Magnetic Domain Patterns R.M

Magnetic domain patterns R.M. Bozorth

To cite this version:

R.M. Bozorth. Magnetic domain patterns. J. Phys. Radium, 1951, 12 (3), pp.308-321. 10.1051/jphysrad:01951001203030800. jpa-00234388

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MAGNETIC DOMAIN PATTERNS By R. M. BOZORTH, Bell Telephone Laboratories, Murray Hill (New Jersey).

Sommaire. 2014 La technique et l’interprétation des diagrammes de poudres magnétiques est briè- vement passée en revue, d’un point de vue historique. Les diagrammes les plus simples observés sont ensuite décrits et expliqués dans la mesure du possible. Dans la troisième Partie, on décrit et discute de nouveaux diagrammes relatifs : a. à un monocristal dont la direction (1 11) est celle de facile aiman- tation (60 pour 100 Co, 40 pour 100 Ni); b. à un monocristal de cobalt; c. à un alliage polycristallin fer-silicium et d. à un alliage polycristallin pour aimants permanents (Alnico 5).

Brief revievsr. --- For many decades iron filings considerably our knowledge of the processes of have been used to portray the directions of lines magnetization. They used single crystals contai- of magnetic force in air and to detect flaws or inho- ning 3.8 weight per cent silicon and having surfaces mogeneitics in magnetic materials. In 1931 it cut nearly parallel to crystallographic planes. The occurred to von Hamos and Thiessen [ 1] to use specimens were annealed and polished carefully, magnetic powder to detect the local inhomogeneities first mechanically and then electrolytically. After irr magnetization that the domain theory predicts. mechanical polishing the powder pattern on a Independently Bitter [2] applied a suspension surface almost parallel to (100) is the cc maze » of siderac (Fe,O,), having particles about 10-4 cm pattern of figure 2 (a), similar to that of figure i. in diameter, to a polished magnetized surface and observed under the microscope that the powder formed parallel lines regularly spaced about o. mm apart and approximately perpendicular to the direction of magnetization. The technique and interpretation of such patterns .was then the subject of study of a number of workers [3]. The preparation of colloid for these studies has been described in some detail by Elmore [4] who recommends a suspension of magne- tite, ground to colloidal dimensions, peptized with hydrochloric acid and protected by one per cent of soap; an improvement on his technique has recently been developed and will be published soon. Elec- trolytic polishing [4] overcomes the objectionable mechanical polishing which disturbs the surfaces. A notable advance was made by McKeehan and Elmore [5] who first observed a well-defined on a i pattern demagnetized single crystal. Figure - Fig. I. n Maze » pattern observed on polished surface of such a also shows pattern (b) and those patterns single crystal of iron; (b) demagnetized, (a) and (c) magne- observed when the magnetization is directed (a) tized in opposite directions. into, or (c) out of, the same portion of the surface as that shown in (b). The suspension used for the experiments was a true colloid of Fe,O, particles After electrolytically polishing and reapplying the small enough to show Brownian movement, and a powder to the same area the result is the « tree » change in magnetization of the magnetic specimen pattern of figure 2 (b). It is evident from this was accompanied by a movement of the lines and other experiments that the maze pattern is immediately visible to the eye. characteristic of a strained surface and that the More recent work, reported in various articles by tree pattern shows the domain boundaries of strain- Williams, Bozorth and Shockley [6], has made free material. visible for the first time the domain boundaries The directions of magnetization in the domains characteristic of unstrained iron, and has improved can be determined in several ways, using techniques

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphysrad:01951001203030800 309

described in the original paper. The result for a is always parallel to one of the crystal axes, and the portion of one tree pattern is shown in figure 2 (c). boundaries separate domains magnetized at goo or The local magnetization in unmagnetized material at 180° to each other.

Fig. 2. - Maze and a tree » patterns, (a) and (b), observed on the same portion of a single crystal after mechanical and eliectrolytic polishing, respectively. Directions of magnetization in the tree pattern are shown at (c).

