8 research outputs found
``Smoke Rings'' in Ferromagnets
It is shown that bulk ferromagnets support propagating non-linear modes that
are analogous to the vortex rings, or ``smoke rings'', of fluid dynamics. These
are circular loops of {\it magnetic} vorticity which travel at constant
velocity parallel to their axis of symmetry. The topological structure of the
continuum theory has important consequences for the properties of these
magnetic vortex rings. One finds that there exists a sequence of magnetic
vortex rings that are distinguished by a topological invariant (the Hopf
invariant). We present analytical and numerical results for the energies,
velocities and structures of propagating magnetic vortex rings in ferromagnetic
materials.Comment: 4 pages, 3 eps-figures, revtex with epsf.tex and multicol.sty. To
appear in Physical Review Letters. (Postscript problem fixed.
Dynamical Toroidal Hopfions in a Ferromagnet with Easy-Axis Anisotropy
Three-dimensional toroidal precession solitons with a nonzero Hopf index,
which uniformly move along the anisotropy axis in a uniaxial ferromagnet, have
been found. The structure and existence region of the solitons have been
numerically determined by solving the Landau-Lifshitz equation.Comment: 6 pages, 4 figure
Static solitons with non-zero Hopf number
We investigate a generalized non-linear O(3) -model in three space
dimensions where the fields are maps . Such maps are
classified by a homotopy invariant called the Hopf number which takes integer
values. The model exhibits soliton solutions of closed vortex type which have a
lower topological bound on their energies. We explicitly compute the fields for
topological charge 1 and 2 and discuss their shapes and binding energies. The
effect of an additional potential term is considered and an approximation is
given for the spectrum of slowly rotating solitons.Comment: 13 pages, RevTeX, 7 Postscript figures, minor changes have been made,
a reference has been corrected and a figure replace
Stationary Precession Topological Solitons with Nonzero Hopf Invariant in a Uniaxial Ferromagnet
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.Comment: 7 pages, 5 figure
Influence of topological constraints and topological excitations: Decomposition formulas for calculating homotopy groups of symmetry-broken phases
Magnetic surface topology in decaying plasma knots
Article / Letter to editorLeids Instituut Onderzoek Natuurkund