Chaotic dynamics of interacting domain walls in uniaxial ferromagnetic films

The nonlinear dynamics of a periodic system of interacting domain walls in a thin ferromagnetic uniaxial film with transverse anisotropy is examined. The interaction between the domain walls takes place through the magnetostatic demagnifying fields of the domains. The equations of motion derived for such a system of walls are solved numerically by a 4–5th-order Runge-Kutta scheme, while the uniformity of the distributions of the phase trajectory, the form of the Poincaré cross section, and the spectral density of the vibrations serve as indicators of the type of oscillations. All the known types of oscillations are observed in a computer simulation of this nonlinear system: periodic, quasiperiodic, and chaotic. The computational results have a universal character for uniaxial, highly-anisotropic ferromagnetic films having a strip domain structure, since the results can be easily scaled for materials with different magnetic characteristics. Fiz. Tverd. Tela (St. Petersburg) 39, 2036–2039 (November 1997)     

The mobility of domain walls in magnetic films

The character of the dependence of domain wall velocityv on magnetic field intensityH varies with film thickness. Possible causes of the nonlinearity ofv(H) in films of some thickness are discussed. It has been shown how the mobility of domain walls varies over a wide range of thicknesses, from ultrathin films to bulk layers. The mobility measured for films up to 500 thick is consistent with the spin damping theory. For thicknesses greater than 1 the experimental data agree well with the eddy current damping theory. The mobility in thinner films is considerably lower than predicted by this theory. It greatly depends on the domain wall structure, magnetic ripple in domains as well as on the structural defects retarding the wall.     

Dynamics of domain walls in ultrathin magnetic films

The domain walls in ultrathin ferromagnetic films with uniaxial magnetic anisotropy are investigated theoretically. It is shown that taking account of the magnetodipole and magnetoelastic interactions leads to the appearance of an effective anisotropy with respect to the direction of the normal to the plane of the wall. The existence of a new type of domain walls—“corner” walls, at which the magnetization vector is rotated in the plane making a certain angle, which depends on the film parameters, with the plane of the domain wall and the static and dynamic properties of these walls are investigated. The dependence of the limiting velocity of the domain walls on the film thickness is found. Zh. éksp. Teor. Fiz. 112, 1476–1489 (October 1997)     

Interaction of domain walls in thin magnetic films

Interactions of pairs of parallel Néel walls are investigated by means of Ritz's method calculations. In the case of the symmetric, thin-film mode of Néel walls, unwinding walls show an attractive and winding walls a repulsive interaction for all distances. The functional dependence of the interaction on the distance of the walls is strongly correlated with the wall profiles of the isolated walls with their characteristic extended tails. For the asymmetric Néel wall mode which occurs in thicker films, an additional repulsive interaction of the magnetization vortices in the wall core is found. This leads for unwinding walls to stable configurations of double walls with separations between two and three times the film thickness.     

Static properties of asymmetric vortex-like domain walls in magnetically uniaxial thick films

The structure and energy of asymmetric vortex-like Bloch and Néel walls in a magnetically uniaxial film with an easy magnetization axis lying in the film plane are investigated by numerically minimizing the total energy within the rigorous micromagnetic approach and the two-dimensional model of the magnetization distribution. The calculations are performed over wide ranges of film thicknesses b (up to b = 1 μm) and magnetic parameters of the films. It is established that the asymmetric vortex-like domain walls are the most universal wall structures in the films under consideration. In magnetically uniaxial films, unlike in magnetically multiaxial films, the asymmetric Bloch walls are always stable.     

Translational motion of domain walls in a strong magnetic field circularly polarized in the basal plane of a uniaxial ferromagnet

A substantially nonlinear theory is developed for the translational motion of domain walls (DWs) in ferromagnets with large easy-axis anisotropy under the influence of a strong magnetic field circularly polarized in the basal plane of the ferromagnet. This theory is a generalization of the well-known theories of DW drift that are limited to an approximation quadratic in the field magnitude. The analytical results are confirmed by computer simulation performed on the basis of the Landau-Lifshitz equations.     

