Experiments with Large Barkhausen Jumps1

K. Sixtus

§ 1. On Large Magnetization Jumps

In ferromagnetic substances, a large part of the change in induction during traversal of the hysteresis loop takes place in the form of Barkhausen jumps. Each such induction jump consists in an abrupt change in the direction of the induction vector in a small region of the substance, of volume about \(10^{-9}\ \text{cm}^3\), in the so-called Weiss region. As Forrer2 and especially Preisach3 have shown, by subjecting a specimen to elastic stresses, these jumps can be enlarged. In a substance with positive magnetostriction, by applying sufficiently large stresses, it is even possible to achieve that all remagnetization in the direction of stretching, i.e. the entire change of induction between positive and negative saturation, occurs by means of one single jump. The reason for such a change in the course of the induction change during magnetization—excluding reversible processes in favor of irreversible ones, and combining the latter into a single jump—is as follows: in the absence of external stresses, the preferential directions[^4] in an individual region are determined by the orienting action of the crystal energy[^5] and by disordered internal stresses. A sufficiently large stress applied from outside, however, forces all magnetization vectors, contrary to the influences just mentioned, to choose one definite preferential direction. In a substance with positive magnetostriction subjected to stretching, it coincides with the direction of the applied force, which thus becomes the easiest direction of magnetization. If the wire is saturated in the positive direction, then, as the field is decreased, the magnetization vector retains its axial position; the residual magnetization is equal to saturation, and only when a certain field strength in the negative direction is reached does the state of magnetization become unstable and the magnetization vector flip through \(180^\circ\). Thus in this case the hysteresis loop is rectangular. The field strength at which this flip occurs is usually called the coercive force. However, since here it has a special meaning, we shall call it the starting field \(H_S\).

The preliminary experiments that served as the starting point for further investigations were carried out on a strongly stretched wire possessing large internal stresses. In it, the limiting case of a rectangular loop is realized only with difficulty. Fig. 1 shows the hysteresis loop for such a wire—

of the wire (14% Ni — 86% Fe) under loads \(\sigma=0\) and \(\sigma=92\ \mathrm{kg/mm^2}\). Although the load \(\sigma=92\ \mathrm{kg/mm^2}\) lies only slightly below the yield point, it is still insufficient for the complete change of induction to occur in a single jump. Evidently, complete axiality of the easiest direction has not yet been attained here. On the contrary, for annealed soft permalloy wire (78.5% Ni — 21.5% Fe), in order to obtain a rectangular loop a load of \(\sigma=10\ \mathrm{kg/mm^2}\) is already sufficient, i.e. less than half the yield point.

Fig. 1. Hysteresis loops of hard wire of diameter \(0.38\ \mathrm{mm}\) (14% Ni — 86% Fe) under loads \(\sigma=0\) and \(\sigma=92\ \mathrm{kg/mm^2}\). The region of jumps is hatched.

Fig. 2. Hysteresis loops of soft permalloy wire of diameter \(0.38\ \mathrm{mm}\) under loads \(\sigma=0\) and \(\sigma=20\ \mathrm{kg/mm^2}\). The jump region is enclosed within the hatched boundaries.

In Fig. 2 the hysteresis loops are presented for \(\sigma=0\) and \(\sigma=20\ \mathrm{kg/mm^2}\). In analyzing Preisach’s experiments, Langmuir pointed out that it is very unlikely that remagnetization should occur at one and the same moment along the entire length of the wire. By analogy with similar processes, he suggested that remagnetization proceeds in the following way: at inhomogeneities existing in the wire, a nucleus of remagnetization may naturally form, which, under favorable conditions, will grow with finite velocity along the whole wire. The experiments undertaken by the author and Tonks to test Langmuir’s idea fully confirmed it. In addition, these experiments provided a number of further data on the nature of the reversal process. This article gives, in the main, a review of the work carried out in this direction at the General Electric Company³.

