# Stationary precession topological solitons with nonzero Hopf invariant in a uniaxial ferromagnet

@article{Borisov2008StationaryPT, title={Stationary precession topological solitons with nonzero Hopf invariant in a uniaxial ferromagnet}, author={Alexander B. Borisov and Filipp N. Rybakov}, journal={JETP Letters}, year={2008}, volume={88}, pages={264-267} }

Three-dimensional stationary precession solitons with nonzero Hopf indices are found numerically by solving the Landau-Lifshitz equation. The structure and existence domain of the solitons are found.

## 4 Citations

### Three-dimensional magnetic solitons

- Physics
- 2011

Results are presented on the theoretical investigation of various three-dimensional structures in magnets, such as cnoidal and spiral hedgehogs in the Heisenberg model, localized textures, structures…

### Binding a hopfion in a chiral magnet nanodisk

- PhysicsPhysical Review B
- 2018

Hopfions are three-dimensional (3D) topological textures characterized by the integer Hopf invariant $Q_H$. Here, we present the realization of a zero--field, stable hopfion spin texture in a…

### Magnetic Skyrmion Materials.

- PhysicsChemical reviews
- 2020

The materials science and materials chemistry of magnetic skyrmions are described using the classification scheme of theskyrmion forming microscopic mechanisms, including the generation of emergent magnetic and electric field by statics and dynamics of skrymions and the inherent magnetoelectric effect.

### Helicity of magnetic vortices and skyrmions in soft ferromagnetic nanodots and films biased by stray radial fields

- Physics
- 2020

The Portuguese team acknowledges the Network of Extreme Conditions Laboratories and Portuguese Foundation of Science and Technology for support through Projects No. NORTE-01-0145-FEDER-022096, No.…

## References

SHOWING 1-10 OF 31 REFERENCES

### Solitons in the continuous Heisenberg spin chain

- Physics
- 1977

Solitons in the continuous Heisenberg spin system are studied in one dimension. We present results for soliton-soliton scattering in the isotropic case. For the anisotropic results we derive the…

### Vortex rings in ferromagnets: Numerical simulations of the time-dependent three-dimensional Landau-L

- Physics
- 2007

Vortex ring solutions are presented for the Landau-Lifshitz equation, which models the dynamics of a three-dimensional ferromagnet. The vortex rings propagate at constant speed along their symmetry…

### Static solitons with nonzero Hopf number

- Physics
- 1997

We investigate a generalized nonlinear O(3) {sigma} model in three space dimensions where the fields are maps from R{sup 3}{union}{l_brace}{infinity}{r_brace} to S{sup 2}. Such maps are classified by…

### Propagating Magnetic Vortex Rings in Ferromagnets

- Physics
- 1999

It is shown that bulk ferromagnets support propagating nonlinear modes that are analogous to the vortex rings, or ``smoke rings,'' of fluid dynamics. These are circular loops of magnetic vorticity…

### Bose-Einstein Condensation of Magnons in Superfluid 3He

- Physics
- 2008

Abstract
The possibility of Bose-Einstein condensation of excitations has been discussed for a long time. The phenomenon of the phase-coherent precession of magnetization in superfluid 3He and the…

### Three-dimensional spiral structures in a ferromagnet

- Physics
- 2002

New types of three-dimensional spiral structures are found in an isotropic ferromagnet.

### Knots and Particles

- Physics
- 1996

Using methods of high performance computing, we have found indications that knotlike structures appear as stable finite energy solitons in a realistic 3+1 dimensional model. We have explicitly…