Published April 18, 2025
| Version v1
Figure
Open
Hopf index of the toroidal magnetic hopfions in cylindrical and spherical dots
-
1.
University of the Basque Country
- 2. Adam Mickiewicz University, 61-712 Poznań, Poland
- 3. Institute of Magnetism, Kyiv, Ukraine
Description
Fig. 1. The Hopf index in the cylindrical dots as a function of the dot radius for the fixed dot aspect ratio . The dot radius is in units of the hopfion radius . The hopfion vorticities : a) – solid green line, b) – dotted red line, and c) dashed blue line.
Fig. 2. The Hopf index in the spherical particles as a function of the particle radius ( is in units of the hopfion radius ). The hopfion vorticities : a) – solid green line, b) – dotted red line, and c) dashed blue line.
Notes
Acknowledgements
The authors are grateful to B.A. Ivanov and M. Krawczyk for fruitful discussions. The research of K.G. and E.T was supported by the National Science Centre of Poland, project no UMO-2023/49/B/ST3/02920
