Straight Domain Research Articles

Dynamic behavior of isolated straight stripe domain in rare earth iron garnet films

The dynamic behavior of an isolated straight stripe domain is reported in garnet films with relatively low damping. In the low drive field region, the translation velocity increases linearly with drive field, then it breaks down over a peak velocity followed by repeated increase and decrease of the velocity with increasing drive field. The peak velocity and the critical field for velocity breakdown are increased by a static in-plane field applied parallel to the walls of stripe domain, while they are scarcely influenced by an in-plane field applied perpendicular to them. In case of ion-implanted film, the peak velocity as well as the critical field depend on the direction of the magnetization within the walls. These experimental results are interpreted quantitatively by a model in which the nucleation, the propagation and the punch-through of the horizontal Bloch lines are considered.

Measurement of magnetic potential distribution and wall velocity in amorphous films

Rare-earth transition metal amorphous thin films which have uniaxial magnetic anisotropy perpendicular to the film plane were prepared by rf-sputtering or thermal evaporation. It was found that these amorphous magnetic films have a large extraordinary Hall effect. We measured the surface potential distribution for various domain patterns in the films. The correlation between the surface potential distribution and the shape of domain pattern was observed. We also measured the relation between the Hall voltage and the position of straight domain wall. From this measurement, we confirmed that the geometry of the element (the ratio of the length L to the width W) affects the positional dependence of Hall voltage, and the sensitive region in the film with respect to the Hall electrodes. We measured the domain wall velocity in Gd-Co amorphous films. Indicial response of the straight domain wall in these films to the pulse magnetic field was obtained.

Domain wall dynamics near the compensation point in amorphous magnetic films

We have investigated the dynamics of an isolated straight domain wall near the compensation temperature in rare-earth transition metal amorphous magnetic films. Wall velocities up to 3.5 × 104cm/sec are observed for applied field up to 550 Oe. Nonlinear dependence of the wall velocity on drive field is observed. The wall mobility in low drive region is very sensitive to the temperature and/or to the coercive force of the film. In high drive region, remarkable transient behavior, that is, very high instantaneous velocity just after the onset of wall motion and velocity break down are detected. Some films have remarkable orthorhombic anisotropy, and in these films the domain wall velocity depends on the direction of the wall motion with respect to the in-plane easy axis of the film. Change of the wall velocity by Permalloy overlay is also observed.

Scratch-modified magnetic domain patterns in garnet films

If a loaded Al2O3 sphere is passed over SmGa and LuTb garnet crystalline films, the domain pattern is modified. The width of the changed pattern is proportional to the diameter of the zone of contact between the sphere and the garnet. The pattern depends on load: a herring-bone type is found at low loads, a parallel pattern at high loads. After a magnetic field has disturbed the pattern, a narrow region of straight domains is left, which persists unless the material is heated above 1100°C. The patterns are independent of the sign of the magnetostriction constants.

Magnetostatic energy of stripe domain patterns

The energy of an array of straight stripe magnetic domains, such as might be found in an epitaxial garnet (bubble) film, is examined theoretically by modifying and extending the results of Kooy and Enz. For a uniform pattern, the energy is conveniently expanded in a Taylor series, using variables which describe the relative widths of the stripe domains. The coefficients in the expansion are familiar transcendental functions of material and sample parameters. An immediate result is an expression for the linear susceptibility (to an applied field normal to the film plane) in terms of the sample thickness and zero-field domain width. The energies for non-uniform patterns, which are interpreted in terms of dispersion curves for waves of displacements of rigid walls from the zero-field positions, are calculated using two approaches. The results of a lattice dynamics model, in which the restoring forces are related to the expansion coefficients, are compared to the results of a model which uses an extension of Kooy and Enz’s result to general periodic domain patterns. The significant differences are attributed to the more accurate treatment by the second calculation of the long-range magnetostatic forces.