Fig. 3. - Effect of increasing tension (a) to (d), on the tree pattern. In (fi tension has been released.

Visible movement of domain boundaries takes at the expense of domains oriented at right angles, place upon application of field or stress. The so that the latter domains disappear almost entirely effect of uniform tension is shown in figure 3. In when the tension is sufficiently large. With release this material tension increases the magnetization of tension the original kind of tree pattern forms, in the direction of the tension, and the mechanism but the details of the pattern are not the same. by which this is accomplished is here apparent : This shows that the boundaries are not fixed to the domains oriented parallel to the axis of tension are structure of the crystal in the way that they are enlarged by displacement of domain boundaries, in the maze pattern, where the local stresses always 310 cause the return of the powder lines to the same places When the surfaces are not parallel or nearly after they have been disturbed temporarily by parallel to simple crystallographic planes, the field or uniform stress. patterns are likely to be more complicated. Figure 4

Fig. 4. - Complicated patterns observed on (1 10) and (i I i) planes.

Fig. 5. -° Patterns on cobalt surfaces cut parallel and perpendicular to the hexagonal axis. shows two examples of such patterns. Although Bitter [7] observed two types of patterns on poly- the simple patterns are well understood, it has not crystalline material and Elmore [8], working with yet been possible to understand in detail the more single crystals, found the hexagonal lace-like patterns elaborate ones. It is believed, however, that the on surfaces parallel to the hexagonal planes (o01 ) basic principles that apply to the simple ones are perpendicular to the crystal axis, and the straight also applicable to the more complex ones. These line patterns on prism planes, as shown in the pho- principles are discussed below. tographs of figure 5, taken by H. J. Williams. Experiments on cobalt have also been instructive. These patterns are in accord with the magnetic 311

properties of cobalt, known to have a direction of are weaker and fall off more slowly with distance, easy magnetization parallel to the crystal axis. in the way that they would expect if the domains are The domains are then expected to be long in the needlelike as assumed. direction of the axis and packed together like a The domain structure around cavities and inclu- bundle of needles (or sheets). The boundaries of sions was investigated theoretically by Néel [10] such domains thus correspond to the patterns. before any direct observations were made. Obser- Moving pictures of the patterns taken with slowly vations of a number of crystal surfaces under the changing field strength show sudden displacements microscope showed the presence of an occasional of the boundaries corresponding to jumps much hole that had formed accidentally during freezing larger than those usually attributed to the Bark- or etching or polishing of the crystal. The patterns hausen effect. around two holes in (100) surfaces are shown in (a) Germer [9] has measured the strength of magnetic and (b) of figure 6. The structure observed was fields close to the surface of an unmagnetized almost identical with that predicted by N6el, cobalt crystal and found that near a hexagonal and can be interpreted with the help of figure 6 (c). face it is of the order of 104 Oe and falls off with Briefly, the energy is lowered by the formation of distance from the surface so that it is relatively « spikes o which help the magnetic poles to spread weak at mm. The fields near prism faces out over a larger area.

Fig. 6. - N6el spikes a around holes in a crystal surface, and their interpretation.

The interpretation of the various structures can Others, interpreted more recently, are referred to be carried out in terms of energies of associated in the third part of this paper. with domain walls, magnetic poles (magnetostatic energy), crystal anisotropy, strain and the inter- Plate Pattern. - A typical « plate» pattern, action of the magnetization with the field if any with domains of closure, is shown in figure 7. be present. The theory has been summarized This is a stable configuration in zero applied field, recently by Kittel [11]. In the next section the for reasons illustrated in figure 8. In the possible simpler types of structure will be discussed on this single domain (a), the poles at the end give rise to basis. The following section describes the appli- magnetostatic energy equal to In (b) cation of the powder pattern technique to various problems, and the new conclusions that can be this is reduced considerably by the introduction drawn from the various experiments will be pointed of the wall, with which is associated some energy. out. In (c) the poles are eliminated completely but there is some strain energy associated with the magne- Interpretation of simple patterns. -- The tostriction of the domains of closure, the material of does fit into the simple domain patterns that were first understood which not space it would occupy may be listed as follows : if unmagnetized. In (d) the energy of magnetostric- tive strain is reduced and the wall Plate further, energy pattern, (100) plane; is increased. Tree pattern on surfaces to nearly parallel (1oo); The various energies may be evaluated and the Neel " spikes " around cavities; configuration calculated for its minimum value. Line pattern on cobalt parallel to [oo . r ] axis. In silicon-iron, the material of figures 2 and 3, the 312

