Physics:Magnetic skyrmionium

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Out-of-plane spin texture of a skyrmion and skyrmionium. Green colour represents spins that point out of the screen and yellow colour represents spins that point into the screen.

In magnetic systems, excitations can be found that are characterized by the orientation of the local magnetic moments of atomic cores. A magnetic skyrmionium is a ring-shaped topological spin texture and is closely related to the magnetic skyrmion.[1][2]

Topological charge

The topological charge can be defined as follows.[3]

[math]\displaystyle{ Q=\int \vec{m}(\vec{r})\cdot (\partial_x \vec{m}(\vec{r}) \times \partial_y \vec{m}(\vec{r})) dr^2/4\pi }[/math]

With this definition, the topological charge of a skyrmion can be calculated to be ±1. A magnetic skyrmionium is a topological quasi particle that is composed of a superposition of two magnetic skyrmions of opposite topological charge adding up to zero total topological charge.[4][5] On this basis one can view the core of a skyrmionium as a skyrmion (yellow central disk in figure) with opposite charge compared to a bigger skyrmion (green disk) in which it is situated.

Magnetic Particles and their topological charge
Spin-Texture Topological Charge
Skyrmion ±1
Skyrmionium 0
Skyrmion-bag with n Skyrmion ±n

Different to magnetic skyrmions, that experience a transverse deflection under current driven motion known as the skyrmion Hall effect[6][7] (similar to the Hall effect), magnetic skyrmioniums are expected to move parallel to electrical-drive currents.[8] The current-driven motion of magnetic excitations is one example of the direct link between topological charge and a physical observable.

Theoretical predictions

Skyrmioniums have been the subject of numerous theoretical investigations.[9][10][11] Besides theoretical predictions concerning the existence of skyrmioniums such as in the 2D Janus mono layer CrGe(Se,Te)3,[12] a lot of research concentrated on their manipulation by electrical currents,[13][14][15] spin currents[16] or spin waves.[17][18] So far, there is only little experimental evidence for the existence of magnetic skyrmioniums. One example is the observation of skyrmionium in a NiFe-CrSb2Te3 hetero-structure.[19]

Potential applications

Magnetic excitations such as skyrmions or skyrmioniums are potential building blocks of next generation spintronic devices, which enable for instance neuromorphic computing.[20][21]

