material system make the family of D2d material exceptional.References: 1. A. Bogdanov, U. Roeßler and K.-H. Mueller, Phys. Rev. B, 66, 214410 (2002) 2. S. Muehlbauer, B. Binz and C. Pfleiderer, Science, 323, 915-919 (2009) 3. A. K. Nayak, V. Kumar and S. S. P. Parkin, Nature, 548, 561 (2017) 4. J. Jena, R. Stinshoff and S. S. P. Parkin, Nano Lett., 20, 59−65 (2019) 5. J. Jena, B. Goebel and S. S. P. Parkin, Nat. Commun., 11, 1115 (2020) 6. J Jena, B. Goebel and S. S. P. Parkin, Submitted., XX,XXX (2020)

Observation of opposite topological charges in single D2d Heusler compound

Magnetic skyrmions have attracted enormous research interest since their discovery a decade ago. Especially the non-trivial real-space topology of these nano-whirls leads to fundamentally interesting and technologically relevant effects – the skyrmion Hall effect of the texture and the topological Hall effect of the electrons. Furthermore, it grants skyrmions in a ferromagnetic surrounding great stability even at small sizes, making skyrmions aspirants to become the carriers of information in the future. Still, the utilization of skyrmions in spintronic devices has not been achieved yet, among others, due to shortcomings in their current-driven motion. In this talk, we present recent trends in the field of topological spin textures that go beyond skyrmions [1]. The majority of these objects can be considered the combination of multiple skyrmions or the skyrmion analogues in different magnetic surroundings, as well as three-dimensional generalizations. We classify the alternative magnetic quasiparticles – some of them observed experimentally, others theoretical predictions – and present the most relevant and auspicious advantages of this emerging field. A special focus is on magnetic antiskyrmions [2], bimerons [3], antiferromagnetic skyrmions [4] and hopfions [5]. These objects (shown in Fig. 1) exhibit advantageous emergent electrodynamic effects compared to skyrmions, either due to their lower symmetry or due to a compensated topological charge.References: [1] B. Göbel, I. Mertig, O. Tretiakov “Beyond skyrmions: Review and perspectives of alternative magnetic quasiparticles” arXiv preprint: 2005.01390 [2] J. Jena*, B. Göbel*, T. Ma, V. Kumar, R. Saha, I. Mertig, C. Felser, S. Parkin. “Elliptical Bloch skyrmion chiral twins in an antiskyrmion system” Nature Communications 11, 1115 (2020). [3] B. Göbel, A. Mook, J. Henk, I. Mertig, O. Tretiakov. “Magnetic bimerons as skyrmion analogues in in-plane magnets” Phys. Rev. B. 99, 060407(R) (2019). [4] B. Göbel, A. Mook, J. Henk, I. Mertig, “Antiferromagnetic skyrmion crystals: Generation, topological Hall, and topological spin Hall effect” Phys. Rev. B. 96, 060406(R) (2017). [5] B. Göbel, C. Akosa, G. Tatara, I. Mertig. “Topological Hall signatures of magnetic hopfions” Phys. Rev. Research 2, 013315 (2020).

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