The dynamical behavior of magnetic domain walls and magnetic bubbles in single-, double-, and triple-layer garnet films

The dynamical behavior of straight magnetic domain walls and propagating magnetic bubbles in single-, double-, and triple-layer lanthanum gallium garnet films is reported. In the study of straight walls in the single-layer films, a good agreement is obtained between the observed and the calculated values of the domain-wall width parameter Δ, the derivative of the peak velocity to in-plane field at high in-plane fields, and the derivative of the saturation velocity to in-plane field at a moderate drive field and high in-plane fields H1. The saturation velocity (at H1=0) decreases with decreasing film thickness, which is in disagreement with theoretical predictions. A propagating bubble in a single-layer film exhibits an overshoot. In double- and triple-layer films, the observed and calculated Δ values disagree in most cases, and the straight wall and propagating bubble saturation velocities are significantly higher than in single-layer films. Overshoots and low-frequency oscillations are observed in the saturation regime of straight walls. The resulting high wall masses are attributed to stacking of horizontal Bloch lines on the film surface(s). From the measurements in in-plane fields, we conclude that the saturation velocity and the peak velocity in a double- and a triple-layer film depend on the polarity of the in-plane field, which is always perpendicular to the straight wall. It is found that the saturation region in double- and triple-layer films can be subdivided in three parts. This is explained qualitatively, and a calculation is made of the saturation velocity in double- and triple-layer films. This calculation shows good agreement with experimental results.

Wall velocity in garnet films at high drive fields

We measured velocities of an isolated straight domain wall at drive fields up to 100 Oe in the materials (YLa) 3 (FeGa) 5 O 12 and (YBi) 3 (FeGa) 5 O 12 . These measurements were performed at in-plane fields up to 200 Oe. When the drive field is increased up to 100 Oe we find that at non-zero in-plane fields the velocity rises from the constant saturation velocity at the lower drives to a higher value. The increase can be as much as a factor of five and velocities up to 300 m-s-1are obtained. We investigated the wall motion by a well-known photometric method and by high-speed streak and framing mode photography. No significant disagreement was found between the results obtained by the two methods.

Observation and analysis of magnetic domain wall oscillations in Ga:YIG films

We report the observation of damped oscillations of a single straight magnetic domain wall stabilized by an externally applied field gradient in a Ga-YIG film (Y2.9La0.1Fe3.8Ga1.2O12). The measurements are performed at various field gradients, in-plane fields, and wall drive fields. We analyzed the results using the Landau-Lifshitz-Slonczewski (LLS) theory and obtained the wall width parameter Δ≡ (A/Ku)1/2 = (0.89±0.15) ×10−5 cm and the corresponding wall mass m0≡ (2πγ2Δ)−1= (5.2±0.9) ×10−11 g cm−2, where A is the exchange constant, Ku is the uniaxial anisotropy constant, and γ is the gyromagnetic ratio of the material; the Gilbert damping constant α=0.005±0.001; and the reduced Landau-Lifshitz damping constant λ/γ2= (1.3±0.3) ×10−9 Oe2 s. The wall mass according to Döring as calculated from γ, A, and Ku is m0=[2πγ2(A/Ku)1/2]−1= (8.1±0.6) ×10−11 g cm−2 and is higher than the experimental value. The observed oscillations allowed an independent determination of the magnetization of the material (4.2±0.8 G) in agreement with a direct measurement (4.8±0.5 G). In an applied in-plane field of 262 Oe the peak velocity was 530 m s−1. This value is lower by a factor of 1.6 compared to the peak velocity predicted from the LLS theory. From an observed asymmetry in the dependence of the wall oscillation frequency on the applied in-plane field we deduced that at the domain wall an effective in-plane field of 23±6 Oe is present, which is in the direction of the stray field at the film-air interface. A model of a film having two layers is proposed to explain this field. At a low in-plane field we observed a wall oscillation with a low frequency, depending on the drive field amplitude. It is not excluded that this slow oscillation is due to a wall containing Bloch lines.

A simple method to determine magnetic field gradients

The position of a straight domain wall in a magnetic field gradient in a narrow bar of magnetically uniaxial material is connected with the magnitude of the field gradient. The corresponding relationship is derived. It allows one to determine the field gradient. from a visual measurement of the coordinate of a domain wall and the known parameters of the platelet.

Interaction of domain walls with localized stress fields in magnetostrictive films

The interaction of magnetic bubble domains with overlying patterned metallizations is described in terms of a model in which local stress fields from the metal edges perturb the energy of domain walls through inverse magnetostriction. Examined in detail is the case in which a straight wall passes under the edge of a metal film deposited in either tension or compression. Using a simple form for the stress field generated at such a boundary, we show that the domain-wall energy is substantially perturbed in the immediate vicinity of the edge. This gives rise to either an attractive or repulsive interaction, depending on the signs of the stress and of the magnetostriction coefficients. The predictions of the model are examined by observing experimentally the interaction of straight domain walls and bubbles with metal stripes under compression. Comparison of the predicted and observed forces required to pull the domain walls away from the metal edges verifies the model calculations over almost two decades of metal stress. The use of a space layer to reduce the stress in the magnetic material is found to significantly lower the bubble-metallization interaction, thereby permitting improved device performance.

