Cycloidal vortex motion in easy-plane ferromagnets due to interaction with spin waves

The dynamics of a non-planar vortex in a two-dimensional easy-plane ferromagnet of finite size is studied. Spin dynamics simulations show small cycloidal oscillations of the vortex around its mean path. In contrast to an earlier phenomenological theory we give a physical explanation: The oscillations occur due to the interaction of the vortex with coherent spin waves which are excited by this vortex at the moment when it starts to move, in order to conserve the total energy and angular momentum. The calculation of these quantities yields the frequencies and amplitudes of the cycloidal oscillations in good agreement with the simulation data. Received 9 December 2002 Published online 4 June 2003 RID="a" ID="a"e-mail: franz.mertens@uni-bayreuth.de     

Topological and dynamical excitations in a classical 2D easy-axis Heisenberg model

The properties of dynamical solitons (magnon droplets) in the classical, two-dimensional anisotropic Heisenberg model with easy-axis exchange anisotropy are studied. The solution of the Landau-Lifshitz equation in the continuum limit for the soliton with topological charge q = 1 is obtained numerically using a shooting method. We analized a wide range of the anisotropy parameter and our results are in good agreement with results obtained from spin dynamics simulations. The dependence of an internal precession frequency of the soliton on both the anisotropy parameter and the radius of the soliton is also investigated. Finally, the limits of applicability of the continuum approach are discussed. Received 22 August 2000     

Kink solutions of the classical transverse field Ising chain

We investigate stationary and travelling wave solutions of the classical one-dimensional transverse field Ising model. Results are given on the existence, shape and stability of kink solutions and periodic solutions. We review recent analytical results (e.g., the proof of existence of a one-parameter family of stationary kink solutions and the proof of existence of travelling wave kink solutions with nonzero velocity c≠ 0) and extend them by the use of numerical methods. Small oscillations arising in the tails of travelling kink solutions are investigated numerically. In the end, stability analysis puts some light on pinning effects. Received 23 February 2001 and Received in final form 4 October 2001     

Switching of vortex polarization in 2D easy-plane magnets by magnetic fields

We investigate the dynamics of out-of-plane (OP) vortices, in a 2-dimensional (2D) classical Heisenberg magnet with a weak anisotropy in the coupling of z-components of spins (easy plane anisotropy), on square lattices, under the influence of a rotating in-plane (IP) magnetic field. Switching of the z-component of magnetization of the vortex is studied in computer simulations as a function of the magnetic field's amplitude and frequency. The effects of the size and the anisotropy of the system on the switching process are shown. An approximate dynamical equivalence of the system, in the bulk limit, to another system with both IP and OP static fields in the rotating reference frame is demonstrated, and qualitatively the same switching and critical behavior is obtained in computer simulations for both systems. We briefly discuss the interplay between finite size effects (image vortices) and the applied field in the dynamics of OP vortices. In the framework of a discrete reduced model of the vortex core we propose a mechanism for switching the vortex polarization, which can account qualitatively for all our results. A coupling between the IP movement (trajectories) of the vortex center and the OP core structure oscillations, due to the discreteness of the underlying lattice, is shown. A connection between this coupling and our reduced model is made clear, through an analogy with a generalized Thiele equation. Received 6 June 2002 / Received in final form 4 November 2002 Published online 6 March 2003 RID="a" ID="a"e-mail: juan.zagorodny@uni-bayreuth.de     

New geometries associated with the nonlinear Schrödinger equation

We apply our recent formalism establishing new connections between the geometry of moving space curves and soliton equations, to the nonlinear Schr?dinger equation (NLS). We show that any given solution of the NLS gets associated with three distinct space curve evolutions. The tangent vector of the first of these curves, the binormal vector of the second and the normal vector of the third, are shown to satisfy the integrable Landau-Lifshitz (LL) equation = ×, ( = 1). These connections enable us to find the three surfaces swept out by the moving curves associated with the NLS. As an example, surfaces corresponding to a stationary envelope soliton solution of the NLS are obtained. Received 5 December 2001 Published online 2 October 2002 RID="a" ID="a"e-mail: radha@imsc.ernet.in     

Evidence of domain wall scattering in thin films of granular CoFe-AgCu

Thin films of the giant magnetoresistive granular CoFe-AgCu system prepared by rf sputtering displayed a great variety of domain-like microstructures with a net out-of-plane component of the magnetization for ferromagnetic volume concentrations above about 0.25. Therefore, magnetic percolation takes place at ferromagnetic concentrations much lower than the physical percolation threshold. The out-of-plane structure of the as-deposited samples in magnetic virgin state consisted of a distribution of both quasi-circular domains and short stripes depending on the ferromagnetic content. Furthermore, these samples present high metastability and a variety of remanent in-plane and out-of-plane microstructures can be achieved as a function of the magnetic history. Besides, the evolution of the magnetic microstructure yields strong training effects on magnetotransport properties, due to the extra contribution of the electron scattering at the domain walls. All in all, the observed behavior is the result of a subtle correlation between perpendicular anisotropy produced by residual stresses, exchange interparticle interactions due to CoFe alloyed in the matrix, and dipolar interactions. Thus, as high structural evolution occurs through annealing, the features of randomly distributed ferromagnetic particles are recovered and, the out-of-plane domain structures and the training effects disappear. Received 30 September 1999     