Fig. 7. -- ~ Plate» pattern with domains of closure, on the (100) surface of an iron-silicon crystal.

is x 1012 ergs : cm2, the saturation magnetostriction [13] in this direction is

and the domain wall energy about i erg per cm2 of wall. For one cm3 of a crystal slab composed of domains L cm long and D cm wide the volume of domains of closure is and the wall D( 2 L ) area is

The sum of the energies is then

per cm3 of crystal, which is a minimum for

or 0.08 for silicon iron. In the crystal of figure 7, Fig. 8. - Theoretical domain structures illustrating the L = 0.22 cm and the calculated and observed energies associated with magnetic poles, domain walls and values of D are o.03 and o.o5cm, respectively. The magnetostriction. agreement is good, considering the approximations made. When a field is the thickness of the domains strain is applied energy diminishes. The theory has been worked out by Néel [14], and confirmed by the data of Bates and Neale [15J. This will not be considered further here. ergs per cm8 of the volume of the domains of closure. Young’s modulus [12] in the direction Tree Pattern. - This was the first of the more 313 complicated patterns shown to be in accord with which there is no domain structure, is our present ideas of domain theory [6]. This pattern is observed when the surface of an iron crystal (positive anisotropy constant) is slightly inclined to the (at angle 0) (100) crystallographic planes, the factor, the volume and its can be understood No being demagnetizing "Yo explanation qualitatively of the hole and the saturation reference to In the domains Is magnetization by figure 9. plate-like of the material around the hole. If domains are formed as in (2), poles are not present at the edges of the cavity but are distributed along the domain boundaries as indicated. In this case there will be

Fig, 9. - Explanation of the tree pattern. that compose most of the crystal the magnetization is parallel to the crystal planes, and therefore the lines of magnetic flux will cut the surface at an angle and produce a density of magnetic poles of ± 1s sin 0 on alternate strips of width W. There will then be a magnetostatic energy proportional to W sin2 0 per unit area. This energy is reduced by formation of the tree patterns even though the wall energy is added. The branches transport flux accross the « trunks » of the treees and as they taper this flux is distributed as magnetic poles over the domain wall separating the branch from the underlying domain. A minimum energy theory has been worked out [6], and this explains the dimensions of the branches and their variation with 0 within a factor of about 2. When the angle 0 becomes larger the branches lie closer together, as shown in flgure I o, and then overlap so that the trunk of the tree becomes completely hidden.

Fig. I o. - Dependence of the tree pattern on the angle between « Spikes ». - N6el’s theoretical investi- the surface and the (1oo) planes. gations of the domain structure around cavities and conclusions, as well as the previous work of Kersten [16], prompted an investigation of the energies associated both with the demagnetization powder patterns in areas where visible cavities (a volume effect) and with the domain walls (area occured in crystal surfaces. Two patterns observed effect) : in (IOO) surfaces have already been shown in figure 6 and they have the form predicted by Néel on purely theoretical grounds. N being the demagnetizing factor of the volume V enclosed the domain the The energetics of this kind of pattern, as already by boundaries, energy unit area of wall and A the total wall area. reported [6] is as follows. per Assume a spherical hole of diameter d and a domain The magnetostatic (or demagnetization) energy having the form of a rotational ellipse of minor associated with a hole [see (1) of f g. 6 (c)] around axis d and major axis l, The demagnetizing factor 314 of this ellipse is value of I for which Ed -~- is a minimum is o.1 o cm and the ratio of j is then approximately 100. The observed ratio for the domain of figure 6 {b) is and the volume and surface are easily calculable. about 50, smaller a factor of 2. This is a satis- The magnetostatic energy is then by factory agreement in view of the simplifications used.

