Simple Domain Structure Research Articles

Domain wall pinning in amorphous CoZrNb films

A series of CoZrNb amorphous films, with thickness t ranging from 200 to 630 nm, has been studied by using several techniques: Kerr imaging, dc and audio frequency hysteresis loops, field dependence of the permeability, torque balance, broadband frequency susceptometer (1 kHz≤f≤500 MHz). Only samples with t≤500 nm have simple domain structures typical of an in-plane anisotropy (with a small dispersion of the easy axis). Although domain walls (DW) are visible, they do not contribute to the initial permeability in the observed frequency range (even in the favorable case where the magnetic field is parallel to the easy axis), but they do play a role on the irreversible magnetization processes as shown by the existence of a critical field Hcr, typical of the onset of irreversible DW motion. These observations are consistant with a model which assumes that the DW are pinned at the film surfaces: the calculations give a negligible DW bulging contribution to the initial permeability, and predict the occurence of a DW unpinning field, thickness dependent as observed.

Investigation of domain structure in lead germanate by cleavage method

Abstract The cleavage method is developed for investigation of the domain structure in lead germanate in samples with simple domain structure. It is verified that cleavage process does not alter domain structure and the observed pattern corresponds to domain pattern at the moment of cleavage. The observed phenomena is viewed as a result of crack growth in anisotropic medium. The method proves to be very useful for investigation of as-grown domain structure consisting of small nonthrough domains.

A Preisach model study of demagnetized states

The question of the existence of a unique demagnetized state arose when several M = 0 magnetic states at H = 0 have been observed for epitaxial garnet films having simple stripe domain structures. The Preisach model of the magnetic hysteresis is capable of describing different demagnetizing processes. A recent vector moving model of the hysteresis properties of particulate magnetic materials predicts that, depending on the demagnetizing process, the demagnetized states are different. Measurements of the initial magnetization process after ac and dc demagnetization of particulate recording media have been perfomed and compared to the predictions of the vector moving model.

Investigation of Bloch wall fine structures by magnetic force microscopy

SUMMARYUsing a magnetic force microscope (MFM), measurements have been performed on single crystal iron whiskers. These samples exhibit a comparatively simple magnetic domain structure and a high degree of crystallographic perfection. STM measurements yield an average surface corrugation of about 3 nm. These nearly ideal boundary conditions permit an investigation of the undistorted surface configuration of Bloch walls in a cubic bulk crystal. Interactions between the stray field configuration of the sample and a ferromagnetic microscope tip have been measured with a new MFM device which is based on direct compliance detection. Measurements have been performed in the constant‐current mode, as well as in the constant‐compliance, mode. Control observation by means of the Kerr magneto‐optic effect permit an interpretation of the obtained MFM data in terms of isolated 180° Bloch walls. The fine structure of these walls has been analysed and compared with results obtained from model calculations.

Magnetic remanence measurements of single particles and the nature of domain patterns in titanomagnetites

In addition to classical body domain patterns, a profusion of complex maze like domain structures have been observed using the Bitter technique on titanomagnetites. Controversy persists over how important a role such complicated domain patterns play in remanent magnetization. We have compared the magnetic properties of single particles, which exhibit complex patterns with those that exhibit simple ones. IRM acquisition and DC and AF demagnetization of IRMs of single particles were measured. We found that both types of grains exhibit similar bulk magnetic properties. The simple patterns reorganize with changing magnetization state while complicated patterns apparently remain constant. We suggest that the remanent magnetization of grains with complicated patterns is carried by the bulk of the particle within which a more simple domain structure controls magnetic behavior.

Domain models of eddy current loss due to normal magnetization in slightly misoriented

In Goss-oriented SiFe laminations, regions exist with a significant normal magnetization component arising from dip misorientation of the crystallites. It has recently been suggested by Imamura and co-workers that this normal magnetization can make a major contribution P_{\perp} to the eddy current losses incurred during cyclic magnetization along the texture axis. P_{\perp} is calculated for three distinct domain models of the magnetization process in laminar crystallites with modest dip misorientation. Contrary to the Imamura work, P_{\perp} is found to be practically negligible for a simple slab domain structure without closure domains. This is because the normal demagnetizing field restricts normal induction to the neighborhood of the domain walls and ensures that its volume average is practically zero. In a second model monotonic reversal of normal magnetization in closure domain structures is also shown to give rise to rather low normal loss P_{\perp} . A third model concerns how closure domains may interact with the major boundaries between slab domains and be swept along with them. Quite substantial losses P_{\perp} are predicted if all closure domains in a zone extending a distance rather greater than the sheet thickness either side of the major domain wall are displaced in this way. However, even this mechanism can explain only a small part of the marked increase in eddy loss with dip misorientation reported, and it is concluded that normal flux is probably not primarily responsible.

