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 other reasons, due to shortcomings in their current-driven motion. In this talk, we present our recent advances in the field of topological spin textures that go beyond skyrmions [1]. The majority of the discussed 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 [2,3,4], bimerons [5], antiferromagnetic skyrmions [6] and hopfions [7]. These objects (shown in Fig. 1) exhibit advantageous emergent electrodynamic effects compared to conventional skyrmions, either due to their lower symmetry or due to a compensated topological charge. As we will show, all four of these objects can be driven parallel to the current, without a skyrmion Hall effect which makes them the ideal bits in data storage devices. Furthermore, we show that the antiferromagnetic skyrmions exhibit a topological version of the spin Hall effect which could help their detection. For bimerons and hopfions we show that the topologically induced Hall response can be distinguished much more easily from the anomalous and conventional Hall effect. This is because their emergent field is perpendicular to the net magnetization and the stabilizing magnetic field; all three quantities are (anti)parallel for skyrmions and most other magnetic nano-objects. Also, we show that some of these objects can even coexist, allowing for an advanced version of the racetrack memory data storage, where a bit sequence could, for example, be encoded by a sequence of skyrmions (‘1’ bit) and antiskyrmions (‘0’ bit); cf. Fig. 2. This concept would be more reliable than conventional racetracks: When the information is encoded by the presence or absence of a single type of topological object, the information is susceptible to thermal motion and interactions between the carriers of information. An unintended change in the bit sequence would lead to a loss of the stored information. Only when the information is encoded by at least two distinct carriers, the bit sequence can become irregular without any harm to the stored data.

**References:**

 [1] B. Göbel, I. Mertig, O. Tretiakov. “Beyond skyrmions: Review and perspectives of alternative magnetic quasiparticles”. Physics Reports in press (2020), arXiv preprint: 2005.01390 [2] J. Jena*, B. Göbel*, S. Parkin. et al. “Elliptical Bloch skyrmion chiral twins in an antiskyrmion system”. Nature Communications 11, 1115 (2020). [3] J. Jena*, B. Göbel*, S. Parkin. et al. “ Evolution and competition between chiral spin textures in nanostripes with D2d symmetry”. Science Advances 6, eabc0723 (2020). [4] P. Sivakumar, B. Göbel, S. Parkin. et al. “ Topological Hall Signatures of Two Chiral Spin Textures Hosted in a Single Tetragonal Inverse Heusler Thin Film”. ACS Nano 14, 13463 (2020). [5] B. Göbel, I. Mertig, O. Tretiakov. et al. “Magnetic bimerons as skyrmion analogues in in-plane magnets”. Phys. Rev. B. 99, 060407(R) (2019). [6] 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). [7] B. Göbel, C. Akosa, G. Tatara, I. Mertig. “Topological Hall signatures of magnetic hopfions”. Phys. Rev. Research 2, 013315 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/1df6edc367627cf9506b431bbb84b52b.jpg)
Overview of the discussed magnetic nano-objects. (a) Magnetic antiskyrmion, (b) magnetic bimeron, (c) antiferromagnetic skyrmion, (d) magnetic hopfion. The arrows correspond to magnetic moments whose color is determined by their orientation.

![](https://assets.underline.io/uploads/markdown_image/1/image/fa4bb03806ecc363261983a4f2311ee5.jpg)
In Heusler materials the anisotropic DMI stabilizes antiskyrmions (red) and elliptically deformed skyrmions (blue). These coexisting types of topologically distinct objects may encode data as ‘0’ and ‘1’ bits, respectively.

 Going Beyond Skyrmions: Alternative Magnetic Nano-Objects for Spintronics

Magnetic skyrmions (Sks) and antiskyrmions (aSks) are topologically protected non-trivial spin textures1, 2. Those objects can be used as magnetic bits in spintronics devices3, 4. However, the presence of the skyrmion Hall effect in the Sk always hinders its movement along the straight path, and the transverse defection of it will cause a problem on reading data in devices. The unwanted Hall effect can be eliminated in aSk host systems2, 5 such that it can be moved in a straight path along the current direction6. Therefore, it is highly desired to prepare nano-stripes along specific crystallographic directions of the aSk host compound. Here we stabilize a single-chain of aSks in nano-stripes of Mn1.4Pt0.9Pd0.1Sn prepared along different crystallographic directions within the tetragonal basal plane7. We observe the enhanced stability of aSks compared to bulk systems without providing in-plane magnetic field components. Additionally, the presence of dipole-dipole interactions with the anisotropic Dzyaloshinskii-Moriya exchange interaction (DMI) in the Heusler compound Mn1.4Pt0.9Pd0.1Sn allows the stability of distinct spin textures called elliptical Bloch skyrmions7,8. The co-existence of elliptical skyrmions (eSks) and aSks is found in nano-stripes at room temperature7. The simultaneous existence of different spin textures in a racetrack has great advantages. It is not needed to write the distances between the magnetic bits anymore, unlike the racetrack of only single type magnetic objects. Our results provide a gateway for the remaining steps towards realizing an advanced version of racetrack storage devices based on magnetic aSks and eSks.

**References:**

1. Mühlbauer et. al., Science 323, 915 (2009). 2. Nayak et. al., Nature 548, 561 (2017). 3. Parkin et. al., Science 320, 190 (2008). 4. Fert et. al., Nat. Nanotechnol. 8, 152 (2013). 5. Jena et. al., Nano Lett. 20, 59 (2019). 6. Huang et. al., Phys. Rev. B 96, 144412 (2017). 7. Jena et. al., Sci. Adv. 6, 49, eabc 0723 (2020). 8. Jena et. al., Nat. Commun. 11, 1115 (2020).

**Images:**

 Evolution and competition between chiral spin textures in nano-stripes with D2d symmetry

In my poster, I have shown the stabilization of two distinct topologically protected spin textures of antiskyrmions and elliptical Bloch skyrmions in a nano-stripe of D2d Heusler compound Mn1.4Pt00.9Pd0.1Sn. The simultaneous presence of different textures can be encoded as distinct data bits and can make an improved version of racetrack devices.

Co-existence of distinct magnetic spin textures in a D2d nano-stripe

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

Observation of opposite topological charges in single D2d Heusler compound (B)

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The energy cost of storing and moving data is enormous, and is growing at such a rapid pace that within a few years the power demand may overwhelm some developed nations. Non-volatile memory (NVM) and neuromorphic computing are enabling critical advances in this area, but there are many scientific and technological challenges. This conference will cover the materials challenges of different memory technologies, from the fundamental processes and mechanisms, to industry perspectives on materials specifications and manufacturing.

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O3: Skyrmions and Beyond

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Presentations

Going Beyond Skyrmions: Alternative Magnetic Nano-Objects for Spintronics

Evolution and competition between chiral spin textures in nano-stripes with D2d symmetry

Co-existence of distinct magnetic spin textures in a D2d nano-stripe

Observation of opposite topological charges in single D2d Heusler compound

Observation of opposite topological charges in single D2d Heusler compound (B)

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