In the very first preliminary experiments an interesting result was obtained, namely: the main field, in which the whole wire is placed and which is necessary to obtain a jump of the magnetization vector, may be lower than the value \(H_S\). It is only necessary that, upon superposition of an additional local field at some point of the wire, the total field should reach the value of the starting field \(H_S\). In this case

instead of natural nuclei not subject to control, which caused reversal at the basic field reaching \(H_s\), we arbitrarily create an artificial nucleus which, at a certain field \(H\), begins to grow. The smallest value of the basic field at which the artificial nucleus can still cause reversal we shall call the critical field \(H_0\). By obtaining nuclei at different strengths of the basic field, it was possible to measure the propagation velocity of the magnetic wave issuing from the artificial nucleus as a function of the field strength over a wide range of fields from \(H_s\) to \(H_0\). We shall begin our discussion with this. Then we shall investigate the dependence of the characteristic fields \(H_s\) and \(H_0\), which may be regarded as observable—or, more precisely, as true coercive forces—on external influences. Finally, we shall study stationary regions of reversal, which we can obtain either by braking or by “freezing” the reversal wave, or by the short-time application of higher local fields. These experiments provide information on the magnetic boundary layers between spontaneous regions with magnetization of opposite directions.

§ 2. PROPAGATION OF MAGNETIZATION IN A WIRE

Fig. 3 gives a diagram of the apparatus on which the experiments were performed. The specimen, for the most part in the form of a wire and more rarely in the form of a ribbon, was placed under tension in a magnetizing coil 65 cm long, producing the main homogeneous field \(H\). At one of the ends of the main field, by means of a short coil, an additional field is produced. Then, for a certain ratio of the fields, a reversal wave arises there, and we can observe its motion along the wire. To measure the velocity of this motion, two coils are placed on the wire at a definite distance from one another; in them, as the wave passes, it induces a voltage pulse. The time interval between these pulses is measured by a tube circuit connected to the coils, using the ballistic method, and from this the velocity of the reversal wave is calculated. The experiments were carried out on wires of iron-nickel alloys of various composition with different mechanical and heat treatment. Here only the results obtained on hardened wire (\(14\%\ \mathrm{Ni} — 86\%\ \mathrm{Fe}\)) and on annealed permalloy wire (\(78.5\%\ \mathrm{Ni} — 21.5\%\ \mathrm{Fe}\)) are selected; their hysteresis loops are given in Figs. 1 and 2. The essential difference between the two

Fig. 3. Diagram of the apparatus for measuring the propagation velocity of reversal.

with the wires consists in the magnitude of the internal stresses; in this respect the specimens represent two limiting cases. The results of the velocity measurements are presented in Figs. 4 and 5. In both cases it is seen that, at all loads, the propagation velocity \(v\) increases with increasing main field. In the hard wire, the experiments with which we shall consider first, this increase is approximately linear (Fig. 4). For a given stress the \(v\)—\(H\) curves terminate on one side at the abscissa \(H_S\), since here

Fig. 4. Propagation velocity of remagnetization in a hard wire (see Fig. 1) and the dependence of \(H_0\) and \(H_S\) on the stresses \(\sigma\)

Fig. 5. Propagation velocity in a soft wire (see Fig. 2) and the dependence of \(H_0\) and \(H_S\) on the stresses \(\sigma\)

natural nuclei begin to form; on the other side they are extrapolated to zero velocity. The field \(H_0\), corresponding to \(v=0\), the so-called critical field, is therefore defined as the field at which a nucleus, once formed, propagates infinitely slowly. Consequently, the remagnetization wave cannot penetrate into that region of the wire in which the field strength is less than \(H_0\). As the load \(\sigma\) increases, the \(v\)—\(H\) curves shift approximately parallel toward weaker fields. This can be explained from the relation between \(H_0\) and \(\sigma\), which will be done in § 5. The dependence of the velocity on the main field for hard wires is well represented by the equation

\[ v = A(H - H_0). \tag{1} \]

Here the quantity \(A\) is fairly constant not only for the given wire and the given stress, but also for different stresses and for wires of different diameters; on the average it is equal to \(A = 250\ \mathrm{m\cdot sec^{-1}\cdot oersted^{-1}}\) for \(15\%\ \mathrm{Ni} — 85\%\ \mathrm{Fe}\).

In permalloy wire, on the contrary, the \(v—H\) curves approach parabolas (Fig. 5). Here, in contrast to hard wire, the \(v—H\) curves shift, with increasing load, toward higher fields, which will also be explained in § 5. The greatest velocity observed in permalloy wire was \(10^3\ \mathrm{m\cdot sec^{-1}}\). This velocity is the greatest, but nevertheless it is still considerably lower than the velocity of sound in metals \((\sim 5\cdot 10^3\ \mathrm{m\cdot sec^{-1}})\).