Domain wall motion in Ga: YIG films

The motion of an isolated straight magnetic domain wall established in a Ga : YIG film (Y2.9La0.1Fe3.8Ga1.2O12) by a gradient field of 2.4 kOe/cm and driven by a homogeneous pulse field Ho is studied experimentally. The measurements are performed at different pulse fields in the presence of a static field of 400 Oe in the plane of the film. At low pulse fields (Ho ≤4.1 Oe), the reduced Landau-Lifshitz damping constant and the wall mobility are obtained λ/γ2 = (2.9 ± 1.2) × 10−9 Oe2s and μ=(1.4±0.4)×104 cm/s/Oe, respectively, from the fit with numerical solutions of the Landau-Lifshitz-Slonczewski (LLS) equations of wall motion. At pulse fields Ho >4.1 Oe, it is found that the wall velocity reduces within a few nanoseconds to a constant value of 110 m/s when a ``critical'' velocity of about 400 m/s is reached. The critical velocity is lower than the peak wall velocity from the LLS formalism by a factor of 2.4 and is reached after 15–40 ns of wall motion, depending on the pulse field.

Wave propagation along domain walls in magnetic films

It is shown by theoretical analysis that domain walls can support two different types of denoted as interface waves and displacement The magnetostatic interface are similar in character to magnetostatic surface waves. The wall displacement are analogous to displacement on strings and to capillary on the surface of liquids, Dispersion relations are derived for both types of waves. The displacement are approximately dispersion free at high wavenumbers. At low wavenumbers their dispersion diagram reflects the incipient instability of the straight domain wall against sinusoidal displacement, which occurs as the field gradient is reduced.

Self-induced interaction of magnetic domains and bubbles with a neighboring current

It was recently pointed out that magnetic domains tend to move parallel with the current in a nearby conductor; the motion is due to Hall currents set up in the conductor by the domain field and is independent of any field gradients due to the unperturbed current. The magnitude of the force that produces this drift is here calculated for the cases of a single straight domain wall and of a circular magnetic bubble. The force is found to be strong enough to produce controlled motion of a magnetic bubble, provided that the magnetic material is optically flat and the current carriers in the conductor have a high mobility.

Influence of an in-plane magnetic field on the domain-wall velocity in Ga: YIG films

Results are reported of an investigation on the velocity of a single straight magnetic domain wall in a Ga:YIG film as a function of the drive field and of a static magnetic field applied perpendicular to the wall in the plane of the film. At all drive fields a substantial increase of the wall velocity was observed when the in-plane field was applied. At an in-plane field of about 400 Oe and at a rather low drive field (2.4 Oe above the coercive field) a maximum value in wall velocity of 270 ms <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> was observed. At higher drive fields the wall velocity decreased to a constant value of 110 ms <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> , independent of the drive field. This behavior can be explained by extending Slonczewski's theory of domain wall motion to the present case. From the observed wall mobility parameter we have calculated the reduced Landau-Lifshitz damping constant <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\lambda/\gamma^{2}</tex> ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3.7 \times 10^{-9}</tex> Oe <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> s). This value is near to the value obtained by Spencer and LeCraw from linewidth measurements in FMR on Ga:YIG spheres ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5 \times 10^{-10}</tex> Oe <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> s).

Formation of normal and hard bubbles by cutting strip domains

This paper describes a new method in which normal bubbles and hard bubbles having arbitrary values of collapse field within a range allowable for a given sample can be produced merely by cutting straight strip domains with single-pulse currents applied to a pair of parallel strip conductors. When cuts are made along the inner edges of the conductor strips, normal bubbles result, while hard bubbles result when cuts are made along the outer edges. The collapse field of hard bubbles thus produced depends upon the orientation of the original straight strip domains with respect to the conductors. Moreover, the "sense" of hard bubbles is uniquely determined by whether the straight strip domains are tilted to the right or left of the perpendicular to the conductors before pulsing. An attempt is made to interpret the experimental results in terms of a mechanism in which a pulse field "overdrives" a domain wall to produce Bloch lines.