Dissipation of the spin wave energy in magnetic multilayer films

It is shown that the penetration of standing spin waves into a layer with high damping is one of the channels of energy dissipation of these waves. The line broadening of spin wave modes due to this layer increases with the mode index and may be much larger than the natural linewidth associated with a layer having low damping. The linewidths of spin wave modes are found to be anisotropic, which is due to the dependence of the penetration depth of spin waves into the high-damping layer on the orientation of the external magnetic field with respect to the film. A theoretical model is proposed, which is consistent with the experimental data.     

Domain walls confined in magnetic nanotubes with uniaxial anisotropy

We present calculations of the different domain wall structures confined in magnetic nanotubes, such as transverse wall, asymmetric vortex wall, branch fashion wall, and horse-saddle wall. The wall structures were calculated by micromagnetic simulations. The tube radii R=50 nm and 100 nm, and aspect ratios length/radius L/R≤15 were considered. The magnetic phase diagrams of the stability of different kinds of the domain walls were plotted as function of the tube aspect ratio L/R and the tube thickness (difference of the outer and inner tube radii).     

On the breakdown of stationary motion of a domain wall in bilayer uniaxial magnetic films with different signs of the gyromagnetic ratio in layers

The motion of an isolated domain wall in bilayer uniaxial magnetic films with a gyromagnetic ratio of different sign in the layers is studied by numerically solving the Slonczewski equations. The gyromagnetic ratio and the thickness of the layers are varied, and threshold values of the field and velocity of the domain wall at which a breakdown of its stationary motion takes place are calculated. It is shown that, for a specific relationship between the thickness and the gyromagnetic ratio of the layers, the field and the velocity for the breakdown of the stationary motion of the domain wall increase infinitely.     

Nonlinear dynamics of vortex-like asymmetric domain walls in magnetic triaxial films

On the basis of numerical solution of the Landau-Lifshitz equation, we investigated the nonlinear dynamic behaviour of 90-degree and 180-degree asymmetric vortex-like domain walls in single-crystal films with cubic symmetry. Films with surfaces of (100) and (110) types are considered. The nonlinear dynamic rearrangement of the internal structure of a wall was investigated. The surface uniaxial magnetic anisotropy is shown to strongly influence the very process of dynamic rearrangement in the internal structure of a wall even up to the complete suppression of the whole process.     

Current-induced domain wall motion with adiabatic and nonadiabatic spin torques in magnetic nanowires

We investigate current-driven domain wall (DW) propagation in magnetic nanowires in the framework of the modified Landau-Lifshitz-Gilbert equation with both adiabatic and nonadiabatic spin torque (AST and NAST) terms. By employing a simple analytical model, we can demonstrate the essential physics that any small current density can drive the DW motion along a uniaxial anisotropy nanowire even in absence of NAST, while a critical current density threshold is required due to intrinsic anisotropy pinning in a biaxial nanowire without NAST. The DW motion along the uniaxial wire corresponds to the asymptotical DW oscillation solution under high field/current in the biaxial wire case. The current-driven DW velocity weakly depends on the NAST parameter β in a uniaxial wire and it is similar to the β = α case (α: damping) in the biaxial wire. Apart from that, we discuss the rigid DW motion from both the energy and angular momentum viewpoints and point out some physical relations in between. We also propose an experimental scheme to measure the spin current polarization by combining both field- and current-driven DW motion in a usual flat (biaxial) nanowire.     

Nonlinear reconfiguration of vortexlike domain walls in magnetically uniaxial films under the action of an external field normal to the easy magnetic axis

The effect of external magnetic field H normal to the anisotropy axis on the energy and configuration of vortexlike asymmetric magnetic walls in a magnetically uniaxial film with an easy magnetic axis parallel to its surface is studied. The investigation is based on minimizing the energy functional of the film with due regard to exchange energy, magnetic anisotropy energy, magnetostatic energy, and Zeeman energy. The range of H below the anisotropy field is found where the asymmetric Néel wall is stable, unlike the case H = 0, when the asymmetric Bloch wall is stable. It is shown that an asymmetric Bloch wall becomes absolutely unstable and reconfigures into an asymmetric Néel wall at some critical values of H = H _⊥. The dependences of critical field H _⊥ on the film thickness and saturation induction at different values of the anisotropy field are determined: field H _⊥ depends on the thickness nonlinearly and on the saturation induction nonmonotonically.     