In hard wire of composition \(15\%\ \mathrm{Ni}—85\%\ \mathrm{Fe}\), the temperature dependence of the propagation velocity was measured. The curves in Fig. 6 were taken from high to low temperatures. Therefore they do not depend on the tempering effect and give a reversible temperature dependence. Both on the slope of the curves and on \(H_0\), temperature has only a small influence. The steepness of the curves increases slightly with increasing temperature, and \(H_0\) decreases only very little with increasing temperature. By contrast, in ordinary soft iron the coercive force between room temperature and \(300^\circ\) falls by almost \(25\%\). The different result obtained in our case is probably determined by the existence of a clearly expressed easiest direction of magnetization.

Fig. 6. Velocity curves at different temperatures for wire of alloy \(15\%\ \mathrm{Ni}—85\%\ \mathrm{Fe}\); \(\sigma = 77\ \mathrm{kg/mm^2}\)

§ 3. PENETRATION OF MAGNETIZATION INTO THE WIRE

Magnetization penetrates in the radial direction into the wire only gradually, with a finite velocity, just as it propagates along the wire. This penetration can best be traced by oscillographic recording of the change in flux

\[ \frac{d\Phi}{dt} \]

in a coil sliding along the wire during the passage of the wave. At a velocity \(v\) of \(10^4\ \mathrm{cm\cdot sec^{-1}}\), the voltage pulse in a coil \(1\ \mathrm{cm}\) long should have a duration of about \(10^{-4}\ \mathrm{sec}\), if one assumes instantaneous penetration to the axis of the wire and, in addition, a plane wave front. The experiment, on the contrary, gives for one definite case a pulse duration 100 times greater and, consequently, a length of the region of remagnetization of \(100\ \mathrm{cm}\). The explanation is that, owing to remagnetization, Foucault currents arise which screen the imposed main field from the middle of the wire and allow the remagnetization to penetrate into the wire only from the surface. If

we shall now, for simplification, neglect the thickness of the boundary layer between oppositely magnetized regions; then from the oscillograms one can obtain the shape of the boundary. By means of the equation \(x=vt\), where \(x\) is the distance of some transverse section from the leading edge of the wave, one can integrate the values of \(\dfrac{d\Phi}{dt}\) found from the oscillograms along the length and, in this way, obtain from the time dependence of the penetration the shape of the front of the remagnetization wave.

In Fig. 7, in addition to the time rise of the induction, there is also given a longitudinal section of the wire at the place of the boundary layer, which, under the assumptions made, has the shape of a funnel; the opening of the funnel is directed forward in the direction of propagation. The fact that the jump here is less than \(2 I_s\) (\(I_s\) is the saturation magnetization) makes it difficult to visualize the boundary surface. In Fig. 7 it is simply assumed that on the axis of the wire there is still a region which has not yet switched.

Fig. 7. Above: increase of the flux in a given section of the wire (time scale) and along the wire (length scale), according to oscillograph data. Below: longitudinal section of the front of the remagnetization wave. Wire of Fig. 1, \(\sigma = 92\ \mathrm{kg/mm^2}\).

A possible objection to the picture of the boundary surface just described will be discussed below. Under the assumption made, oppositely directed magnetization vectors abut against this surface; because of this it represents a surface with magnetic charges, which create a certain field. An approximate, simple calculation shows that the radial component of the field, which, unlike the axial component, can be determined by itself, is of the order of magnitude of 10 oersteds. One might suppose that fields of such magnitude disturb the strict axial character of the induction; however, this is not so. Measurements on a twisted wire (see § 5) showed that the permeability for fields perpendicular to the predominant direction is practically equal to unity, so that a field of 10 oersteds has no influence whatever on the magnetization. If this simple circumstance, which occurs in real cases, is not taken into account, we shall greatly complicate the calculation, which is what makes, for example, S. Koch’s theory\(^4\) unnecessarily complicated.

For the time being we have confined ourselves to the transmission of experimental data.

However, the retardation of the penetration of magnetization into the wire can also be calculated mathematically \[3\] under certain assumptions. First, one may assume that the reversal of magnetization at any point of the wire can occur only when the local field reaches the value \(H_0\). Second, we shall consider the field caused only by the eddy currents arising as a result of the reversals, and shall neglect the demagnetizing field and the energy of the boundary between differently magnetized regions.