Order by thermal disorder in 2D planar rotator model with dipolar interactions

The energy of a square planar rotator model of spins interacting via dipolar forces is minimized by infinite inequivalent configurations corresponding to spins arranged on four interpenetrating sublattices making angles , , , with a reference axis, being arbitrary. This infinite degeneracy of the ground state is accidental in nature and one expects that it is removed by thermal fluctuations in agreement with Monte Carlo simulation. Indeed we find that the elementary excitation energies which depend on lead to a free energy which is a function of with minima at and corresponding to columnar configurations. This selection of columnar configurations out of the infinite ground state manifold is an example of order by thermal disorder. Received 4 August 1998     

Low temperature thermodynamics of inverse square spin models in one dimension

We present a field-theoretic renormalization group calculation in two loop order for classical O(N)-models with an inverse square interaction in the vicinity of their lower critical dimensionality one. The magnetic susceptibility at low temperatures is shown to diverge like with a=(N-2)/(N-1) and . From a comparison with the exactly solvable Haldane-Shastry model we find that the same temperature dependence applies also to ferromagnetic quantum spin chains. Received: 20 February 1998 / Revised: 27 April 1998 / Accepted: 30 April 1998     

Spin-wave theory for finite classical magnets and superparamagnetic relation

Analytical calculations based on finite-size spin-wave theory and Monte Carlo (MC) simulations are performed to investigate the validity of the well-known relation m(H, T) = M(H, T)B _D[M(H, T) H/T] between the induced magnetization m of the magnetic particle and its intrinsic magnetization M for the Ising and isotropic classical models (B _D(x) is the Langevin function, D is the number of spin components, is the number of atoms in the particle). It follows from general arguments and from our analytical results for the Heisenberg model at T≪T _c that this relation is not exact for any finite D and nonzero temperature. Nevertheless, corrections to this formula remain very small practically in the whole range T < T _c if ≫ 1, as confirmed by our Monte Carlo calculations. At T T _c/4 there is a good agreement between the MC and finite-size spin-wave calculations for the field dependence of m and M for the Heisenberg model with free boundary conditions. Received 1st December 2000     

The glassy phase of Gallager codes

Gallager codes are the best error-correcting codes to date. In this paper we study them by using the tools of statistical mechanics. The corresponding statistical mechanics model is a spin model on a sparse random graph. The model can be solved by elementary methods (i.e. without replicas) in a large connectivity limit. For low enough temperatures it presents a completely frozen glassy phase (q _EA = 1). The same scenario is shown to hold for finite connectivities. In this case we adopt the replica approach and exhibit a one-step replica symmetry breaking order parameter. We argue that our ansatz yields the exact solution of the model. This allows us to determine the whole phase diagram and to understand the performances of Gallager codes. Received 9 April 2001     

Shape anisotropy and magnetic domain structures in striped monolayers

We study the effect of dipolar interactions on a magnetic striped monolayer with a microscopic unit cell of square symmetry, and of size spins. Even if the aspect ratio r=N _x /N _y is very large, an in-plane shape anisotropy is always negligible, except if N_y is fairly small (N _y <40). In-plane domains are not possible, except for values of the dipolar coupling larger than the domain wall energy. Received: 11 July 1997 / Revised: 24 September 1997 / Accepted: 24 October 1997     

Soliton dynamics in damped and forced Boussinesq equations

We investigate the dynamics of a lattice soliton on a monatomic chain in the presence of damping and external forces. We consider Stokes and hydrodynamical damping. In the quasi-continuum limit the discrete system leads to a damped and forced Boussinesq equation. By using a multiple-scale perturbation expansion up to second order in the framework of the quasi-continuum approach we derive a general expression for the first-order velocity correction which improves previous results. We compare the soliton position and shape predicted by the theory with simulations carried out on the level of the monatomic chain system as well as on the level of the quasi-continuum limit system. For this purpose we restrict ourselves to specific examples, namely potentials with cubic and quartic anharmonicities as well as the truncated Morse potential, without taking into account external forces. For both types of damping we find a good agreement with the numerical simulations both for the soliton position and for the tail which appears at the rear of the soliton. Moreover we clarify why the quasi-continuum approximation is better in the hydrodynamical damping case than in the Stokes damping case. Received 22 August 2001 and Received in final form 7 December 2001     

