Sidewise Motion Research Articles

Equivalent circuit analysis of a ferroelectric-photoconductor memory device

An analysis of an equivalent circuit representing a ferroelectric photoconductor memory device has been performed. The purpose of this work is to provide a basis for describing the transient switching characteristics of the ferroelectric-photoconductor memory element. Two models describing the polarization reversal in the ferroelectric have been investigated. The first model assumes that the polarization charge is a nonlinear function of the voltage that is applied to the ferroelectric. This represents a simple generalization of an RC model for which the ferroelectric is assumed to have a well defined threshold field and allows one to qualitatively describe the partial switching of the ferroelectric. The second model of polarization reversal assumes that domain wall motion is activated, described adequately by the sidewise motion of domains, and dependent upon the instantaneous electric field in the ferroelectric domain. Domain statistics involving domain overlap as well as polarization reversal condition...

Worm motion of domain walls in permalloy films

Abnormal wall motion in Permalloy films was observed by Kerr magneto-optic apparatus under hard-axis pulse drive with nanosecond rise time. Although this phenomenon is like creeping, the observed domain tip and sidewise motion is not monotonous, but looks like worm motion. Each domain expands and shrinks quasi-periodically, and the net magnetization along the easy direction is never constant. This phenomenon depends closely on the field strength and pulse width as well as the rise time of the drive pulse. The thickness range of the films observed was from 330 to 3500 Å, and for the films of thicknesses below 860 Å, worm motion never occurred. This suggests that the Bloch wall configuration is essential for such motion, and this was also verified by Bitter patterns. Worm motion was detected not only by Kerr magneto-optic apparatus, but also as a change of amplitude of transverse induced voltage measured with a strip line and sampling oscilloscope system. A theoretical velocity of walls during worm motion was estimated assuming a simple model for Bloch walls and compared with experimental results. The so-called creeping in the Bloch wall thickness region was found to be closely related to the worm motion of domain walls.

FURTHER EXPERIMENTS ON THE DISLOCATION INTERNAL FRICTION PEAKS WITH ANOMALOUS AMPLITUDE EFFECTIN Al-0.5% Cu ALLOY AND THE DISLOCATION KINK ATMOSPHERE MODEL

用低频扭摆进一步研究了在Al-0.5％Cu合金中观察到反常位错内耗峯的条件。结果指出,对于完全退火的试样来说,需要有适当的冷加工量,但是对于高温淬火试样则不需要冷加工。用位错气团模型定性地解释了过去所观测到的表现反常振幅效应的时效内耗峯和温度内耗峯;同时指出,简单的气团模型在作定量的解释时,遇到了下述的困难:(i)在测量内耗所用的交变应力的作用下,位错线所能够拖着气团移动的距离太短。(ii)为了气团能够被位错拖着移动,组成气团的溶质原子必须具有比通常大很多个数量级的扩散系数。(iii)根据气团模型,从理论上计算出来的使位错拖着气团以临界速度而移动时,所需的临界应力比观测值大几百倍。提出了溶质原子沿着位错弯结而扩散的气团模型,这个改进模型能够初步解决上述困难,并能定性地解释所观测的结果。这个模型所依据的基本假设是,要观测到反常内耗现象,位错线上必须具有一定数目的弯结。要得到这种弯结,可以对于退火试样进行适量的冷加工,或者把试样从高温淬火。带着弯结的位错线能够通过弯结的沿边运动而实现垂直于位错线方向的移动。可以假定,气团只在弯结两端的直位错段处形成,在弯结本身上并不形成气团。在弯结的沿边振动的过程中,聚集在弯结两端的溶质原子可以沿着位错管道进行来回的短程扩散。已知沿着位错管道的扩散具有比在正常晶体点阵中扩散时大得多的扩散系数。

Switching Transient in NaNO2

The switching transient in NaNO2 was observed in a temperature range between about 100°C and the Curie temperature and in an applied electric field range up to 7 kv/cm. The shape of the switching transient depended remarkably on temperature; in the immediate neighborhood of the Curie temperature it was asymmetric, and it approached to a symmetric one as temperature decreased. Judged by Fatuzzo's theoretical consideration, the nucleation density would increase abruptly in the neighborhood of the Curie temperature and in the low temperature region the sidewise motion of the domain wall would be predominant. The field dependence of the switching transient showed only a slight change.

Some New Thin-Film Shift Register Designs

Thin-film shift registers have been designed which utilize smooth controlled domain wall motion that occurs in tapered-edge magnetic films. Films used are long and narrow with an easy axis parallel to the short dimension. Information in the form of a sequence of domains of reversed magnetization is introduced serially at one end of an initially saturated film and propagated along the film by sidewise motion of the domain boundaries. Two shift registers are described which differ in the method of bringing the domain walls to predetermined positions during the shifting sequence. One method, denoted as graded coercive force, utilizes a pattern of local, rapid variations in the wall motion coercive force and a time sequence of uniformly applied drive fields to correctly position the domain walls at specific locations. The other method uses the nonuniform drive fields produced by a set of specially shaped conductors to step domains along a film of uniform wall motion coercive force. At present, the operating principles of graded coercive force devices have been verified and working models of shift registers utilizing nonuniform drive fields have been operated.