Then, for the total time of penetration into a wire of radius \(a\), we obtain

\[ \delta t=\frac{4\pi^{2}a^{2}\Delta I}{\rho c^{2}(H-H_0)} =3.94\cdot 10^{-8}\,a^{2}\Delta I/\rho(H-H_0), \tag{2} \]

where \(\Delta I\) is the change of induction during the jump, and \(\rho\) is the specific resistance. For a ribbon of thickness \(2b\) we have

\[ \delta t=7.88\cdot 10^{-8}\,b^{2}\Delta I/\rho(H-H_0). \tag{3} \]

Comparison of the quantities calculated by these formulas with the time taken from the oscillograms gives, for the wire, when \(H-H_0\) is varied, a constant multiplier between the measured and calculated values, the measured times being greater than the calculated ones. This multiplier is the larger, the smaller the thickness of the wire. This shows that although formula (2) correctly reflects the dependence of \(\delta t\) on \(\Delta I\), \(\rho\), and \((H-H_0)\), the dependence on thickness predicted by it contradicts the observations. Experimentally, \(\delta t\) decreases linearly with decreasing radius, whereas the formula requires a quadratic dependence. In order to obtain agreement between the formula and experiment, instead of \(a^2\) one may substitute the quantity \(\alpha\cdot a\), where \(\alpha\), for a certain number of wires of different composition and thickness, is equal to \(0.35\) mm. Then, for those wires for which \(H_0\) lies between \(1.40\) and \(8.36\) oersted, the deviation of the calculated quantities from the measured ones is in most cases no more than 20%. Later measurements by Sixtus and Tonks, which have not yet been published, were carried out on very soft materials. At a wire radius \(a=0.19\) mm (wire I: \(78.5\%\) Ni—\(21.5\%\) Fe; \(H_0=0.07\) oersted; wire II: \(15\%\) Ni—\(85\%\) Fe, \(H_0=0.67\) oersted), the equation with \(a^2\) gives good agreement with experiment, but at \(a=0.065\) mm (wire III: \(78.5\%\) Ni—\(21.5\%\) Fe, \(H_0=0.12\) oersted) agreement can be achieved only by introducing \(\alpha=0.20\) mm. These new data in any case show that \(\alpha\) is not a constant and that the formula with \(a^2\), at such small thicknesses, satisfies experiment the better, the smaller the critical field in the wire under consideration.

A general formula for penetration can be established if, first of all, one takes into account the surface energy of the boundary, to which we shall return somewhat more closely at the end of the following paragraph.

§ 4. LENGTH OF THE BOUNDARY SURFACE

Despite the fact that in the question of propagation there still exist some ambiguities, in the last paragraph (§ 6) it will be shown that the quantity \(\delta t\) is in general explained by the effect of eddy currents. In the equation \(\lambda = v \cdot \delta t\), where \(\lambda\) is the length of the boundary surface, \(\delta t\) is the primary independent quantity. The question arises: is \(v\) or \(\lambda\) the other fundamental quantity? One may regard the velocity as the fundamental quantity. However, up to now it has not been possible to derive it from atomic properties (I. Waller’s investigations in this direction are mentioned by Bloch\(^5\)). With new investigations the length of the boundary surface has acquired significance. If this consideration is justified in fact and \(\lambda\) can be calculated from definite magnetic and energy relations, then it will no longer be necessary to regard the velocity of propagation as the fundamental quantity.

The boundary surface, near its moving boundary, produces a forward-moving field, which is added to the existing fundamental field. Steinberg\(^6\) put forward the hypothesis that, in translational motion of the boundary, such a \(\lambda\) is established that at the front end the total field just reaches the magnitude of the starting field \(H_S\). Thanks to the new investigations of Döring (see the following article), this hypothesis loses its plausibility. From this one may rather conclude that \(\lambda\) will be established so that the following relation is fulfilled: energy of the eddy currents \(+\) surface energy \(+\) demagnetizing energy \(= (H - H_0)\Delta I\). The corresponding calculation has not yet been carried out. Likewise, in an exact calculation of the penetration time, all three kinds of energy must be taken into account. Since only part of \((H - H_0)\Delta I\) is converted into eddy currents, the equation for the penetration time includes not \((H - H_0)\), but only a part of it, so that the calculated \(\delta t\) will become larger and will be in better agreement with experiment.