Asymmetric vortex-chain domain walls in triaxial magnetic (110) films

Vortex-like structures of domain walls in triaxial magnetic (110) films are studied within a strict micromagnetic approach and a two-dimensional magnetization distribution approximation by numerically minimizing the total energy functional that includes all main types of interactions, among them the exchange, magnetic-anisotropy, and dipole-dipole (in the continuum approximation) interactions. It is demonstrated that, because of the unusual anisotropy, chains of asymmetric vortex structures can arise in this type of films and that the vortices in the structures increase in number with the film thickness.     

Experimental investigation of the magnetic structure of domain walls in thin ferromagnetic films

The structure of domain walls in thin magnetic films has been studied by the Lorentz method using electron microscopy. The possible existence of the coinciding and opposite directions of rotation of the magnetization vector in Néel domain walls has been proved experimentally. The domain walls separating 90° domains have been found in single-crystal magnetic films. These walls consist of domains with a considerably smaller area than 90° domains.     

A novel type of domain walls with two-dimensional magnetization distribution in magnetic triaxial films

On the basis of numerical minimization of total energy in magnetic triaxial ferromagnetic films with a surface of a (1 1 0)-type, we investigated two-dimensional structures of domain walls within a rigorous micromagnetic approach that takes into account all the main interactions including the dipole–dipole one. Novel two-vortex and three-vortex domain wall structures are established to exist. The profiles of domain wall structures and their stability regions are studied.     

Nonlinear dynamic structure rearrangement of vortexlike domain walls in magnetic films with in-plane anisotropy

The nonlinear dynamic behavior of vortexlike domain walls in magnetic uniaxial films having an in-plane anisotropy was investigated within a rigorous micromagnetic approach in the framework of a two-dimensional magnetization distribution by numerically solving the Landau–Lifshitz equations (with the Gilbert damping parameter) with allowance for all the main interactions, including the dipole–dipole one. The studies were carried out on magnetic soft films with an anisotropy axis lying in their plane in a dc magnetic field parallel to an easy axis and a pulsed magnetic field normal to it. New possibilities for controlling the nonlinear dynamic rearrangement of the internal structure of domain walls and their velocities in fields both above and below the critical field are established. The wall motion in the field above the critical one is nonstationary.     

Dynamics of vortexlike domain walls in triaxial magnetic films with the Goss orientation of the surface

The stationary dynamics of vortexlike domain walls in films with three magnetic axes and Goss orientation of the surface is studied for the first time with a micromagnetic method that exactly takes into account all basic types of interaction (including dipole-dipole interaction). Consideration is carried out using a 2D model of magnetization distribution by numerically solving Landau and Lifshitz’s nonlinear equations with attenuation in the Gilbert form. Dynamic configurations of domain walls are established, and the dependences of the domain wall velocity on an applied magnetic field, damping parameter, and magnetic film thickness are found.     

Spin polarized current controlled dynamics of domain walls in magnetic films with in-plane anisotropy

We study the dynamic properties of asymmetric vortex Bloch walls and classical 1D Néel walls controlled by a spin-polarized current in magnetic films with in-plane anisotropy. It is shown that fairly high velocities of domain walls (up to 100 m/s) can be obtained for the current density in the range j = 10⁶–10⁸ A/cm². The nonlinear dependence of the wall velocity on the film thickness and the linear dependence of the velocity on the current density and inverse damping parameter are found.     

Dynamics of a domain wall in two-layer uniaxial magnetic films with the same gyromagnetic ratios in the layers

Motion of an isolated domain wall in two-layer uniaxial magnetic films with the same gyromagnetic ratios in the layers is investigated by solving the Slonczewski equations using a numerical method. The steady-state motion regimes are established for the domain with the angle of magnetization vector departure from the wall plane exceeding π. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 76–82, April, 2007.