Scattering of magnetic solitons in two dimensions

The European Physical Journal B - Condensed Matter, 2002

Vortex-antivortex pairs in 2D easy-plane ferromagnets have characteristics of solitons in two dimensions. We investigate numerically and analytically the dynamics of such vortex pairs. In particular we simulate numerically the head-on collision of two pairs with different velocities for a wide range of the total linear momentum of the system. If the momentum difference of the two pairs is small, the vortices exchange partners, scatter at an angle depending on this difference, and form two new identical pairs. If it is large, the pairs pass through each other without losing their identity. We also study head-tail collisions. Two identical pairs moving in the same direction are bound into a moving quadrupole in which the two vortices as well as the two antivortices rotate around each other. We study the scattering processes also analytically in the frame of a collective variable theory, where the equations of motion for a system of four vortices constitute an integrable system. The features of the different collision scenarios are fully reproduced by the theory. We finally compare some aspects of the present soliton scattering with the corresponding situation in one dimension.

The dynamics of vortices in a 2D Heisenberg antiferromagnet with an easy-plane anisotropy is studied numerically within the discrete spin model as well as analytically within a continuum approximation based on a suitable extension of the relativistic nonlinear σ model. We find that two like vortices scatter at 90 ◦ during a headon collision, whereas a vortex-antivortex pair is annihilated into spinwave radiation emitted mainly at 90 ◦. When a uniform bias field is applied, vortex dynamics is affected rather profoundly and acquires the characteristic features of the Hall effect of electrodynamics or the Magnus effect of fluid dynamics. In particular, a single vortex is always spontaneously pinned, two like vortices form a rotating bound state, and a vortex-antivortex pair undergoes Kelvin motion. Finally, in the presence of a bias field, vortices are shown to be the prominent topological excitations even for an isotropic Topological magnetic solitons have been studied extensively in ...

Nonlinearity, 1998

The dynamics of vortices in a 2D Heisenberg antiferromagnet with an easy-plane anisotropy is studied numerically within the discrete spin model as well as analytically within a continuum approximation based on a suitable extension of the relativistic nonlinear σ model. We find that two like vortices scatter at 90 • during a headon collision, whereas a vortex-antivortex pair is annihilated into spinwave radiation emitted mainly at 90 • . When a uniform bias field is applied, vortex dynamics is affected rather profoundly and acquires the characteristic features of the Hall effect of electrodynamics or the Magnus effect of fluid dynamics. In particular, a single vortex is always spontaneously pinned, two like vortices form a rotating bound state, and a vortex-antivortex pair undergoes Kelvin motion. Finally, in the presence of a bias field, vortices are shown to be the prominent topological excitations even for an isotropic antiferromagnet.

Physical Review E, 2000

In the framework of the complex cubic-quintic Ginzburg-Landau equation, we perform a systematic analysis of two-dimensional axisymmetric doughnut-shaped localized pulses with the inner phase field in the form of a rotating spiral. We put forward a qualitative argument which suggests that, on the contrary to the known fundamental azimuthal instability of spinning doughnut-shaped solitons in the cubic-quintic NLS equation, their GL counterparts may be stable. This is confirmed by massive direct simulations, and, in a more rigorous way, by calculating the growth rate of the dominant perturbation eigenmode. It is shown that very robust spiral solitons with ͑at least͒ the values of the vorticity Sϭ0, 1, and 2 can be easily generated from a large variety of initial pulses having the same values of intrinsic vorticity S. In a large domain of the parameter space, it is found that all the stable solitons coexist, each one being a strong attractor inside its own class of localized two-dimensional pulses distinguished by their vorticity. In a smaller region of the parameter space, stable solitons with Sϭ1 and 2 coexist, while the one with Sϭ0 is absent. Stable breathers, i.e., both nonspiraling and spiraling solitons demonstrating persistent quasiperiodic internal vibrations, are found too.

Physical Review E, 2008

We report results of collisions between coaxial vortex solitons with topological charges ϮS in the complex cubic-quintic Ginzburg-Landau equation. With the increase of the collision momentum, merger of the vortices into one or two dipole or quadrupole clusters of fundamental solitons ͑for S = 1 and 2, respectively͒ is followed by the appearance of pairs of counter-rotating "unfinished vortices," in combination with a soliton cluster or without it. Finally, the collisions become elastic. The clusters generated by the collisions are very robust, while the "unfinished vortices," eventually split into soliton pairs.