§ 5. CRITICAL FIELD AND STARTING FIELD

Tension. In the small graphs of Figs. 4 and 5 one can see how the critical field \(H_0\) (which will be dealt with first) depends on the magnitude of the applied load. In both cases, as the load increases, \(H_0\) at first falls rapidly and then more slowly, tending toward a certain limiting value which is reached in Fig. 5. The influence of the load thus differs essentially from the influence of internal stresses. It is known that distortions caused by working and impurities increase the coercive force. This is also clearly seen in both wires under investigation: the value of \(H_0\) is higher in the hardened wire, and considerably lower in the soft annealed wire. Precisely in permalloy, whose behavior was studied in detail by Preisach\(^7\), internal stresses, owing to the very small magnetostriction, can change very little; moreover, in these alloys the crystallographic magnetic energy is very small, which likewise

thereby, like the internal stresses, creating different preferred directions from region to region.

For a fuller clarification of the relation between \(H_0\) and \(\sigma\), Fig. 8 gives further curves obtained by Preisach for annealed permalloy. Here too \(H_0\) falls with increasing load \(\sigma\) to a certain residual value \(H_{0R}\), which is reached at \(\sigma \sim 5\ \mathrm{kg/mm^2}\). This load must exceed the magnitude of the internal stresses in order essentially to balance the latter and create a preferred direction everywhere along the axis of the wire. At higher \(\sigma\), \(H_0\) remains constant. In individual cases there was observed, it is true, a slight secondary rise of \(H_0\), which evidently was already due to plastic stresses in the wire and which we shall not consider further. Preisach also indicated the cause of the different behavior of hard wire. In this case the internal stresses are so large that we cannot establish one single preferred direction of magnetization even with the aid of stresses lying near the yield limit.

Fig. 8. Critical field \(H_0\) and starting field \(H_s\) as functions of the stress \(\sigma\) (permalloy, according to Preisach)

According to Bloch and Preisach, \(H_0\) splits into two parts. First, there is a residual value \(H_{0R}\), which exists also for a uniform preferred direction, and, second, an additional field \(H_{0z}\), which is different from zero in the case when the axis of the wire is not yet the direction of easiest magnetization throughout the entire wire.

\(H_{0R}\) is caused by local fluctuations of the lattice constant and is measured by the energy required for the reversal wave to overcome such an obstacle. In contrast, \(H_{0z}\) is measured by the work that must be performed against the energy of magnetic anisotropy and the magnetoelastic energy of the stresses of regions not yet oriented. In his work Preisach considers a model by means of which it is possible to describe the behavior not only of \(H_0\), but also of the residual magnetization and the permeability at residual magnetization.

In Figs. 4, 5, and 8, besides \(H_0\), the starting field \(H_s\) is also given for limiting cases of hard and soft wire. In the case of hard wire, \(H_s\) decreases with increasing tension in the same way as \(H_0\). In the case of soft wire, on the contrary, \(H_s\) continually increases with increasing \(\sigma\). From Fig. 8 it is seen that \(H_s\) reaches a value,

27 times larger than \(H_0\). Intermediate cases were also observed, when \(H_S\) first falls and then, beginning with a certain value of the tension, rises again. As will be shown in § 6, the magnitude of the starting fields is determined by the size of the remagnetization nuclei. We accept the fact of the existence of such nuclei, which are magnetized oppositely to the main part of the wire, without touching on the question of their origin, which is still unclear. Here we wish to note only that \((H_S-H_0)\) is a measure of the energy needed for spontaneous magnetization to occur by growth of the nucleus. It is probable that in the wire of Fig. 8 the natural nuclei at \(\sigma = 18\ \mathrm{kg/mm^2}\) are especially small, and therefore a very large energy is required for spontaneous growth to take place.

Torsion. Up to now we have dealt only with such cases in which, under tension, only one magnetic preferred direction arose, parallel to the axis of the wire. In this case this preferred direction always coincided with the applied field. However, a preferred direction can also be obtained at any angle up to \(45^\circ\) to the axis by not only stretching the wire but also twisting it. If we only twist, then the preferred direction will be at an angle of \(45^\circ\). The direction of the field can likewise be changed in any manner if, in addition to the longitudinal field, a circular field is also superposed by passing a current through the wire. Both the torsion and the circular field in the transverse section are, of course, not constant; both decrease from their greatest value at the surface of the wire to zero on its axis. In what follows we choose the sign (direction) for the elastic stresses and the magnetic field as shown in Fig. 9; when numerical values are denoted, the values at the surface of the wire are always meant.

