REVIEW ON DOMAINS IN THIN MAGNETIC SAlMPLES

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REVIEW ON DOMAINS IN THIN MAGNETIC SAlMPLES

E. Feldtkeller

To cite this version:

E. Feldtkeller. REVIEW ON DOMAINS IN THIN MAGNETIC SAlMPLES. Journal de Physique

Colloques, 1971, 32 (C1), pp.C1-452-C1-456. �10.1051/jphyscol:19711154�. �jpa-00213974�

JOURNAL DE PHYSIQUE

Colloque. C l, supplkment au no 2-3, Tome 32, Fe'vrier-Mars 1971, page C 1 -

452

REVIEW ON DOMAINS IN THIN MAGNETIC SAlMPLES

by E. FELDTKELLER

Forschungslaboratorien der Siemens AG, Munchen, Germany

RCsumC. - Nous passons en revue la structure et la configuration des domaines magnetiques dans des Bchantillons suffisamment minces ne contenant que des configurations de domaines a deux dimensions.

Des domaines larges sont observes dans des khantillons monocristallins, dans des Cchantillons a cristallites orientes et dans des Bchantillons a cristallites petits par rapport a l'iipaisseur des parois. Leur aimantation est parallkle a la surface de 1'6chantillon ou forme une structure en bandes dependant de l'epaisseur, et de l'importance et l'orientation de l'ani- sotropie.

Des petits domaines sont observes lorsque la dimension des cristallites est comparable a l'epaisseur des parois de domaine.

Abstract.

-

The structure and configuration of the magnetic domains in samples thin enough to contain only two- dimensional domain configurations, is reviewed.

Large domains are observed in single-crystal samples, in samples with oriented crystallites, and in samples with crys- tallites small compared to the wall thickness. Their magnetization lies parallel to the sample surface or shows a stripe structure, depending on the thickness and on the anisotropy magnitude and orientation.

Very small domains are observed if the crystallite size is comparable to the domain wall thickness.

I. Introduction.

-

Magnetic domain configura- tions have been reviewed in several books [l, 23 and review articles [3, 41. In bulk samples, surface domain configurations are observed and the internal configu- ration may be concluded in certain cases from these observations. In thin samples, however, two-dimen- sional domain configurations exist (i. e., the orien- tation of the magnetization does not depend on the coordinate along the thickness dimension). Therefore, the complete domain configuration is observed by observing the surface configuration, for these samples.

The present paper is constricted to this kind of samples and relates the observed domain structures to recent observations of other properties of these samples.

Because anisotropies and surface stray fields deter- mine the domain configurations, and because the crystal anisotropy generally is the most important anisotropy contribution, essentially different domain configurations exist in samples with different crystal symmetries, different crystallite sizes, and different crystal lattice orientations with respect to the sample surfaces. The paper is subdivided in correspondence t o these differences. It contains therefore chapters on samples consisting of randomly oriented small crystallites, samples consisting of randomly oriented crystallites with sizes comparable to the wall thick- ness, and single-crystal samples or samples consisting of large or homogeneously oriented crystallites with cubic or hexagonal (magnetically uniaxial) crystal symmetry.

11. Crystal lattice axes oriented homogeneously in regions large compared to the wall thickness.

- Tn

single- crystal samples, in samples containing large crystal- lites, and in samples containing a large number of small crystallites with uniform orientation, the magne- tization may be oriented along one or several of the easy crystal axes within the region of homogeneous lattice orientation. The domain configuration depends on the number and orientation of these easy axes.

Different configurations are, therefore, observed in samples with cubic symmetry and in samples with only one easy axis.

1. CUBIC

^CRYSTAL SYMMETRY.

- Thin samples with cubic lattice symmetry have been investigated in the form of thin platelets grown be chemical vapor deposition (Fe platelets by Gemperle

[ 5 ] ,

Ni platelets by De Blois [6, 71) or in the form of thin films with homogeneously oriented crystallites prepared by epitaxial evaporation onto a single-crystal substrate (for instance MgO or NaCl, by Sato et al.

[g,

91 and many others, for instance [10, 1 l]).

Single-crystal platelets are much more perfect than epitaxially grown films. The platelets seem to be the most perfect magnetic samples available at all. Large reversible wall displacements have been observed in them.

If some (or a t least one) of the crystal easy axes lie within the sample plane, the magnetization within any domain is oriented homogeneously along one of theseeasy axes. For instance, for iron with the (001) plane oriented parallel to the sample surface, the magnetization of every domain lies along one of the

< 100 > directions lying in the sample plane. In this special case, the domain walls are, therefore, 1800 walls or 900 walls oriented parallel to ( 100 ) or ( 110 ) planes, respectively (Fig. la). By this wall orientation the walls are free of magnetic poles and the wall area is minimized. Inhomogeneities, for instance strains or the grain boundaries in films with homogeneously oriented crystallites, lead to a ripple structure within the domains [9, 101.