Etched Structures Dependent on Sidewise Motion of 180° Domains in BaTiO3

Sidewise motion of 180° domains in BaTiO3 single crystals during electrical poling with a wet electrode technique results in etch pit patterns strikingly similar to dislocation patterns in other crystals. The etching behavior of the pits is also consistent with that of small 180° domains in this material. Very small inclusions are also revealed in a poled and etched crystal as small round 180° domains representing regions which could not be reversed by the electric field. It is suggested that dislocations in tetragonal BaTiO3, may also be revealed in this manner. The origin of the small circular 180° domains is revealed by a photomicrograph of the “hanging up” of a moving 180° domain wall as it encounters defects during sidewise motion through the crystal. Based on this photomicrograph a wall energy calculation was made for the 180’domain in a BaTiO3 single crystal in which the sidewise motion of the wall is treated as a surface tension phenomenon. Good agreement with the accepted value of 1.4 ergs per cm2 was obtained if a correction was made for the potential drop through the material of lower dielectric constant used in the poling process.

Nucleation and Growth of Ferroelectric Domains in BaTiO3 at Fields from 2 to 450 kV/cm

The nucleation and movement of 180° domain walls in BaTiO3 crystals with salt-water electrodes has been observed directly by partial switching and repeated differential etching at applied fields from 2 to 450 kV/cm. Most of the polarization was found to be reversed by sidewise growth of new domains at these fields, as it is at lower fields, but the sidewise wall velocities are higher, as high as 105 cm/sec. The nuclei are originally circular cylinders, becoming squared up by sidewise growth whose lowest velocity is along the 100 crystal axis. The sidewise wall velocity and the nucleation rate each vary as E1.4, thereby causing the known E−1.4 variation of ts. The nucleation rate dependence is not understood, but the wall-velocity dependence agrees strikingly with a previously uncalculated prediction of the Miller-Weinreich theory. This indicates that, at both high and low applied fields, the apparent sidewise motion of 180° domain walls is due to the nucleation and forward growth of knife-shaped steps on the previously existing wall.

Magnetic Films: Nucleation, Wall Motion, and Domain Morphology

Nucleation fields for the reversal of magnetization in thin iron-nickel films were experimentally measured. The reversal was observed by the Kerr magneto-optical effect. Different regions or types of imperfections were observed at which lower nucleation fields are required than for the more perfect regions. Small regions of study in the ``interior'' of the film were localized by using an inhomogeneous field a millimeter or less in extension. Nuclei formed reproducibly about a center, with a statistical probability of formation which depended on the pulse length and field strength. A mode value of nucleation can be associated with a given center. The average of the mode values for different centers increased somewhat with film thickness, and showed a marked dependence upon composition, with a minimum value for films containing 80–85% nickel. Repeated pulsing with fields smaller than those required for nucleation increased the size of nuclei, while maintaining the same lenticular shape, to limiting dimensions which increased with film thickness. At higher fields, wall motion was observed in detail for two types of motion: (1) the tip of the domain was displaced along the easy axis with an axial or ``endwise'' extension; (2) the ``180° wall'' was displaced along the hard axis with a normal or ``sidewise'' extension. Endwise extension takes place at lower fields than sidewise extension. Evidence was obtained to indicate that an energy barrier exists for sidewise motion, e.g., repeated 1.5-μsec pulses caused no motion, whereas a single 20-μsec pulse did. With very narrow drive wires or with thick films, additional nucleation took place instead of ``sidewise'' motion of the wall; otherwise, domains could be enlarged at will. Some films were produced which required larger fields to ``erase'' or contract the domain lengthwise than for tip extension. The instabilities and general morphology of the domains as they depend on composition, film thickness, distance of extension of the inhomogeneous field along the easy axis, and the magnitude of the drive field were studied. Certain configurations led to a morphology of many small nuclei, which eventually were dense enough to join into a single domain; other configurations showed domain growth by wall motion and a large domain formed from very few nuclei. Very small nuclei were generally unstable, disappearing in a short time after formation. The smallest stable nucleus observed was about 0.25 mm×0.04 mm. The transition in behavior between 1.0- and 0.5-μsec pulses stresses the importance of multiple-nucleation processes in the nonuniform rotation region. The finescale observations on fields for nucleation and wall motion make possible comparisons with the processes taking place when the complete specimen is switched in a B-H loop tester.