Fig. 9. Critical field in a twisted wire with simultaneous switching on of the longitudinal \(H\) and circular \(H_t\) fields (wire of 15% Ni—85% Fe, length \(80\ \mathrm{cm}\)).

Preissach\(^2\) has already indicated that large jumps can be obtained in Fe—Ni wires by twisting. A study of the phenomena occurring in this case, especially of the behavior of the critical field, became possible later in the study of its dependence on the circular field\(^3\), III. Again a wire of diameter \(0.38\ \mathrm{mm}\) was taken, and its fields \(H_0\) were determined for various torsions and circular fields. In Fig. 9 each point represents the field on the surface of the wire, both in magnitude and in direction. For different twistings of the wire the values of \(H_0\) lie at pri-

proportionally on straight lines and on lines parallel to one another, which form an angle of \(45^\circ\) with the axes. Consequently, the field components in the direction normal to the lines, for each point of one and the same line, are approximately the same; they give the true critical field for the given stress. The direction of this normal corresponds, evidently, to the magnetically preferential direction. Thus we see that only the component of the field along the easiest direction produces jumps, even if the component perpendicular to it is much larger. The same result is obtained on stretched wires, with longitudinal and circular fields. A circular field four times greater than the critical field produced no effect on the latter.

If one compares the stresses arising under torsion and their influence on the critical field with the case of pure tension, it turns out that one and the same value \(H_0\) under torsion is attained at smaller stresses than under tension. The question of how far this is due to simultaneously arising compressive stresses or to the existing preferential orientation of the crystallites has not yet been studied.

The maximum value of the magnetization jump in a twisted wire is, evidently, \(2I_s\), but only the axial component of this jump is observed, equal to

\[ \frac{2I_s}{\sqrt{2}} . \]

In practice this value is not reached. For example, Preisach\(^2\), in the case of an alloy of \(80\%\) Ni—\(92\%\) Fe and pure Ni, obtained a maximum jump of \(0.5 \cdot 2I_s\). This may be explained as follows. In order to create the direction of easiest magnetization near the axis of the wire, the wire must be twisted so strongly that plastic flow already occurs in the outer zones, and as a result the critical field there again begins to grow. Thus it is impossible to attain the homogeneous stress necessary for a single jump.

If we plot the limiting magnetization as a function of the longitudinal field, in the presence of torsion and of longitudinal and circular fields, a hysteresis loop is obtained that is asymmetric with respect to the origin of the coordinates. Large Barkhausen jumps on the two branches of the hysteresis loop occur at different fields and have unequal magnitude. This can easily be seen from the graph in Fig. 9.

Pressure and bending. Stresses produced by means of pressure or bending can also lead to large jumps. For substances with negative magnetostriction, pure compression should lead to the goal\(^1\); however, this is difficult to realize. Therefore, so far the experiments have been carried out mainly with bending, with Ni serving as the material under investigation. Because of the negative magnetostriction of Ni in the regions of compression formed

\(^1\) The question of the influence of external stresses on the magnetic anisotropy is presented in greatest detail in the article by Gans (Ann. Phys., 42, 680, 1935). Translator’s note.

under bending, an axial direction of easiest magnetization appeared. However, the relation between \(H_0\) and \(H_S\) has not yet been determined. The jump in bent Ni reaches a magnitude of \(0.5\cdot 2I_S\)^{8}.

Large jumps without external tensions. Often soft permalloy specimens give large Barkhausen jumps even without external tensions. Large jumps can also be observed in some Ni—Fe—Co alloys (for example, 35% Ni—20% Fe—45% Co) under special heat treatment. The propagation of the magnetization wave in them differs in no essential way from the case of Ni—Fe alloys under load \(^{3,\mathrm{II}}\); but under load and torsion the jumps disappear.

Single crystals in the direction of easiest magnetization have a very steep magnetization curve; however, in ordinary specimens large Barkhausen jumps cannot be observed because of the demagnetizing field of the ends. Bozorth \(^{9}\) overcame this difficulty by giving his specimen the form of a frame, this frame being cut from a single crystal parallel to the directions of easiest magnetization; the hysteresis loop obtained in this case was almost rectangular and had vertical portions whose length was only slightly less than \(2I_S\) \(^{1}\).