References

  1. ↑ Ishida, Yuichi; Kondo, Kenji (2020-02-20). "Theoretical comparison between skyrmion and skyrmionium motions for spintronics applications" (in en). Japanese Journal of Applied Physics 59 (SG): SGGI04. doi:10.7567/1347-4065/ab5b6b. ISSN 0021-4922. Bibcode: 2020JaJAP..59GGI04I. https://iopscience.iop.org/article/10.7567/1347-4065/ab5b6b. 
  2. ↑ Ponsudana, M.; Amuda, R.; Madhumathi, R.; Brinda, A.; Kanimozhi, N. (2021-10-01). "Confinement of stable skyrmionium and skyrmion state in ultrathin nanoring" (in en). Physica B: Condensed Matter 618: 413144. doi:10.1016/j.physb.2021.413144. ISSN 0921-4526. Bibcode: 2021PhyB..61813144P. https://www.sciencedirect.com/science/article/pii/S0921452621003306. 
  3. ↑ Xia, Jing; Zhang, Xichao; Ezawa, Motohiko; Tretiakov, Oleg A.; Hou, Zhipeng; Wang, Wenhong; Zhao, Guoping; Liu, Xiaoxi et al. (2020-07-06). "Current-driven skyrmionium in a frustrated magnetic system". Applied Physics Letters 117 (1): 012403. doi:10.1063/5.0012706. ISSN 0003-6951. Bibcode: 2020ApPhL.117a2403X. https://aip.scitation.org/doi/10.1063/5.0012706. 
  4. ↑ Kolesnikov, Alexander G.; Stebliy, Maksim E.; Samardak, Alexander S.; Ognev, Alexey V. (2018-11-16). "Skyrmionium – high velocity without the skyrmion Hall effect" (in en). Scientific Reports 8 (1): 16966. doi:10.1038/s41598-018-34934-2. ISSN 2045-2322. PMID 30446670. Bibcode: 2018NatSR...816966K. 
  5. ↑ "skyrmionium" (in en), Wiktionary, 2019-09-29, https://en.wiktionary.org/w/index.php?title=skyrmionium&oldid=54410555, retrieved 2022-01-02 
  6. ↑ Jiang, Wanjun; Zhang, Xichao; Yu, Guoqiang; Zhang, Wei; Wang, Xiao; Benjamin Jungfleisch, M.; Pearson, John E.; Cheng, Xuemei et al. (2017). "Direct observation of the skyrmion Hall effect" (in en). Nature Physics 13 (2): 162–169. doi:10.1038/nphys3883. ISSN 1745-2481. https://www.nature.com/articles/nphys3883. 
  7. ↑ Chen, Gong (2017-01-23). "Skyrmion Hall effect" (in en). Nature Physics 13 (2): 112–113. doi:10.1038/nphys4030. ISSN 1745-2481. https://www.nature.com/articles/nphys4030. 
  8. ↑ Kolesnikov, Alexander G.; Stebliy, Maksim E.; Samardak, Alexander S.; Ognev, Alexey V. (2018-11-16). "Skyrmionium – high velocity without the skyrmion Hall effect" (in en). Scientific Reports 8 (1): 16966. doi:10.1038/s41598-018-34934-2. ISSN 2045-2322. PMID 30446670. Bibcode: 2018NatSR...816966K. 
  9. ↑ Bo, Lan; Zhao, Rongzhi; Hu, Chenglong; Shi, Zhen; Chen, Wenchao; Zhang, Xuefeng; Yan, Mi (2020-03-03). "Formation of skyrmion and skyrmionium in confined nanodisk with perpendicular magnetic anisotropy" (in en). Journal of Physics D: Applied Physics 53 (19): 195001. doi:10.1088/1361-6463/ab6d98. ISSN 0022-3727. Bibcode: 2020JPhD...53s5001B. https://iopscience.iop.org/article/10.1088/1361-6463/ab6d98. 
  10. ↑ Song, Chengkun; Jin, Chendong; Wang, Jinshuai; Ma, Yunxu; Xia, Haiyan; Wang, Jianing; Wang, Jianbo; Liu, Qingfang (2019-07-23). "Dynamics of a magnetic skyrmionium in an anisotropy gradient" (in en). Applied Physics Express 12 (8): 083003. doi:10.7567/1882-0786/ab30d8. ISSN 1882-0778. Bibcode: 2019APExp..12h3003S. https://iopscience.iop.org/article/10.7567/1882-0786/ab30d8. 
  11. ↑ Yang, Jaehak; Park, Hyeon-Kyu; Park, Gyuyoung; Abert, Claas; Suess, Dieter; Kim, Sang-Koog (2021-10-25). "Robust formation of skyrmion and skyrmionium in magnetic hemispherical shells and their dynamic switching". Physical Review B 104 (13): 134427. doi:10.1103/PhysRevB.104.134427. Bibcode: 2021PhRvB.104m4427Y. https://link.aps.org/doi/10.1103/PhysRevB.104.134427. 