The CPA solution of the anomalous Lyapunov exponent for disordered binary chains

The Coherent Potential Approximation (CPA) self-consistent equation is calculated for a binary disordered chain introducing a simple transformation. The transformation reduces the CPA equation to a cubic polynomial whose complex roots are related to the Green function and their relation to the complex Lyapunov exponent is also established. This solution fruitfully captures essential aspects of the well-known anomalous scaling behaviors in a different and advantageous way. It is found that the anomalous behavior is strongly effected by the nature of these roots. A small disorder expansion is carried out for comparison with the previous weak disorder calculations. We found that the CPA reproduced the anomalous behavior of the exact calculations. Received 22 April 2002 Published online 1st October 2002 RID="a" ID="a"e-mail: avgin@bornova.ege.edu.tr     

Dynamics of topological solitons in two-dimensional ferromagnets

Dynamical topological solitons are studied in classical two-dimensional Heisenberg easy-axis ferromagnets. The properties of such solitons are treated both analytically in the continuum limit and numerically by spin dynamics simulations of the discrete system. Excitation of internal mode causes orbital motion. This is confirmed by simulations.     

Stabilization of the long-range magnetic ordering by dipolar and magnetoelastic interactions in two-dimensional ferromagnets

The possibility of the long-range magnetic order stabilization in two-dimensional ferromagnets with the account of dipolar and magnetoelastic interactions is investigated. The mechanisms of the magnetic order stabilization by both types of interactions are studied. The Curie temperature is estimated. The comparisons with experimental data are made. Received 22 June 2001 and Received in final form 17 January 2002     

solitons in quantum Hall systems

We present here an elementary pedagogical introduction to CP_N solitons in quantum Hall systems. We begin with a brief introduction to both CP_N models and to quantum Hall (QH) physics. We then focus on spin and layer-spin degrees of freedom in QH systems and point out that these are in fact CP_N fields for N = 1 and N = 3. Excitations in these degrees of freedom will be shown to be topologically non-trivial soliton solutions of the corresponding CP_N field equations. We conclude with a brief summary of our own recent work in this area, done with Sankalpa Ghosh. Received 17 November 2001 Published online 2 October 2002 RID="a" ID="a"e-mail: doug0700@mail.jnu.ac.in     

Skyrmions on an elastic cylinder

For a spin-polarized electron gas on an elastic cylinder in an external axial magnetic field and an axial electric field we find that the corresponding Euler-Lagrange equation is the double sine-Gordon (DSG) equation with an exact 2π-skyrmion solution. The DSG skyrmion is stabilized, without Coulomb repulsion, by the curvature of the cylinder. It adopts a characteristic length ξ which is smaller than the radius of the cylinder. For an elastic cylinder this mismatch of length scales causes a deformation of the cylinder in the region of the skyrmion. Received 23 October 2001 / Received in final form 8 March 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: rossen.dandoloff@ptm.u-cergy.fr     

Delocalization and wave-packet dynamics in one-dimensional diluted Anderson models

We study the nature of one-electron eigen-states in a one-dimensional diluted Anderson model where every Anderson impurity is diluted by a periodic function f(l). Using renormalization group and transfer matrix techniques, we provide accurate estimates of the extended states which appear in this model, whose number depends on the symmetry of the diluting function f(l). The density of states (DOS) for this model is also numerically obtained and its main features are related to the symmetries of the diluting function f(l). Further, we show that the emergence of extended states promotes a sub-diffusive spread of an initially localized wave-packet.Received: 7 July 2003, Published online: 19 November 2003PACS: 63.50. + x Vibrational states in disordered systems - 63.22. + m Phonons or vibrational states in low-dimensional structures and nanoscale materials - 62.30. + d Mechanical and elastic waves; vibrations     

The spin-1/2 anisotropic Heisenberg-chain in longitudinal aaand transversal magnetic fields: a DMRG study

Using the density matrix renormalization group technique, we evaluate the low-energy spectrum (ground state and first excited states) of the anisotropic antiferromagnetic spin-one-half chain under magnetic fields. We study both homogeneous longitudinal and transversal fields as well as the influence of a transversal staggered field on the opening of a spin-gap. We find that only a staggered transversal field opens a substantial gap. Received 16 April 2002 / Received in final form 4 July 2002 Published online 17 September 2002     

Properties of supersymmetric integrable systems of KP type

The recently proposed supersymmetric extensions of reduced Kadomtsev-Petviashvili (KP) integrable hierarchies in N = 1, 2 superspace are shown to contain in the purely bosonic limit new types of ordinary non-supersymmetric integrable systems. The latter are coupled systems of several multi-component non-linear Schr?dinger-like hierarchies whose basic nonlinear evolution equations contain additional quintic and higher-derivative nonlinear terms. Also, we obtain the N = 2 supersymmetric extension of Toda chain model as Darboux-B?cklund orbit of the simplest reduced N = 2 super-KP hierarchy and find its explicit solution. Received 13 September 2001 Published online 2 October 2002 RID="a" ID="a"e-mail: nissimov@inrne.bas.bg RID="b" ID="b"e-mail: svetlana@inrne.bas.bg