Moving Boundaries. - Simple geometry has been a factor of ’ included to take account of observed in at least two experiments on the move- 25 being° ment of domain boundaries a the of the domains themselves, and accompanying change permeability of magnetization with changing applied field. the wall energy is Williams and Shockley [6] observed a simple structure in a hollow rectangle with sides parallel to [100] directions, and they have described [17] some Using the appropriate numerical values d=o.oo1 cm, experiments on the movement of such a boundary Is = 1580, ew = 1.5 ergs : cm2, the calculated with slow and rapid changes in magnetic field.

Fig. I I. - Effect of Néel «"spikes » on the movement of a Bloch wall.

Spikes such as those just described have an impor- in figure II. When the principal wall moves tant effect on the movement of large domain walls, close to the spike the latter joins on to it and hinders as noted by Williams and Shockley [ 6] and illustrated its movement away from the hole, because energy 315

Fig. 2. - Movement of a well during magnetization parallel to a [on] ] direction in a (100) plane.

Fig. 13. - Pattern on a (oi i) surface of a cobalt-nickel crystal in which [I I I] is the direction of easy magnetization. 316 is consumed in forming the additional wall. This Patterns. - Cobalt-nickel crystal. - The mechanism seems to be important in the inter- geometry of patterns on the materials of cubic pretation of hysteresis loss and coercive force and symmetry already examined is closely connected is discussed by Shockley and Williams in an accom- with the fact that their directions of easy magnetiza- panying paper. tion are [100]. Heretofore no simple patterns have A moving boundary composed of a number of been reported on crystals, like nickel, in which the segments of straight lines is observed in a (100) directions of easy magnetization are [111]. It plane when magnetized parallel to a [001] direction seemed probable that the failure to observe patterns (fig. 12). The boundaries that move are between in such crystals was connected with the fact domains magnetized antiparallel to each other their crystal anisotropy was too small (for nickel ( 1 8 0 ° wall). the anisotropy constant K is 60 ooo as compared

Fig. 14. - Effect of magnetization on the pattern on the cobalt-nickel crystal.

with 280 ooo for iron containing several per cent All of the theoretically expected angles between of silicon). Consequently a crystal of a cobalt- adjacent domains - 180°, 109°, 71° - are observed. nickel alloy containing 60 per cent cobalt and having It is also noticed that the domain structure is smaller a constant of about 200 ooo according to Shih [18], than that observed on iron-silicon crystals. This has been prepared by slow cooling of the melt difference in size may be due to the more compli- as described by Walker, Williams and Bozorth [19]. cated pattern that may be expected in a structure The surface of the crystal was cut parallel to a (0 1 1) having 8 instead of 6 directions of easy magnetiza- plane so that 4 of the 8 directions of easy magne- tion and having no goo boundaries. tization were parallel to the surface. The pattern The effect of a magnetic field, applied parallel to and its interpretation are shown in figure 13. the [110] direction, is shown in figure The 317

Fig. I5. --- Patterns on the (roo) surface of cobalt; a. positive field, b. zerolfield, c. negative field, parallel to the axis.

Fig. 16. - Pattern on cobalt (100) surface, with small field applied normal to the surface.