2007

We study the dynamics of vortex-antivortex (VA) pairs in an infinitely thin ferromagnetic film with easy-plane anisotropy. These are localized excitations with finite energy that are characterized by a topological (skyrmion) number N = 0,+1,-1. Topologically trivial (N=0) VA pairs undergo Kelvin motion analogous to that encountered in fluid dynamics. In contrast, topologically nontrivial (N = +1,-1) VA pairs perform

2010

We report the existence of stable symmetric vortex-type solutions for two-dimensional nonlinear discrete dissipative systems governed by a cubic-quintic complex Ginzburg-Landau equation. We construct a whole family of vortex solitons with a topological charge S = 1. Surprisingly, the dynamical evolution of unstable solutions of this family does not alter significantly their profile, instead their phase distribution completely changes. They transform into two-charges swirl-vortex solitons. We dynamically excite this novel structure showing its experimental feasibility.

Nature Physics, 2005

Confinement in nanomagnets alters their energetics and leads to new magnetic states, for example, vortices. There are many basic questions concerning dynamics and interaction effects that remain to be answered and nanomagnets are convenient model systems for studying these fundamental physical phenomena. A single vortex in restricted geometry, also known as a nonlocalized soliton, possesses a characteristic translational excitation mode that corresponds to spiral-like motion of the vortex core around its equilibrium position. Here we investigate the dynamics of magnetic soliton pairs confined in lithographically defined Permalloy ellipses using a microwave reflection technique. Strong resonances were detected experimentally in the sub-GHz frequency range and, by comparing with micromagnetic simulations, assigned to the translational modes of vortex pairs with parallel or antiparallel core polarizations. Although the vortex polarizations play a negligible role in the static interaction between two vortices, their effect dominates the dynamics.

Physical Review B, 2007

We evaluate a zero-point quantum correction to a Belavin-Polyakov soliton in an isotropic 2D ferromagnet. By revising the scattering problem of quasi-particles by a soliton we show that it leads to the Aharonov-Bohm type of scattering, hence the scattering data can not be obtained by the Born approximation. We proof that the soliton energy with account of quantum corrections does not have a minimum as a function of its radius, which is usually interpreted as a soliton instability. On the other hand, we show that long lifetime solitons can exist in ferromagnets due to an additional integral of motion, which is absent for the σ-model. PACS numbers: 75.10.Hk, 75.30.Ds, 05.45.Yv Solitons are known to play an important role in several branches of field theory and condensed matter physics, see Ref. 1 for a review. In particular, solitons treated as nonlinear excitations are important in 1D and 2D magnetism [2, 3, 4]. A serious impediment in studying 2D spin systems arises due to the absence of exact analytical solutions for most models. Thereupon special attention is deserved to models which admit an analytical treatment. One of the well-known examples is a model of the 2D isotropic ferromagnet (FM), which provides an exact analytical soliton, the so-called Belavin-Polyakov (BP) soliton . In terms of the normalized magnetization, m = (sin θ cos φ, sin θ sin φ, cos θ), the soliton structure m BP is described by the formula [5]

Lecture Notes in Physics, 2000

Theories, simulations and experiments on vortex dynamics in quasi-two-dimensional magnetic materials are reviewed. These materials can be modelled by the classical two-dimensional anisotropic Heisenberg model with XY (easy-plane) symmetry. There are two types of vortices, characterized by their polarization (a second topological charge in addition to the vorticity): Planar vortices have Newtonian dynamics (evenorder equations of motion) and exhibit strong discreteness effects, while non-planar vortices have non-Newtonian dynamics (odd-order equations of motion) and smooth trajectories. These results are obtained by a collective variable theory based on a generalized travelling wave ansatz which allows a dependence of the vortex shape on velocity, acceleration etc.. An alternative approach is also reviewed and compared, namely the coupling of the vortex motion to certain quasi-local spinwave modes. The influence of thermal fluctuations on single vortices is investigated. Different types of noise and damping are discussed and implemented into the microscopic equations which yields stochastic equations of motion for the vortices. The stochastic forces can be explicitly calculated and a vortex diffusion constant is defined. The solutions of the stochastic equations are compared with Langevin dynamics simulations. Moreover, noise-induced transitions between opposite polarizations of a vortex are investigated. For temperatures above the Kosterlitz-Thouless vortex-antivortex unbinding transition, a phenomenological theory, namely the vortex gas approach, yields central peaks in the dynamic form factors for the spin correlations. Such peaks are observed both in combined Monte Carlo-and Spin Dynamics-Simulations and in inelastic neutron scattering experiments. However, the assumption of ballistic vortex motion appears questionable.