  12. ↑ Zhang, Yun; Xu, Changsong; Chen, Peng; Nahas, Yousra; Prokhorenko, Sergei; Bellaiche, Laurent (2020-12-10). "Emergence of skyrmionium in a two-dimensional ${\mathrm{CrGe}(\mathrm{Se},\mathrm{Te})}_{3}$ Janus monolayer". Physical Review B 102 (24): 241107. doi:10.1103/PhysRevB.102.241107. https://link.aps.org/doi/10.1103/PhysRevB.102.241107. 
  13. ↑ Göbel, Börge; Schäffer, Alexander F.; Berakdar, Jamal; Mertig, Ingrid; Parkin, Stuart S. P. (2019-08-20). "Electrical writing, deleting, reading, and moving of magnetic skyrmioniums in a racetrack device" (in en). Scientific Reports 9 (1): 12119. doi:10.1038/s41598-019-48617-z. ISSN 2045-2322. PMID 31431688. Bibcode: 2019NatSR...912119G. 
  14. ↑ Xia, Jing; Zhang, Xichao; Ezawa, Motohiko; Tretiakov, Oleg A.; Hou, Zhipeng; Wang, Wenhong; Zhao, Guoping; Liu, Xiaoxi et al. (2020-07-06). "Current-driven skyrmionium in a frustrated magnetic system". Applied Physics Letters 117 (1): 012403. doi:10.1063/5.0012706. ISSN 0003-6951. Bibcode: 2020ApPhL.117a2403X. https://aip.scitation.org/doi/10.1063/5.0012706. 
  15. ↑ Obadero, S. A.; Yamane, Y.; Akosa, C. A.; Tatara, G. (2020-07-31). "Current-driven nucleation and propagation of antiferromagnetic skyrmionium". Physical Review B 102 (1): 014458. doi:10.1103/PhysRevB.102.014458. Bibcode: 2020PhRvB.102a4458O. https://link.aps.org/doi/10.1103/PhysRevB.102.014458. 
  16. ↑ Zhang, Xichao; Xia, Jing; Zhou, Yan; Wang, Daowei; Liu, Xiaoxi; Zhao, Weisheng; Ezawa, Motohiko (2016-09-19). "Control and manipulation of a magnetic skyrmionium in nanostructures". Physical Review B 94 (9): 094420. doi:10.1103/PhysRevB.94.094420. Bibcode: 2016PhRvB..94i4420Z. https://link.aps.org/doi/10.1103/PhysRevB.94.094420. 
  17. ↑ Li, Sai; Xia, Jing; Zhang, Xichao; Ezawa, Motohiko; Kang, Wang; Liu, Xiaoxi; Zhou, Yan; Zhao, Weisheng (2018-04-02). "Dynamics of a magnetic skyrmionium driven by spin waves". Applied Physics Letters 112 (14): 142404. doi:10.1063/1.5026632. ISSN 0003-6951. Bibcode: 2018ApPhL.112n2404L. https://aip.scitation.org/doi/10.1063/1.5026632. 
  18. ↑ Shen, Maokang; Zhang, Yue; Ou-Yang, Jun; Yang, Xiaofei; You, Long (2018-02-05). "Motion of a skyrmionium driven by spin wave". Applied Physics Letters 112 (6): 062403. doi:10.1063/1.5010605. ISSN 0003-6951. Bibcode: 2018ApPhL.112f2403S. https://aip.scitation.org/doi/full/10.1063/1.5010605. 
  19. ↑ Zhang, Shilei; Kronast, Florian; van der Laan, Gerrit; Hesjedal, Thorsten (2018-02-14). "Real-Space Observation of Skyrmionium in a Ferromagnet-Magnetic Topological Insulator Heterostructure". Nano Letters 18 (2): 1057–1063. doi:10.1021/acs.nanolett.7b04537. ISSN 1530-6984. PMID 29363315. Bibcode: 2018NanoL..18.1057Z. https://doi.org/10.1021/acs.nanolett.7b04537. 
  20. ↑ Wang, Junlin; Xia, Jing; Zhang, Xichao; Zheng, Xiangyu; Li, Guanqi; Chen, Li; Zhou, Yan; Wu, Jing et al. (2020-11-16). "Magnetic skyrmionium diode with a magnetic anisotropy voltage gating". Applied Physics Letters 117 (20): 202401. doi:10.1063/5.0025124. ISSN 0003-6951. Bibcode: 2020ApPhL.117t2401W. https://aip.scitation.org/doi/full/10.1063/5.0025124. 
  21. ↑ Grollier, J.; Querlioz, D.; Camsari, K. Y.; Everschor-Sitte, K.; Fukami, S.; Stiles, M. D. (2020-03-02). "Neuromorphic spintronics" (in en). Nature Electronics 3 (7): 360–370. doi:10.1038/s41928-019-0360-9. ISSN 2520-1131. PMID 33367204. 



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