structure, originally of complicated geometry, resolves are between domains in which the directions of itself in high fields to a series of lines at right angles magnetization differ by i ogo. to the direction of the applied field, the direction of magnetization alternating in adjacent domains Cobalt. - Although patterns have previously between the two [111]] directions oriented most been observed on cobalt, as mentioned above, nearly to the direction of the field. The boundaries three pictures recently taken by H. J. Williams 318 are reproduced here 15) because interesting domains is enhanced by applying a small normal regularities are observed in the pattern. The field. The specimen surface is slightly inclined specimen, cut with a surface parallel to a (I 00) plane, to the hexagonal axis, so the magnetic poles on the is magnetized parallel to the surface in the direction surface are alternately north and south poles in of the hexagonal axis [001]. In figure 15, b is successive domains. The verticle field enhances unmagnetized while a and c are magnetized in the pole strength on half of the domains and neu- opposite directions. The displacements of alternate tralizes the poles on the other domains, so that lines in opposite directions shows that the boun- the colloid is attracted in the one kind and not in daries move so that more material is magnetized the other. parallel to the field and less antiparallel to it. Careful comparison of a and c shows also that Polycrystalline material. - In some commercial the lines which move upwards in one move down- silicon-iron sheet material used for transformer wards in the other so that imperfections that appear cores the separate crystals are aligned with their [ 100] in a thinner domain in a are in a thicker domain axes approximately parallel to the long dimension in c. of the sheet. A powder photograph of such material In figure 16 the contrast between neighboring 1 ~), taken by H. J. Williams, shows that domain

Fig. 17. - Pattern on polycristalline iron-silicon alloy, showing that domains sometimes cross grain boundaries. boundaries often cross crystal boundaries. This to 1300° C and cooled at the « normal » rate occurs when the [100] directions in adjacent crystals of 20 C : s to 8ooo C and then quenched in oil. A are almost parallel, and one believes that the crystals magnetic field was present from gooo C to room must also be nearly aligned in 3-dimensional space temperature. Examination by the powder technique so that the platelike domains of the two crystals shows the existence of long domains, about 0.02 mm will join together along planes of contact that go in width, aligned approximately parallel to the below the surface observed. The alignment in field present during the heat treatment. They some of the crystals is obviously too poor for domains cut across crystal boundaries with no substantial to cross crystal boundaries. change in direction (see fig. 18) and show that the magnetization is everywhere parallel or antiparallel Alnicos. - In a recent study of the mechanism to the field used during heat treatment. In this in Alnico 5 (5 1 per cent Fe, 2l~ per cent Co, 14 per cent material the magnetization is obviously not parallel Ni 8 per cent Al, 3 per cent Cu) heat treated in a to the easy crystallographic direction nearest to the magnetic field, Nesbitt has observed powder pattern heat-treating field, as it is believed by Hoselitz that help in understanding the nature of this maetrial. and McCaig [20] to be in material heat-treated in In a series of experiments a specimen was heated a somewhat different manner. 319

Fig. 18. - Pattern on Alnico V : domains crossing crystal boundaries.

Fig. 19. - Movement of domain boundaries during magnetization of Alnico V.

When a field is applied for measurement parallel is square, and the evidence indicates that magneti- to the heat-treating field, domain boundaries are zation proceeds by displacement of the boundary observed to move Ig). The hysteresis loop between antiparallel domains. When the measuring 320

Fig. 20. - Rotation of magnetization of domains in Alnico V when magnetized at right angles to field present during heat treatment.

field is applied at right angles to the heat-treating the atomic ordering that exists in these alloys, as field the powder patterns show domain rotation shown by X-rays. without boundary displacement (see f g. 20). This I am indebted to Messrs H. J. Williams and is in agreement with the form of the magnetization E. A. Nesbitt for several of the photographs repro- curve, which rises almost linearly to saturation duced in this article, and to Mr J. C. Walker for at about 4oo to 450 Oe. assistance with the experimental work, especially in the of the of the These show that domains preparation single crystals experiments large cobalt-nickel alloy. having a strongly preferred orientation exist when the material is prepared in the manner described. When the material is cooled at the normal rate to Remarque de M. Bates. - I congratulate temperatures lower than 8ooo C the domains are Dr Bozorth on his beautiful pictures on alnico V. I much smaller, and when the material is aged myself have tried on and off for four years to obtain at 6ooo C no domain has so far been detected in the tem, but without success. Was the crystal sur- unmagnetized condition. Recently Nesbitt has face prepared in a special way or was the dry powder observed their formation upon the application of technique used ? a field to material the usual Alnico 5 treat- given de M. - Le monocristal de in a field and The coercive Question Epetboin. ment-cooling aging. cobalt at-t-il subi au un elec- force of the domains pr6alable polissage quenched specimen having large Au des difficult6s rencontr6es is 15 Oe, that of the specimen having smaller trolytique ? sujet M. le Prof. Bates, me souvients dans notre domains is 35o, while that of the material given par je que laboratoire M. Amine a obtenu deux diff6- the usual Alnico 5 treatment is 600. aspects rents de la surface polie d’un alnico, suivant que l’on The manner in which the preferred direction of utilisait un bain a base d’acide phosphorique à magnetization is fixed in the structure is not yet chaud (8oo C) ou d’acide perchlorique-anhydride known, but it is possible that it is connected with ac6tique. 321