Motion of 180° Domain Walls in BaTiO3 under the Application of a Train of Voltage Pulses

A study has been made of the sidewise motion of 180° domain walls in single-crystal BaTiO3 under the application of a train of voltage pulses. Measurements of the sidewise wall velocity as a function of the pulse amplitude, pulse width, and pulse repetition rate can be explained in terms of a surface layer model recently proposed for BaTiO3. These data constitute the first experimental verification of some of the important phenomena consequent on the model. This model assumes that a surface charge density of 2Ps, where Ps is the spontaneous polarization, is deposited immediately behind an advancing 180° domain boundary on the interface between the bulk ferroelectric material and the anomalous surface layer. This charge distribution gives rise to an electric field Eb′ in the bulk of the material with a component opposite in direction to the field applied to move the wall. It is found that relaxation of Eb′ begins in about 0.3 msec and continues for times in excess of 1 sec. This relaxation is not due to a simple, single time-constant, mechanism. Any fast relaxation, if present, must take place in times less than 1 μsec. After a 180° wall is at rest sufficiently long so that relaxation of Eb′ has occurred, application of an external applied field results in a wall velocity which depends on the magnitude of the wall displacement. In particular, the wall velocity decreases (due to Eb′ which increases) with increasing wall displacement. Analyses of the data show that the lateral or sidewise range of the field from the elements of charge which give rise to Eb′ is of the order of 2000 A so that once the wall has moved this distance, the effect of Eb′ at the wall, and hence the wall velocity, becomes constant. With thin crystals in the absence of an external applied field, Eb′ gives rise to wall displacements of the order of 100 A in a direction opposite to that of the wall motion which produced Eb′. The decrease in wall velocity observed when the wall displacement per pulse is of the order of a unit cell is consistent with a nucleation-controlled mechanism proposed earlier for the wall motion. Pulse data on crystals with different impurity concentrations and electrode materials show that the relaxation of Eb′ and the lateral range r, and hence the surface layers inferred from these data, are not markedly dependent on these parameters. Other data on the dc wall velocity indicate that for a velocity of 10−3 cm/sec, the potential drop across the surface layer is 1.0±0.1 v, and that it is independent of the crystal dopings and the electrode materials tested. These data indicate that the average field in the bulk required for a given wall velocity is not a constant independent of the type of electrode or the impurity concentration. The approximate constancy of the measured characteristics of the surface layers makes the dependence of the wall velocity on the impurity content and the electrode material difficult to explain in terms of the model considered.

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.”

Motion of 180° Domain Walls in Metal Electroded Barium Titanate Crystals as a Function of Electric Field and Sample Thickness

The domain dynamics of polarization reversal in metal electroded BaTiO3 single crystals have not been adequately described in the literature. The present paper contains quantitative measurements of the velocity of the sidewise motion of 180° domain-walls in BaTiO3 crystals, most of which were electroded with 200-A thick films of Au. The wall velocity has been measured as a function of several variables including the applied electric field, the crystal thickness and the impurity content added to the crystal growth melts. The wall velocity as a function of the field E is described by v∞ exp (−δ/E) where δ and v∞ are constants over several decades of velocity. The quantities δ and v∞ are the activation field and extrapolated wall velocity for E=∞, respectively. This field dependence of the wall velocity is the same as that reported previously for liquid electroded specimens. The thickness dependence of the wall velocity, which is through δ, is very pronounced and similar to that observed in measurements of other variables under different experimental conditions. The present data are explained in terms of a surface layer estimated to be of the order of 100-A thick. It is suggested that high fields within the surface layer may give rise to electron field emission and the electroluminescence which is observed during polarization reversal. Effects on the wall motion which persist for times of the order of minutes are ascribed to dielectric relaxation phenomena. The observed dependence of the wall motion on the impurity content of the cyrstal, and several other parameters, may result from changes in the characteristics of the surface layer.

Mechanism for the Sidewise Motion of 180° Domain Walls in Barium Titanate

Mechanism for the Sidewise Motion of 180° Domain Walls in Barium Titanate

Domain Formation and Domain Wall Motions in Ferroelectric BaTiO3Single Crystals

The nucleation and growth of ferroelectric domains in barium titanate have been studied as a function of applied electric field and temperature. The optical and electrical measurements were made on thin single-crystal plates normal to $c$, the polar direction. When the electric field applied along this direction is reversed, new domains with opposite polarization are formed. The manner of growth of these domains is very different from that of domain growth in ferromagnetic materials. The sidewise motion of the 180\ifmmode^\circ\else\textdegree\fi{} side walls (walls between domains with antiparallel polarization) which is common in ferromagnetic crystals is almost never found in barium titanate. Instead its polarization is changed by the formation of very many new anti-parallel domains which are extremely thin (${10}^{\ensuremath{-}4}$ cm) and appear to grow only in the forward direction. The explanation of this behavior is found in the weak coupling between the dipoles perpendicular to the dipole direction. The wall thickness is small, of the order of one to a few lattice constants; the wall energy in BaTi${\mathrm{O}}_{3}$ is of the order of 10 erg/${\mathrm{cm}}^{2}$. Electrical pulsing experiments substantiate the optical observations very clearly. Pulsing the samples at different temperatures shows that the nucleation rate of new domains is accelerated at elevated temperatures. Furthermore, the growth of the new domains is faster at higher temperatures. Experimental results are presented showing how the switching current and the switching time depend on applied electrical field, on temperature, and on the size of the sample.