§ 6. LARGE OPPOSITELY MAGNETIZED REGIONS

In the preceding paragraphs we considered the conditions for the occurrence of large jumps, as well as the propagation of the magnetic boundary surface during a jump. The eddy currents arising during its motion make it difficult to study the essential features at the boundary surface. Therefore an experiment was arranged to obtain a large reversal nucleus by braking the wave or by the short-time application of a local field. This makes it possible to study the boundary surface better in the stationary state; these experiments are described below. We shall consider here only the simplest case, when the direction of easiest magnetization is parallel to the axis of the wire. By a large reversal nucleus we shall mean such a section of the wire whose magnetization is opposite to the magnetization of its main part.

Braking of the propagation of the wave. The propagation of magnetization along a wire can be braked by applying a local field \(^{3,\mathrm{IV}}\). This local field, which can be obtained, for example, by means of a short coil, must be antiparallel to the main field and exceed a certain mini-

\(^{1}\) In a kind brief communication Dr. Bozorth informed me that a rectangular hysteresis loop was obtained on a specimen of an alloy 65% Ni—35% Fe, cooled in a magnetic field (J. F. Dillinger and R. M. Bozorth, Physics, 6, 279, 1935). Such a material may, in a continuously maintained external field, require many minutes for complete remagnetization.

small value which depends in a complicated way on the magnitude of the main field and on the length of the braking coil. If the local field is too weak, then only a slowing of the propagation of the remagnetization wave occurs at the given place; after passing through this region the wave begins to propagate with its former velocity. In the case of complete braking of the propagation, the indicating coil placed behind the braking coil does not detect remagnetization. If the braking field is removed, the wave again begins to propagate. The flux curves of the braked wave, which were recorded ballistically by means of a moving indicator coil, had exactly the same form as the curves given above in Fig. 7, but were only considerably shorter; they were the shorter, the higher was the main field in which the wave was being frozen. From the character of these curves it may be considered that the frozen boundary surface has the form of a funnel and differs from the form of the moving surface only in depth.

A critical examination of the measurement results leads to the natural conclusion that propagation of the boundary during braking proceeds until the total field over the whole surface reaches the value \(H_0\). This can be confirmed for the greater part of the boundary surface; the demagnetizing field of the boundary surface is to a considerable degree, namely toward the ends, negative, i.e. directed opposite to the main field and approximately equal to \((H - H_0)\). On the contrary, near the front end this calculation is insufficient; here it is positive and counteracts the braking field. In any case, even here the surface energy must be taken into account in order to encompass the phenomenon completely.

Here one must also mention unpublished experiments in which the moving boundary surface was frozen in its initial form by switching off the main field. Then the wire was gradually etched and the change of flux at various thicknesses along the wire was recorded; from the change in the flux curves one can directly derive the form of the boundary surface. The experiments essentially confirmed the initial assumption of a funnel-shaped form.

Remagnetization grains. Up to now the discussion has concerned regions of remagnetization which were stable only when the field in the wire was either maintained for a prolonged time below \(H_0\) by a local braking field, or when the field as a whole was reduced to a value smaller than \(H_0\). In what follows a method will be described for obtaining such regions also at \(H > H_0\) and keeping them stable. \(^{3,}\)

In the preface it was said that in the main field \(H\), with \(H_0 < H < H_s\), propagation of remagnetization in the wire can begin if at some place the field strength is brought, by superposing an additional field \(H_{ao}\), up to the value of the starting field \(H_s\). It was found that with a short-term application of the additional field \(H_{ao}(=H_s-H)\), say for a duration \(t_1 = 10\) milli-

seconds, propagation will not occur. If, for the same duration, the magnitude of the supplementary field is increased above \(H_{ao}\), then at a certain value \(H_a\) propagation will begin. With a changed duration \(t_2\) the effect will also be different, and for the start to begin another field \(H_a > H_{ao}\) is needed: it is determined from the condition that, for a given main field, the product \((H_a - H_{ao})t\) must remain approximately constant.

If this critical value of the product is not reached even because the pulse duration is too short, then the start does not occur, but some changes take place in the wire. This can be noticed because now the main field need not be brought up to \(H_S\) in order to obtain propagation.

