Visualization of the Barkhausen effect by magnetic force microscopy

By visualization of the Barkhausen effect using magnetic force microscopy we are able to provide detailed information about the physical principles that govern the magnetization reversal of a granular ferromagnetic thin film with perpendicular anisotropy. Individual Barkhausen volumes are localized and distinguished as either newly nucleated or grown by domain wall propagation. The Gaussian size distribution of nucleated Barkhausen volumes indicates an uncorrelated random process, while grown Barkhausen volumes exhibit an inverse power law distribution, which points towards a critical behavior during domain wall motion.     

Concept of the field-driven domain wall motion memory

In this paper, the concept of field-driven domain wall motion memory is presented. It is confirmed that a domain is shifted with a carefully designed non-uniform field by micromagnetic simulations. The shift of a domain—a bit—can be established by the motion of two domain walls to the same direction and the same distance. In order to get a better understanding of the domain wall motion under the non-uniform transverse magnetic field, we investigate the motion of the transverse Néel-type domain wall by micromagnetic simulations and the collective coordinate approach. The validity of the equation of motion for the domain wall is confirmed by the micromagnetic simulations as functions of the gradient of the non-uniform field, the saturation magnetization, and the Gilbert damping parameter α.     

Effect of fluctuations on the forced motion and interactions of domain walls in one-dimensional magnetic systems

Forced motion of a domain wall in the presence of fluctuations of external magnetic field and those of the parameters of the magnetic medium is studied. Calculations for the models of magnetic systems described by the sine-Gordon and Landau-Lifshitz equations are presented. It is shown that the driven motion of domain walls is characterized by the time-independent velocity distribution function which is used to calculate various statistical characteristics of the domain wall. Analysis of the mean velocity of the steady motion of the domain wall leads to the conclusion that the presence of a fluctuating magnetic field results in an increase of the effective relaxation constant of the magnetic system. In case of the sine-Gordon model the mean radiation power accompanying the forced motion of the domain wall is calculated. Inelastic interactions of two domain walls of opposite polarities are described.     

Efficiency of shear surface wave transformation by the motion of the confining domain wall

The transformation of a shear surface magnetoelastic wave by the motion of the 180° confining domain wall in a ferromagnet is considered. Changes in the wave spectrum due to the motion of the wall are correlated with the variations of the energies of the elastic and magnetic subsystems. The efficiency of surface wave transformation by the domain wall motion is estimated in terms of energy. The frequency dependences of the mean energy density of the wave are found. It is shown that the energy density grows with wall velocity.     

Magnetic noise as the cause of the spontaneous magnetization reversal of RE–TM–B permanent magnets

The relation between the macroscopic spontaneous magnetization reversal (magnetic viscosity) of (NdDySm)(FeCo)B alloys and the spectral characteristics of magnetic noise, which is caused by the random microscopic processes of thermally activated domain wall motion in a potential landscape with uniformly distributed potential barrier heights, is found.     

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.     

Temperature dependence of the spin torque effect in current-induced domain wall motion

We present an experimental study of domain wall motion induced by current pulses as well as by conventional magnetic fields at temperatures between 2 and 300 K in a 110 nm wide and 34 nm thick Ni80Fe20 ring. We observe that, in contrast with field-induced domain wall motion, which is a thermally activated process, the critical current density for current-induced domain wall motion increases with increasing temperature, which implies a reduction of the spin torque efficiency. The effect of Joule heating due to the current pulses is measured and taken into account to obtain critical fields and current densities at constant sample temperatures. This allows for a comparison of our results with theory.     

Hysteresis mediated by a domain wall motion

The position of an interface (domain wall) in a medium with random pinning defects is not determined unambiguously by the instantaneous value of the driving force, even on average. Employing the general theory of the interface motion in a random medium, we study this hysteresis, different possible shapes of the hysteresis loop, and the dynamical phase transitions between them. Several principal characteristics of the hysteresis, including the coercive force and the curves of dynamical phase transitions obey scaling laws and display a critical behavior in the vicinity of the mobility threshold. At finite temperature the threshold is smeared and a new range of thermally activated hysteresis appears. At a finite frequency of the driving force there exists a range of the non-adiabatic regime in which not only the position, but also the average velocity of the domain wall, displays hysteresis.     

Dynamics of magnetic domain wall motion after nucleation: dependence on the wall energy

The dynamics of magnetic domain wall motion in the FeNi layer of a FeNi/Al2O3/Co trilayer has been investigated by a combination of x-ray magnetic circular dichroism, photoelectron emission microscopy, and a stroboscopic pump-probe technique. The nucleation of domains and subsequent expansion by domain wall motion in the FeNi layer during nanosecond-long magnetic field pulses was observed in the viscous regime up to the Walker limit field. We attribute an observed delay of domain expansion to the influence of the domain wall energy that acts against the domain expansion and that plays an important role when domains are small.     

Domain dynamics and magneto-electronics in magnetic thin films and nanowires

Recent theoretical results are highlighted that illustrate some of the interesting phenomena associated with magnetic domain boundary walls. Two problems will be discussed: dynamics associated with domain wall propagation, and effects related to spin transport through domain walls. For the first problem, an example of wall interaction and motion through a random potential will be discussed with reference to the general problem of roughening transitions. Images of domain dynamics in thin films of ion irradiated Co reveal a de-roughening transition associated with long range magnetostatic interactions between pairs of domain walls. A scaling theory of this transition is described in which a curious type of dynamic hysteresis can occur. For the second problem, results from calculations of ballistic charge and spin transport through domain boundary walls are discussed in terms of an effective circuit model.     