Magnetic domains in construction steel

The magnetic domain structure in constructional steel has been studied using a ferrofluid technique. We observed domains of four types which have been described and classified. A correlation is observed between the type of domain structure and grain size. For a simple antiparallel domain structure, a relationship exists between the grain size and domain wall spacing. The coefficient characterizing the magnetic interaction between grains is suggested, and a model is proposed which gives a linear relation between sqrt (domain length) and domain wall spacing. This model gives us a reasonable agreement with experiment and is compared with the results obtained using different models. The size of a single-domain grain was also estimated using the suggested model.

Magnetic domain structures of elastically and plastically deformed iron whiskers

Iron whiskers have a simple domain structure, a Landau structure. In the compression zone of a bent-iron whisker a characteristic change of the domain structure can be observed. Some special structures of bent-iron whiskers in different magnetic fields will be discussed.

Ferromagnetic resonance in periodic domain structures

We have recalculated the Smit and Beljers FMR mode frequencies for thin multi-domain magnetic platelets (disks) with uniaxial magnetocrystalline anisotropy K taking the finite aspect ratio of the domains into account. The magnetic anisotropy axis (z-axis) was taken to be perpendicular to the disk plane; the external magnetic field H was applied in the disk plane. The demagnetization energy coefficients of the periodic magnetic structures were found by the method of Kaczér and Murtinová. Below magnetic saturation the normalized FMR frequencies are: (a) for stripe domain arrays with H normal to the walls, Ω2+= (1−p)(1+2r−2p)−h2, Ω2−= (1−p)2−h2; (b) for bubble domain arrays, Ω2+= (1−p)(1+r−3p/2)−(1−r−p/2)(1−p)−1h2, Ω2−= (1+r−3p/2)[1−p−(1−p)−1h2], with HA=2K/M, Ω=ω/γHA,h=H/HA, r=2πM/HA and p=NzzM/HA. As the domain aspect (width/height) ratio tends toward zero, p→0 and the Ω2+, − expressions reduce respectively to (a) the stripe resonance expressions given by Smit and Beljers, (b) the first two bubble resonance expressions found in Kaczér and Gemperle. Our attempts to correlate these results with published experimental data are inconclusive; often the samples were too thick to support simple domain structures or relevant information was not provided.

Static neutron depolarization measurements of ferromagnetic domain structures in a FeSi picture frame crystal

The simple domain structure of a FeSi picture frame crystal (3.5 wt.% Si) has been investigated by means of the neutron depolarization technique. This technique is based on a three-dimensional analysis of the polarization of a polarized neutron beam after transmission through the specimen. The influence of the domain walls and the stray fields around the crystal on the various neutron polarization directions is discussed. By changing the neutron path through the crystal, the spontaneous magnetic induction has been obtained: B s = 2.1 Vs/m 2. The results of these experiments will be used in time-dependent neutron depolarization measurements.

Magnetization jumps in simple domain structures

We recorded magnetization jumps during the very slow motion of Bloch walls. Complex and negative jumps are observed and can be reproduced by analog simulation of Preisach grains. Magnetostatic couplings arise from wall bending and allow changes of configuration.

Frequency spectrum of the Barkhausen noise of a moving 180° domain wall

The simple domain structure of frame-type single crystals of silicon-iron allows the controlled movement of a 180° domain wall. If a constant mean wall velocity is impressed by an electronic control circuit, the field necessary to move the wall uniformly can be measured as a function of the wall position and yields most directly information about the force exerted by the crystal defects during the irreversible wall displacement. The frequency spectrum of the noisy driving field is measured and is interpreted in terms of the fluctuating interaction forces. Preliminary experimental data are communicated.

Theory of eddy current losses in finite width sheet exhibiting simple bar-like domain structures

In the present paper we outline the analysis and present the analytical expressions for the eddy current losses for the case of 'N' domains where 'N' may be any integer. The only assumptions made in this analysis are: (1) constant conductivity; (2) infinite length in the direction of magnetization; and (3) sinusoidal motion of domain walls for sinusoidal application of field. For various values of 'N' the losses computed from these expressions are compared to those predicted by the Pry and Bean model. When N \rightarrow \infin, W (width of crystal) \rightarrow \infin and for a constant finite domain size our model reduces to that of Pry and Bean, and for N = 2 we obtain Agarwal and Rabins results. However, these limits are never realized in real materials, and it is shown that for realistic domain width to sheet thickness ratios, the losses per unit volume computed from the model presented here are significantly lower than those predicted from the Pry and Bean model.

Magnetic domain properties of FeBO3

The magnetic domain structures of regularly shaped samples of FeBO3 have been studied using the Faraday effect. Simple strip domain structures, induced by magnetostriction, were used to determine domain wall widths and domain wall mobility. A comparison of measured and calculated domain wall widths reveals a disparity of two orders of magnitude. This is explained in terms of a complex wall structure at the intersection of Néel and Bloch walls. The sources of large scatter obtained in the mobility results are discussed, and an alternative method of measurement is suggested. It is shown that the relaxation mechanism present in the mobility measurements is not that producing the ferromagnetic resonance linewidth.