Fig. 10. Curves of the magnetization flux of nuclei of various magnitudes in a demagnetized wire (\(15\%\ \mathrm{Ni}—85\%\ \mathrm{Fe}\)). The numbers \(a\), \(b\), and \(c\) give the corresponding thicknesses of the nuclei: \(a — 0.110\), \(b — 0.077\), \(c — 0.044\ \mathrm{mm}\)

Fig. 11. Relation between the thickness of the nuclei, calculated from the maxima on the flux curves (see Fig. 10), and the starting field \(H'_S\).

These observations lead one to suppose that a nucleus of a definite magnitude, in a definite field, retains the ability to excite remagnetization. The correctness of this can be shown, at least for large nuclei, by measurement. A supplementary field \(H_a > H_S - H\), 10 mm long, which is insufficient to start spontaneous propagation, is applied for some time to a certain field \(H > H_0\). Motion of the indicating coil in a definite region of the wire gives a measurable ballistic deflection, which shows partial remagnetization of the wire. From the measured flux curves (Fig. 10) one can draw a conclusion about the form and position of the nuclei. It may be thought that here, as in the case of spontaneous propagation, the penetration of demagnetization from the surface decreases, and the nucleus may be represented as a ring. However, there is a significant difference between the two cases; so long as no reversal occurs, the permeability of the wire is equal to unity, whereas during reversals of magnetization

permeability is substantially higher. Since the penetration time is approximately proportional to the permeability, the additional field will penetrate at full strength through the entire cross-section of the wire before the nucleus grows. Hence we come to the conclusion that the nucleus may grow at any point of the cross-section of the wire, but most probably in distorted places. The thickness of the nucleus can be determined exactly from the maxima of the flux curves if one makes the assumption, valid in the case of long nuclei, that the entire flux due to the nucleus crosses the search coil. However, deriving the dimensions of the nucleus from the flux curves encounters difficulties. We assume that the nucleus has the form of an ellipsoid of revolution, whose minor axis is calculated from the maxima of the flux curves, while the major axis corresponds to the length of the flux curve. The nucleus corresponding to the largest flux curve in Fig. 10 has a length of 135 mm and a thickness of 0.11 mm, with a wire diameter of 0.38 mm.

After measuring the nucleus we begin slowly to increase the main field until spontaneous growth sets in. During this increase of the field the thickness of the nucleus does not change, as we conclude from the invariability of the maxima on the flux curves. Let us denote by \(H'_s\) the value of the main field at which growth of the nucleus begins. Figure 11 shows the relation between \(H'_s\) and the height of the maximum on the flux curve of the nucleus, for which \(H'_s\) is determined, for a wire of \(15\%\) Ni—\(85\%\) Fe. The closer the main field approaches the value \(H_s\), the smaller the dimensions of the nucleus necessary for starting; if its length is less than the internal diameter of the search coil, then the flux maximum can no longer be measured with sufficient accuracy. Likewise, one cannot directly measure the natural nucleus, which begins to grow in the field \(H_s\), because of the smallness of its dimensions. But we can obtain approximately its thickness by extrapolating the curve in Fig. 11 from the last measured point, and estimate its length from the lengths observed for large nuclei. For the thickness we then obtain a value less than a micron, and for the length several millimeters. Consequently, the volume of the natural nucleus is, in order of magnitude, the same as the volume of the regions that produce the ordinary Barkhausen effect.

The question of why these nuclei are stable in a field whose magnitude is sufficient for their growth, i.e., why the spontaneous growth of the nuclei is delayed, is analogous to the questions that arise in studying the formation of condensation nuclei in supersaturated vapor. This first of all requires clarification of the role played by surface energy; in the magnetic case one must also add the demagnetizing field of the nucleus. The equilibrium conditions lead to the result that the total field at the surface of the nucleus, owing to the demagnetizing field, is reduced from \(H\) to \(H_0\). However, this condition is not satisfied at the ends of the nucleus, since there the demagnetizing field is positive, and therefore the total—

… field even exceeds \(H\). The problem can be solved, as Döring showed, only if one takes into account the surface energy of the magnetic boundary surface. This solution is set forth in the following article.

References

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1. Probleme der Technischen Magnetisierungskurve. J. Springer, 1938. Ed. R. Becker. Translated by S. V. Vonsovsky. ↩

2. I.e., directions of easy magnetization. Translator’s note. ↩

3. Magnetic anisotropy energy. Translator’s note. ↩