Magnetic Domain Wall Dynamics Research Articles

Some aspects of the nonlinear dynamics of magnetic domain walls

In this paper elements of chaos theory are applied to the study of the dynamics of a previously proposed model for a 180° Bloch wall under the action of an alternating magnetic field in materials without nonferromagnetic inclusions. The new element brought to these studies is the comparison between the powers of the chaotic and controlled oscillations. This comparison implied firstly the design of a method for finding periodic orbits and then the setting of a chaos control method. A parametric method was chosen, in which a control parameter proportional to the field's amplitude was used, and which offers more possibilities than that of a previously reported work. The existence of periodic orbits with smaller dissipation than that of the chaotic trajectory is proved.

A general model for power dissipation by domain wall movement in thin ferromagnetic films

In this work we present a model for magnetic domain wall (DW) dynamics in metallic ferromagnets with uniaxial anisotropy. The model allows us to consider both viscous and eddy current dampings. While the latter mechanism involves only one degree of freedom — the coordinate of the DW, the former involves all degrees of freedom of the spins in magnetic domains and in DW’s. The structure of the DW itself must then be considered, the conjecture used allowing one to describe the spin precessions which may appear in low quality factor Q materials. The model built is nonlinear, allowing one to deal with the set of complex susceptibilities characterizing the response to an ac drive field in strongly nonlinear circumstances, and has a general character, due to the normalized quantities used. In this work we analyze the susceptibility and the dissipated power spectra as functions of a dc transversal field, which can be treated only by this kind of models. We show that the viscous damping can become comparable to eddy current damping when precessions are excited.

An adaptive computational method for domain wall dynamics (abstract)

The dynamics of magnetic domain walls is a subject of intensive computer simulation of last years. Now it is well understood, that strongly twisted structures (like horizontal Bloch lines) of domain walls can be created. In some cases this HBL can have a very small localization region. Appearance of such inconvenient objects, like HBL, states a new scale for numerical model and it required a significant increase of node number for the uniform grid model. The main idea of the new adaptive computational method for LLG equation for two-dimensional (2D) domain wall dynamics is to inject and delete additional nodes only to the HBL localization region, using a special target function, which is based on the twisting angle of the domain wall. Node injection occurs when HBL is created, and node deleting occurs when HBL is breakthrough. The conjugated gradient method was used for fast demagnetization field computation by two Dirichlet problems for Poisson equations. We show an effective application of this method for 2D computations of domain wall dynamics for bubble film with parameters: Q=4, D=3(l), α=0.2, h=(0,8,−3), (Ms) [Here Q is the quality factor of the film, D the film thickness in characterization units, α the damping parameter, h the external magnetic field in Ms units, 8(Ms) the value of in-plane magnetic field via chirality, −3(Ms) is the driven magnetic field.] We found that HBL has very strong localization in this case. To carry out this computation we need nx×nz=65×162 for uniform grid sytem, and only nx×nz=33×60 for adaptive grid system. A color computer movie was created for this case. The new mechanics of HBL generation and breakthrough is discussed. Here we can see significant asymmetry in HBL generation: two HBL created at one moment at the lower surface of the film, but upper HBL goes to the upper surface of the film and the lower goes to the opposite direction. The next pair of HBL is created at the lower surface of the film at the same place.

Dynamics of magnetic domain walls with loosely spaced vertical Bloch lines

The dynamics of a magnetic domain wall containing vertical Bloch lines (VBLs) has been investigated using numerical methods. The wall is of the kind found in thin-film materials with a large anisotropy perpendicular to the plane of the film. The VBLs are all of the same chirality and are periodically repeated along the wall at equal spacing. The wall is driven by an applied field perpendicular to the film plane and the VBLs move gyrotropically. Both the wall and VBLs, starting from an equilibrium shape, soon attain a constant velocity. Distortion of the wall and structure from the equilibrium shape is evident and increases with field. The wall and VBL velocity both increase with field but neither are linear so that the ratio of VBL velocity to wall velocity decreases with applied field. For an applied field extrapolated to zero, the wall velocity agrees with the value predicted by the analytical rigid wall model and the ratio decreases by 50% for higher fields because of the distortion.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Complex dynamics in domain wall motion

A simple model, exactly solvable except at two points, which simulates the dynamics of a single magnetic domain wall crossing a single impurity site in a ferromagnetic material, is solved numerically for some ranges of parameters. The dynamics are complex and very sensitively dependent on the physical parameters: the frequency and strength of the applied field, the strength of the pinning, the reversible permeability, the effective mass of the domain wall, the wall viscosity, and the amount of energy retained by the wall when it breaks free of the pinning site. An example of parameter choice that results in frequency quintupling is given. Phase space portraits, return maps, and total energy spectra are used to display the results.

Domain wall widening in high drive fields

Magnetic domain wall dynamics in garnet film was investigated in a wide range of drive fields (H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</inf> ) using high speed photography. It is shown that the wall widening, the so-called dynamic diffuse wall begins at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H_{z}\geqH_{cr}</tex> where the velocity, after reaching its saturation, starts to increase again. The dynamic domain wall formation can be interpreted on the basis of the theory of spinodal decomposition, i.e. as the quasi-periodic fluctuation of the wall surface.

Some personal reminiscences of the history of Bloch walls

We have studied the magnetic properties and domain wall dynamics in Fe-rich microwires subjected to stress-annealing. The hysteresis loops of Fe-rich microwires were considerably affected by stress-annealing. We obtained drastic decrease in coercivity and change in the character of hysteresis loops from rectangular to linear in stress-annealed Fe-rich microwires. For the wires after stress-annealing at variable temperatures we obtained a graded magnetic behavior with local hysteresis loops shapes and features (coercivity, remanent magnetization) changing along the sample length. In the samples subjected to local stress-annealing we created an artificial source of domain wall injection allowing the manipulation of domain wall dynamics. The observed stress-induced anisotropy could be related to the internal stress relaxation after annealing and the interplay of compressive “back-stresses” arisen after stress annealing and axial internal stresses.

New developments in the dynamics of magnetic domain walls and bubbles

A short review is given of some new developments in the dynamics of magnetic domain walls and bubbles in materials for bubble applications. The velocity versus drive field relationship is considered and the influence of an external in-plane field and of the inhomogeneity of the film is discussed. Heavy wall effects and bubble overshoots will be mentioned.

Recent developments in the dynamics of magnetic domain walls and bubbles

A condensed review will be given of some recent developments in the dynamics of magnetic domain walls and magnetic bubbles in garnet materials for bubble applications. Special attention is given to the velocity versus drive field relationship. Non-linear effects, time-dependent effects and heavy walls are discussed. Methods to suppress the non-linear effects and the heavy walls are considered.

Influence of gyromagnetic ratio on magnetic domain wall dynamics

We have investigated the dynamics of magnetic domain walls in three epitaxial garnet films with g values of 1.07, 4.8, and ≳30, and having wall mobilities of 880, 930, and 820 cm/sec Oe, respectively. Bubble collapse measurements in the films with g=1.07 and 4.8 showed velocity saturation with the approximate values 1500 and 8000 cm/sec, respectively. The film with g≳30 showed no saturation, and velocities up to 6×104 cm/sec were observed. These results are consistent with the expected increase in the Slonczewski and Walker critical velocities with increasing g value. Large g values make it possible to operate magnetic bubble circuits at higher frequencies than is otherwise the case.