Polarized neutron techniques for the observation of ferromagnetic domains

Simple domain structures were observed in iron-silicon and cobalt-iron single crystals by three techniques using polarized neutrons. The first method involves scanning the specimen with a fine beam and measuring the depolarization suffered by the beam after transmission: it can only detect regions where the magnetization direction deviates from the direction of polarization of the beam, and cannot differentiate domains with antiparallel magnetization. The second method, based on the determination of the ratio of the Bragg-diffracted intensities when the polarization of a fine beam is reversed, provides, when the specimen is scanned, a map of the domains. The third technique, polarized neutron diffraction topography, provides photographs of the domain structure. The possibilities of these techniques for the observation of domains within bulk specimens are discussed.

Magnetization processes in iron whiskers with the landau domain structure

The dependence of the magnetic properties of iron whiskers upon field, time, and temperature have been determined experimentally using transformer circuits with whiskers as cores. A procedure for obtaining, recognizing, and maintaining the simple Landau domain structure has been found. A mathematical model has been developed which adequately describes most of the experimental observations. Some applications of the understanding gained are mentioned.

Measurement of domain wall mobility in GdIG

The promise of memory and logic applications for magnetic bubble domains has heightened the general interest in the occurrence and behavior of cylindrical domains in various materials. A train of short magnetic field pulses transforms the usual demagnetized snakelike domain pattern into a minimum-energy circular domain pattern which is stable with no dc bias field. This work maps the limits on field pulse width and height for producing the array. Domain wall mobility studies have also been made making use of the simple domain structure. The mobility studies suggest that there are regions of the sample where the local mobility is as much as ten times the average value. This leads to a simple model for the formation of the bubble array from the labyrinth structure, involving the “pinching off” of the snakes. Similar experiments on orthoferrite having very uniform properties fail to produce bubble domains, tending to support the model. Detailed results are presented.

Influence of coercive force on iron losses at low frequencies

Previous authors have calculated low-frequency eddy-current losses in bars and thin sheets assuming a simple domain structure of plane parallel walls. Use is made of these earlier results to derive a wall equation which includes coercive-force terms, attention being concentrated on the case of large wall excursions.From a comparison of calculated loss curves with previously published experimental work on oriented silicon iron, it is considered that the appropriate representation of coercive force is by a constant term, analogous to dry friction. This suggests that for the simple domain structure considered the hysteresis component of total loss per cycle is independent of frequency for any given peak flux density. Attention is paid to the effect on losses of varying waveshapes of B and H.Differences between practical domain structures and the idealised case are used to explain observed differences between the loss curves, and the conclusion is drawn that in practice the hysteresis loss is likely to be a function of frequency as well as of flux density.

Hysteresis Loops associated with a Simple Domain Structure

The complex domain structures existing in most ferromagnetic specimens prevent precise information about individual domain processes from being obtained from technical magnetization curves. Experiments on ring specimens of a magnetically annealed Perminvar-type alloy show that reversal of magnetization in such specimens involves only one 180° domain wall. Rings of varying external to internal diameter ratio were used, and the hysteresis loops of all specimens could be explained using a simple theoretical model. All specimens except those whose hysteresis loops were controlled by nucleation processes had the same coercive field, 0.09 oersted. This field gave a direct measure of the impedance to motion of an isolated 180° wall. The experiments also show that the use of a specimen with large external to internal diameter ratio effectively reduces the slope of the sides of the measured (B, H) loop; a close approach to a rectangular loop is possible only in specimens with small radial width. The effects of nucleation are evident in all of the loops, and in the case of the specimens with the smallest radial width, the loop shapes are controlled entirely by nucleation.

Studies of the Propagation Velocity of a Ferromagnetic Domain Boundary

Experimental results are given on the velocity of propagation of a single domain boundary in a crystal of silicon iron with a simple domain structure. In weak applied magnetic fields (\ensuremath{\sim}0.003 oersted) the velocity is given by a relation of the form $v=G(H\ensuremath{-}{H}_{0})$, where $G$ is a constant \ensuremath{\sim}4 cm/sec./oersted in this crystal, and ${H}_{0}\ensuremath{\cong}0.003$ oersted is the starting field. Calculation of the eddy current losses accompanying the motion of a plane boundary gives a theoretical expression for $G$ in good agreement with experimental values; the predicted linear dependence on the resistivity was approximately verified by measurements at 78\ifmmode^\circ\else\textdegree\fi{}, 194\ifmmode^\circ\else\textdegree\fi{}, and 293\ifmmode^\circ\else\textdegree\fi{}K. In stronger fields (g5 oersteds) there is evidence that the wall closes on itself, and the experimental velocity of collapse of the wall as deduced from flux changes agrees with the theoretical result based on a model of eddy current losses accompanying a collapsing cylindrical boundary. The results have a bearing on the well-known eddy current anomaly, namely, the fact that the total loss in a ferromagnetic material undergoing a.c. magnetization is often two or three times larger than the eddy-current and hysteresis losses calculated in the usual way assuming a spatially uniform and isotropic classical permeability.