Temperature Dependence of Magnetic Domains and Wall Structures

The high voltage Lorentz microscopy was successfully used to observe changes with temperature; of domain structures and metallurgical structures in an iron film set on the hot stage combined with a goniometer. The microscope used was the JEM-1000 EM which was operated with the objective lens current cut off to eliminate the magnetic field in the specimen position. Single crystal films with an (001) plane were prepared by the epitaxial growth of evaporated iron on a cleaved (001) plane of a rocksalt substrate. They had a uniform thickness from 1000 to 7000 Å.The figure shows the temperature dependence of magnetic domain structure with its corresponding deflection pattern and metallurgical structure observed in a 4500 Å iron film. In general, with increase of temperature, the straight domain walls decrease in their width (at 400°C), curve in an iregular shape (600°C) and then vanish (790°C). The ripple structures with cross-tie walls are observed below the Curie temperature.

Domain structures in magnetic materials with high crystalline anisotropy

Some of the factors which affect domain structures in magnetic materials with high magnetocrystalline anisotropy include crystal perfection, nonmagnetic or weakly magnetic inclusions, and the nature of grain boundaries. In whisker-like barium ferrite crystals about 3 μm in thickness straight (180°) domain walls were observed in the basal plane. Reverse domains did not nucleate at fields of over -5000 Oe after first saturating the crystals in a positive magnetic field. In less perfect crystal platelets of about the same thickness the domain structures form in what may be described as a convoluted pattern, and after saturating in a positive magnetic field, reverse domains nucleate in positive fields of from +100 to +1000 Oe. An analysis of the convoluted patterns has shown disclination structures of several types. The influence of internal defects as well as the effect of surfaces, nonmagnetic inclusions, and grain boundaries on domain structures in magnetic materials with high crystalline anisotropy are described and discussed.

Instability of an Isolated Straight Magnetic Domain Wall

An isolated straight magnetic domain wall along the y axis results when a thin slab of magnetic material in the xy plane is exposed to a nonuniform z axis magnetic field of the form Hz=βx, if β is sufficiently large. The behavior of this magnetic system as β decreases is discussed. A magnetic energy calculation shows that sinusoidal deviations from the straight wall become energetically favorable at a critical value βc. The wavelength of this distortion at βc and βc are both expressed in terms of magnetic material properties. Experimental observations of this instability in YbFeO3 are given, and the magnetic parameters determined this way are in reasonable agreement with those obtained by using other methods. Effects of material inhomogeneieties are discussed, and the transition from the initially distorted straight wall to the demagnetized state of stripe domains is shown.

Propagation of Transverse Domain Walls in Thin NiFeCo Films

A new phenomenon of straight transverse domain walls has been observed in longitudinal propagation of walls in thin films. When the drive field is sufficiently large, the domain wall is observed to become nearly straight losing the jagged configuration typical of static transverse walls. If the drive field is rotated away from the longitudinal direction, the direction of propagation rotates the opposite way, but the wall remains straight. A model is suggested, relating the transverse component of external field near a skewed domain wall and the coherent rotation threshold in the material to the observed wall motion phenomena. The films were NiFeCo,1 nonmagnetostrictive, vacuum-evaporated on glass substrate, and 1000 to 3000 Å thick. The cobalt content was varied from 5% to 35%. The measured anisotropy, nucleation,1 and wall motion fields ranged, respectively, 6 to 40 Oe (Hk), 5 to 20 Oe (Hs), and 2 to 5 Oe (H0), the values in each case increasing with increasing cobalt content. Longitudinal domain wall velocities up to 5000 m/sec were observed. The velocity-drive field relation is strongly curved, lying between V=kH2 and V=kH3. The value of wall motion field (H0) does not appear to be directly related to the velocity-field curve, and H0 clearly does not act as subtraction from H.2 Wall velocity is sensitive to film thickness and composition, increasing with thickness and decreasing with increasing cobalt content.

Kinematic Theory of Ferroelectric Domain Growth

Sidewise motion of 180° wall in ferroelectric barium titanate is described, applying the kinematic wave theory developed by Lighthill-Witham. The rather peculiar shapes of the domain in growing and in shrinking processes, observed by Miller and Husimi, can be derived purely kinematically. 180° wall is described as an assembly of steps. Orientation of the wall is described by step density. There is a part of constant orientation that moves with a constant velocity, which is shown to be identical to the kinematic wave velocity. Round squares observed in the growing process and straight domain fronts in the shrinking process are fairly well explained as a result of propagation of kinematic waves, assuming a suitable functional relationship between the velocity and the density of the progressing steps. Discontinuity of wall orientation is interpreted as “kinematic shock wave.”