Influence of a transport current on a domain wall in an antiferromagnetic metal

We consider the influence of an electric current on the position of a domain wall in an antiferromagnetic metal. We first microscopically derive an equation of motion for the Néel vector in the presence of current by performing, in the transport steady state, a linear-response calculation in the deviation from collinearity of the antiferromagnet. This equation of motion is then solved variationally for an antiferromagnetic domain wall. We find that, in the absence of dissipative or non-adiabatic coupling between magnetization and current, the current displaces the domain wall by a finite amount and that the domain wall is then intrinsically pinned by the exchange interactions. In the presence of dissipative or non-adiabatic current-to-domain-wall coupling, the domain wall velocity is proportional to the current and is no longer pinned.     

Modes of periodic domain wall motion in ultrathin ferromagnetic layers

Magnetization reversal in a periodic magnetic field is studied on an ultrathin, ultrasoft ferromagnetic Pt/Co(0.5 nm)/Pt trilayer exhibiting weak random domain wall (DW) pinning. The DW motion is imaged by polar magneto-optic Kerr effect microscopy and monitored by superconducting quantum interference device susceptometry. In close agreement with model predictions, the complex linear ac susceptibility corroborates the dynamic DW modes segmental relaxation, creep, slide, and switching.     

Domain wall creep in epitaxial ferroelectric Pb(Zr(0.2)Ti(0.08)O(3) thin films

Ferroelectric switching and nanoscale domain dynamics were investigated using atomic force microscopy on monocrystalline Pb(Zr(0.2)Ti(0.8))O(3) thin films. Measurements of domain size versus writing time reveal a two-step domain growth mechanism, in which initial nucleation is followed by radial domain wall motion perpendicular to the polarization direction. The electric field dependence of the domain wall velocity demonstrates that domain wall motion in ferroelectric thin films is a creep process, with the critical exponent mu close to 1. The dimensionality of the films suggests that disorder is at the origin of the observed creep behavior.     

Structure and dynamic properties of the twisted magnetic domain wall in an electric field

The structure of the domain wall in a magnetically uniaxial ferromagnetic film placed in an external electric field has been studied. It has been shown that the domain wall has a complex twisted structure whose characteristics (thickness, profile, and limit velocity of steady motion) depend on the film thickness, quality factor, and external electric field. The effect of the electric field on the domain wall is caused by inhomogeneous magnetoelectric coupling taking place in domain walls with a twisted structure.     

Controlled domain wall motion by current into patterned-U Ni80Fe20 wires

The current-induced domain wall motion was observed experimentally in the case of the domain wall trapped at the semicircular arc within the U shape Ni₈₀Fe₂₀ wire. The measurement of the current-induced domain wall motion was achieved by adding a biased field before switching field and a critical current density was measured. We found two magnetic domain structures in the U pattern. At zero fields, the vortex domain wall nucleated at the semicircular arc of the U pattern. Continuous magnetic state without wall was investigated in near-switching field.     

Analysis of the complex permeability of monocrystalline MnZnFeII ferrite

A method of analysis is discussed by means of which the domain wall susceptibility and rotational susceptibility of monocrystalline MnZn ferrite can be distinguished. It is based upon a measurement of the frequency dependence of the disaccommodation occurring in the ferrite. From this analysis it appears that below 1 MHz the domain wall motion is the dominating magnetization process in MnZn ferrite, whereas above 3 MHz the rotational susceptibility prevails. Between 1 and 3 MHz, μ′ and μ″ are determined mainly by the rotational- and wall-susceptibility, respectively. Hence, when applied in magnetic video heads, the ferrite may generate electrical noise as a result of the dissipation accompanying the wall motion.     

Numerical approaches on driven elastic interfaces in random media

We discuss the universal dynamics of elastic interfaces in quenched random media. We focus on the relation between the rough geometry and collective transport properties in driven steady-states. Specially devised numerical algorithms allow us to analyze the equilibrium, creep, and depinning regimes of motion in minimal models. The relevance of our results for understanding domain wall experiments is outlined.     

Steady motion of the magnetic vortex under the magnus force in weak ferromagnets

The problem of steady motion of the magnetic vortex in a moving domain wall under the action of the Magnus force in weak ferromagnets was studied. Dynamic bending of the domain wall containing a moving vortex was analyzed. The formulas describing the dependences of the vortex velocity on the velocity of the domain wall in which it moves were derived.     

Real time dynamic domain observation in bulk materials

The paper briefly reviews the development of domain observation techniques used to study basic properties of electrical steels. A new real-time, dynamic, high magnification domain observation technique is presented as an example of a state-of-the-art system, capable of imaging non-repetitive domain wall motion at power frequencies. Advantages of real-time domain observation over stroboscopic magneto-optic studies are presented and the need for real-time observations in developing future loss theories is proposed. Possible relationships between Barkhausen noise, hysteresis and non-repetitive wall motion in electrical steels are suggested and finally examples of non-repetitive wall motion in other magnetic materials are illustrated.