- Réponse de M. Bates. -- We have done some A une question de M. Guillaud, M. Bates répond. experiments on electrolytic polishing and have The field applied perpendicular to the surface was devised a bridge circuit for controling it. This is not measured exactly; but it was of the order to be described in a forthcoming paper in Journ. of 13o Oe. Scient. Instr. Remarque de M. Hoselitz. - The powder patterns de M. Sucksmith. - I would like to Remarque shown by Dr Bozorth to occur on Alnico V when obtain a three dimensional of a domain picture quenched from 8ooo C can be explained without which should be on of in cobalt, simple account any additional assumptions from our views (HOSELITZ direction of the the single easy magnetization. and MCCAIG, Nature, 1949, 164, p. 581; Proc. Phys. What is the reason for assuming that they are Soc., I go9, B, 62, p. 163). Magnetostriction and other « needles » or « sheets » since the right hand picture measurements on this material in the fully heat of the figure 5 suggests that they are rods whose treated condition have shown that the magneti- cross section is that of a cluster hexagonal sation energy can be represented by a cubic term

-- a in one Remarque de M. Shockley. It may be appro- and uniaxial term probably acting of the directions. The order of of priate to point out that in figure 17 presented by [100] magnitude Dr Bozorth there appear domains of closure which these energy are up to I o ergs : cc. In the quenched can be understood in material described by Dr Bozorth, these values may terms of the relationship be considerably smaller and I cannot comment on between the crystal grain this particular case. boundary and crystal However, as mentioned by Dr Bozorth, similar are observed Nesbitt in the axes. The diagram pre- powder patterns by heat treated but in sented here (fig. 21 ) repre- fully material, only relatively fields. sents a grain boundary high ABC which is symmetrical If a field of about 5oo Oe is applied in the pre- between the two crystals ferred direction of magnetisation, the field energy for the segment BC. For term HJS becomes of the same order of magnitude the segment BC, domains as the magnetic anisotropy term estimated in our Fig. 21. - Domain structure can form di- experiments, and it is consequently likely that at fields near a grain boundary. along easy rections with no free of this magnitude, the actual field direction will become the direction of the Hence it poles generated on the magnetisation. boundary. Between points A and B, however, can be understood that no unidirectional domains there will be magnetic poles. The magnetostatic are observed by powder patterns until fields of about the coercive force are when most energy of these poles may be reduced by introducing applied, reentrant spike domain which reduce the density domains will be very hearly aligned with the field direction and domains boundaries on the grain boundary. The effect of one such consequently many spike is shown in the diagram; in figure 17 of will have disappeared. Thus large unidirectional domains will exist in this condition. Bozorth’s aticle, a number of such spikes are present. boundaries The generation of such spikes are frequently observed Demande de M. Bauer. - Serait-il de to be discontinuous and consequently irreversible. possible faire ces des dont le This that in material an exp6riences pour corps point suggests polycristalline de Curie est voisin de la ordinaire appreciable contribution to the coercive force and temperature be made discontinuities in the et de voir comment les domaines changent avec hysteresis may by la pattern of domain walls, a process quite similar to temperature ? that discussed by N6el. Reponse n6gative de MM. Bozorth et Bates. REFERENCES.

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