If no easy axis lies parallel to the sample plane (as for Ni with (001) orientation of the surfaces), the magnetization is oriented homogeneously parallel to one of the sample plane's easiest directions as long as the sample thickness is smaller than about the wall thickness (smaller than 0.6 pm for nickel). Except in the neighborhood of the sample edges, the domain walls are 1800 walls oriented along { 100 ) planes and 90° walls oriented along { l00 ) planes in thin nickel samples with the sample surfaces oriented along (001) and with no field applied (Fig. lb).

In thicker samples (thicker than 0.6 pm for nickel, thicker than 0.3 pm for Ni-Fe with 3-10 % Fe) the magnetization is able to locally orient along the easy

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711154

REVIEW ON DOMAINS I N THIN MAGNETlC SAMPLES C 1

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453

axes in spite of the shape anisotropy of the sample.

The demagnetizing field is kept small by a stripe confi- guration with narrow stripes magnetized along diffe- rent easy axes (Fig. Ic). The stripes represent a local oscillation of the magnetization between two easy directions. Oscillation half periods (stripes pacings) of

FIG. 1. - a) Domain configuration in a part of a Fe platelet 0.65 pm thick, after Gemperle [51.

b) Domain configuration in a part of a Ni platelet 0.4 pm thick, after De Blois [6].

c) Domain configuration in a 97 Ni-3 Fe platelet 0.54 pm thick, after De Blois [ 7 ] , and schematical explanation of the stripe

structure.

0.7 pm and more have been observed by Bitter tech- nique. The stripe walls may or may not be oriented parallel to the net-magnetization direction of the domains [6].

In 80/20 nickel-iron oriented films with their small crystal anisotropy, the induced uniaxial anisotropy may be stronger than the crystal anisotropy. Domains like those reported in chapter IV for non-oriented- crystallite films, with zig-zag walls and a considerable ripple structure, are observed in these films [l l].

2. UNIAXIAI.

CRYSTAL ANISOTROPY. -

The domain configurations of thin samples with essentially uni- axial crystal anisotropy have been observed for cobalt [l, 121, hexagonal ferrites [13, 141, magnetoplumbite [ l , 15, 161, and some orthoferrites [16, 171.

If the easy axis lies parallel to the sample plane, straight 180° walls parallel to the easy axis and perpen- dicular to the sample surface are observed.

More interesting is the case that the easy axis is oriented perpendicular to the sample surface. In this case, the 180° walls between domains magnetized parallel to the easy directions, are free of poles for all orientations perpendicular to the sample plane.

On the other hand, the domain magnetization oriented perpendicular to the surface is connected with large stray fields. For this reason, the domains in the dema- gnetized state are meander shaped stripes.

Instead of selecting one of the materials mentioned above and reprinting its domain configuration from the literature, a fish carrying exactly the same pattern as that observed by magneto-optic methods for these materials, is shown in figure 2. The photograph was

FIG. 2

-

Indo-pscific fish Siganus javus photographed 1969 in the Aquarium of Amsterdam. It carries the pattern known as domain pattern for uniaxial materials with easy axis perpen- dicular to surface. The length of the animal is about 15 cm.

taken the day before the Intermag Conference opened in Amsterdam in April 1969.

Msilek and Kamberskf [l81 have calculated the domain width to have

_-

a minimal value of wmi,

⁼

10 n J A K / ~ , M: in magnetic uniaxial samples of the thickness 5 n JAKJ~, M:. The domain width is larger than wmi, in thicker or thinner samples. The formulas contain the exchange constant - A, aniso- tropy constant

K,

and the spontaneous magnetiza- tion M,.

The domains may be well resolved with the usual domain observation techniques because in the most materials mentioned above, the domain width wmi, is sufficiently larger than the optical resolution dis- tance. In thin cobalt foils, the domain width is smaller than the light wave length but the domains could be observed by Lorentz microscopy [ l , 121.

In MnBi films, on the other hand, only domain clusters have so far been resolved. The theoretically expected domain width is essentially smaller than the light wave length [IS], and Lorentz micrographic experiments have not yet been successfull.

What has been observed [19,20] are domain clusters

growing for instance in a reversing field applied to

a saturated film. While within the remaining, not

reversed domains the saturation Faraday rotation

of the material is still observed, an essentially smaller

rotation is observed within the reversed clusters.

C 1

-

^{454 E.} FELDTKELLER

Apparently, the clusters contain much smalIer domains table initial susceptibility

D

(cc RIS

D)

films [[22,23,25]

not resolved microscopically, i. e. the small Faraday and more recent papers]. Becituse a susceptibility rotation of the clusters results from averaging over can never be rotated but at best the field orientation small s ~ i n - U D . . and s~in-down domains. with maximal or minimal susceptibility, this name should positively be avoided, a& the -symmetry of 111. Random crystallite orientation with a crystallite the angular behaviour should better be described size to the thickness.

-

As long as by the rotatable remanence direction of the samples.

the crystallite size in a polycristalline sample is large com~ared to the ma~netic domain wali thickness

U

in the material, the domain configuration typical for the crystal symmetry as described above, is observed in every crystallite [21]

:

The domain walls have diffe- rent orientations in differently oriented crystals, and in thin films where the cross-tie density along a cross- tie wall depends on the anisotropy magnitude within the film plane (i. e. on the lattice orientation with respect to the film plane), the crystallites show different cross-tie densities (Fig. 3).

