Interaction of a breather with a magnetization wave in a ferromagnet with light-axis anisotropy

We use the dressing method to find exact solutions of the Landau-Lifshitz equation for a ferromagnet with light-axis anisotropy. These solutions describe the interaction of a nonlinear precession wave of arbitrary amplitude with solitons. We analyze the change of the internal structure and the physical parameters of the solitons as a result of their interaction with the magnetization wave. We find an infinite series of integrals of motion that stabilize the soliton on the background of the pumping wave.     

Relaxing solitons of a biaxial ferromagnet

Theoretical and Mathematical Physics - We use the Riemann problem on a torus to obtain and analyze new analytic solutions of the Landau–Lifshitz model that describe the nonlinear dynamics of...     

Correlation functions of a Heisenberg ferromagnet in the paramagnetic region

Conclusions In the present paper, in the framework of the coupled-mode approximation for the second-order equations (2.6)–(2.9) we have obtained an approximate closed system of equations (2.10)–(2.14) for the spin correlation functions of a Heisenberg ferromagnet in a vanishing external magnetic field and at temperatures above the critical temperature ( _c )., In principle, Eqs. (2.10)–(2.14) make it possible to investigate the behavior of the correlation functions in the entire investigated temperature range, including the critical point. Equations (2.10)–(2.14) are very complicated, and a numerical calculation is needed to analyze them.In the fourth section, we obtained interpolation formulas that make it possible to describe in some detail the behavior of the spectral density at both high and low frequencies. It would be expedient to find first the solution, of the simplified system of equations obtained from (2.10)–(2.14) by replacement of the Green's function (2.10) and the spectral density (3.2) by their interpolation expressions (4.2) and (4.3). Substituting (4.3) in (3.3) and (3.4), we obtain equations for and , in terms of which all the remaining quantities can be expressed. The solution obtained from the simplified system can be used further as initial approximation in the solution of the system of equations (2.10)–(2.14). However, this problem goes beyond the framework of the given paper.V. A. Steklov Mathematics Institute, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 52, No. 1, pp. 147–160, July, 1982.     

Bounds on the micromagnetic energy of a uniaxial ferromagnet

We identify the optimal scaling law for a nonconvex, nonlocal variational problem representing the magnetic energy of a uniaxial ferromagnet. Our analysis is restricted to a certain parameter regime, in which the surface tension is sufficiently small relative to the other parameters of the problem. © 1998 John Wiley & Sons, Inc.     

The hysteretic event in the computation of magnetization

Summary Simulations of magnetic and magnetostrictive behavior based on micromagnetic theory exhibit hysteresis. These systems have a highly nonlinear character involving both short range anisotropy and elastic fields and dispersive demagnetization fields. Hysteresis occurs even in the absence of an imposed dynamical mechanism, for example, a Landau-Lifshitz-Gilbert dissipative equation for the magnetic moment, and is symptomatic of the way the system navigates a path through local minima of its energy space. It is not sensitive to the particular method: We implement continuation based on the conjugate gradient method, although the same results were obtained by, for example, a Newton’s method. The phenomenon is robust: Computational experiments confirm that the shape of the loop is invariant over several decades of mesh refinement. Our experience has led us to hold that optimization procedures have the propensity to become marooned at local extrema when applied to nonconvex situations and that this presents a fundamental challenge to analysis. Understanding and controlling such phenomena present the opportunity to develop predictive tools and diagnostics. For example, since the energy picture is mesh-independent, computing on a fairly coarse grid suffices to establish its character.     

Solvability of a problem of magnetization

Vilnius University. Translated from Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 31, No. 4, pp. 622–632, October–December, 1991.     

Finite-gap solutions of two-dimensional isotropic ferromagnet with fixed boundary conditions

For the model of the two-dimensional stationary Heisenberg magnet, real finite-gap solutions that describe the main structures that are almost periodic with respect tox andy are constructed. Some solutions of boundary-value problems are considered.St Petersburg Branch, V. A. Steklov Mathematics Institute, Russian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 94, No. 1, pp. 165–172, January, 1993.     

Thermodynamics of the two-dimensional Heisenberg ferromagnet in the framework of the renormalization-group approach

A method of describing the thermodynamic functions of two-dimensional isotropic Heisenberg ferromagnets based on a generalization of the 2 + expansion is proposed. Interpolation formulas constructed in the framework of this approach make possible a smooth passage to the results obtained by the methods of high-temperature expansions.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 104, No. 3, pp. 530–537, September, 1995.