Exact hopfion vortices in a 3D Heisenberg ferromagnet

Balakrishnan, Radha; Dandoloff, Rossen; Saxena, Avadh

doi:10.1016/j.physleta.2023.128975

Exact hopfion vortices in a 3D Heisenberg ferromagnet

Journal Article · Wed Jun 21 00:00:00 EDT 2023 · Physics Letters. A

DOI:https://doi.org/10.1016/j.physleta.2023.128975· OSTI ID:2318950

Balakrishnan, Radha ^[1]; Dandoloff, Rossen ^[2]; ^[3]

Institute of Mathematical Sciences, Chennai (India)
Univ. of Sofia (Bulgaria)
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: 89233218CNA000001; AC52-06NA25396

OSTI ID:: 2318950

Alternate ID(s):: OSTI ID: 1987974

Report Number(s):: LA-UR--22-20711

Journal Information:: Physics Letters. A, Journal Name: Physics Letters. A Vol. 480; ISSN 0375-9601

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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36 MATERIALS SCIENCE
97 MATHEMATICS AND COMPUTING
Homotopy
Hopfions
Linking number
Material Science
Mathematics
Preimages
Skyrmions
Stability

Exact hopfion vortices in a 3D Heisenberg ferromagnet

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