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Exact hopfion vortices in a 3D Heisenberg ferromagnet
Abstract
Here, we find exact static soliton solutions for the unit spin vector field of an inhomogeneous, anisotropic three-dimensional Heisenberg ferromagnet. Each soliton is labeled by two integers n and m. It is a (modified) skyrmion in the z = 0 plane with winding number n, which twists out of the plane m times in the z-direction to become a 3D soliton. Here m arises due to the periodic boundary condition at the z-boundaries. We use Whitehead’s integral expression to find that the Hopf invariant of the soliton is an integer H = nm. It represents a hopfion vortex. Plots of the preimages of this topological soliton show that they are either unknots or nontrivial knots, depending on n and m. Any pair of preimage curves links H times, corroborating the interpretation of H as a linking number. We also calculate the exact energy of the hopfion vortex, and show that its topological lower bound has a sublinear dependence on H. Using Derrick’s scaling analysis, we demonstrate that the presence of a spatial inhomogeneity in the anisotropic interaction, which in turn introduces a characteristic length scale in the system, leads to the stability of the hopfion vortex.
- Authors:
-
[3]
- Institute of Mathematical Sciences, Chennai (India)
- Univ. of Sofia (Bulgaria)
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 2318950
- Alternate Identifier(s):
- OSTI ID: 1987974
- Report Number(s):
- LA-UR-22-20711
Journal ID: ISSN 0375-9601
- Grant/Contract Number:
- 89233218CNA000001; AC52-06NA25396; DEAC52-06NA25396
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physics Letters. A
- Additional Journal Information:
- Journal Volume: 480; Journal ID: ISSN 0375-9601
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE; 97 MATHEMATICS AND COMPUTING; Mathematics; Material Science; Skyrmions; Hopfions; Linking number; Preimages; Stability; Homotopy
Citation Formats
Balakrishnan, Radha, Dandoloff, Rossen, and Saxena, Avadh. Exact hopfion vortices in a 3D Heisenberg ferromagnet. United States: N. p., 2023.
Web. doi:10.1016/j.physleta.2023.128975.
Balakrishnan, Radha, Dandoloff, Rossen, & Saxena, Avadh. Exact hopfion vortices in a 3D Heisenberg ferromagnet. United States. https://doi.org/10.1016/j.physleta.2023.128975
Balakrishnan, Radha, Dandoloff, Rossen, and Saxena, Avadh. Wed .
"Exact hopfion vortices in a 3D Heisenberg ferromagnet". United States. https://doi.org/10.1016/j.physleta.2023.128975.
@article{osti_2318950,
title = {Exact hopfion vortices in a 3D Heisenberg ferromagnet},
author = {Balakrishnan, Radha and Dandoloff, Rossen and Saxena, Avadh},
abstractNote = {Here, we find exact static soliton solutions for the unit spin vector field of an inhomogeneous, anisotropic three-dimensional Heisenberg ferromagnet. Each soliton is labeled by two integers n and m. It is a (modified) skyrmion in the z = 0 plane with winding number n, which twists out of the plane m times in the z-direction to become a 3D soliton. Here m arises due to the periodic boundary condition at the z-boundaries. We use Whitehead’s integral expression to find that the Hopf invariant of the soliton is an integer H = nm. It represents a hopfion vortex. Plots of the preimages of this topological soliton show that they are either unknots or nontrivial knots, depending on n and m. Any pair of preimage curves links H times, corroborating the interpretation of H as a linking number. We also calculate the exact energy of the hopfion vortex, and show that its topological lower bound has a sublinear dependence on H. Using Derrick’s scaling analysis, we demonstrate that the presence of a spatial inhomogeneity in the anisotropic interaction, which in turn introduces a characteristic length scale in the system, leads to the stability of the hopfion vortex.},
doi = {10.1016/j.physleta.2023.128975},
journal = {Physics Letters. A},
number = ,
volume = 480,
place = {United States},
year = {Wed Jun 21 00:00:00 EDT 2023},
month = {Wed Jun 21 00:00:00 EDT 2023}
}
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