FIG. 4. - Lorentz micrograph of a 81/19 Ni-Fe film evapo- rated onto a SiO film at 400 ^{O C ,} shown during the magnetiza- tion reversal by a field H = ' Hc = 4 kA/m applied antiparallel to the remanence direction (vertical). The large coercivity and the small domain size is caused by the crystallite size being

in the order of the domain wall thickness. After [24].

FIG. 3. ^- Lorentz micrograph of a nickel-iron film 30 nm thick deposited epitaxially on a copper sheet. The film contains large crystallites with different orientations of the crystal lattice and of the domain walls, and different cross-tie densities.

After Fuchs and Politycki 1211.

If, however, the crystallite size is comparable to the domain wall width, the magnetization is not able to follow the local changes of the preferred directions, and a domain pattern with especially small domains is observed [22-241, in which it is rather difficult to distinguish between domains and domain walls (Fig. 4). Films of this kind have a relatively large coercivity compared.to films with smaller crystallites and to samples with larger crystallites.

Because of the random distribution of the crystallite orientation, and because the anisotropy field descri- bing the induced in-plane diffusion anisotropy is small compared to the coercivity of these films, the net magnetization behaves like in an isotropic material.

I. e., the net magnetization remains in any direction of the sample plane after the sample has been satu- rated along that direction. In a small-amplitude field applied in such a remanent state, the susceptibility depends on the angle between the applied a-c field and the remanent magnetization direction. For this reason, films of this type have sometimes been called <<rota-

IV. Random crystallite orientation with a crystallite size essentially smaller than the wall thickness.

-

If the size of randomly oriented crystallites is small compared to the wall thickness, the magnetization nearly averages over the crystallites and their aniso- tropies because of its exchange stiffness. Domains essentially larger than the crystallites are the result.

The variations in the lattice orientation are only able to cause small-angle inhomogeneities of the magnetization direction (called magnetization c( rip- ple

>>),

and even this is only the case if the samples are thin enough (thinner than, for instance, 1 pm) and if they do not possess a strong superposed ani- sotropy with its easy axis perpendicular to the sample plane (called cc perpendicular anisotropy

B).

In thicker samples with a weak cc perpendicular anisotropy

^>)

or in samples thicker than 0,l pm with a strong per- pendicular anisotropy, a very regular stripe structure within the domains with the magnetization rotated out of the sample plane is observed.

1. STRIPE

DOMAIN FILMS. -

In nickel-iron films

with negative magnetostriction (more than 81 % Ni

content), planar stresses within the film plane lead

to a magnetic anisotropy the easy axis of which is

oriented perpendicular to the film plane. Besides

this, a shape anisotropy of the film grains and grain

boundaries (resulting from the growth from isolated

nuclei) may lead to a perpendicular anisotropy even

in films with zero magnetostriction. As has been

predicted by Kittel [26], films with a perpendicular

anisotropy consist of narrow stripes with alternating

magnetization components perpendicular to the film

plane as soon as the film thickness is larger than a

certain threshold value which depends on the aniso-

tropy magnitude [27-291. For 81/19 Ni-Fe films the

thickness threshold lies between 0.2 pm and 0.5 pm

REVIEW ON DOMAINS IN THIN MAGNETIC SAMPLES C 1

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⁴⁵⁵

and increases with increasing deposition tempe- rature [29].

The magnetization has always a remarkable compo- nent parallel to the film plane. In every domain, the stripes are oriented parallel to this component, i. e.

parallel to the net magnetization of the domain. The magnetization configuration within a domain (or of the whole film in the remanent state after saturating the film parallel to the film plane) is shown schema- tically in figure 5a. In an alternating field applied along

FIG. 5.

-

Remanent magnetization configuration (a) and hys- teresis loop (b) of a stripe domain film in a field applied parallel to the film plane. (~ysteresis loop after Hanson et a1 [29].)

the film plane, films of this type show a hysteresis loop like that presented in figure 5b, with coercive field strengths up to 3 kA]m [29] and saturation field strengths up to 15 kA/m [30]. The magnetization reversal by wall motion does not lead to a saturation.

The films are saturated by a rotation of the stripe magnetizations into the film plane in fields essentially larger than the coercivity.

The films are called stripe domain films [31] or mottled films [22, 301, or rotatable-anisotropy films r22,271. It must, however, be stressed that no magnetic

is essentially smaller for the ripple than for stripe domains and lies in the order of 1 degree only.

The net magnetization within a domain of these films is primarily controlled by diffusion anisotropies (based on strains or on crystallite imperfection align- ments) and by interactions from domain walls and from the sample surface [34]. When the magnetization is rotated by a small field, the reorientation of the ripple configuration is essential in addition [35, 361.

A ripple structure of the magnetization has been observed in small-crystallite films (films evaporated onto substrates colder than 350

OC

or deposited elec- trolytically under the influence of a component inhi- biting the crystal growth) of a large number of diffe- rent materials including materials ferromagnetic only at low temperatures. A Lorentz micrograph of an EuS film taken at 10 OK [37] is shown in figure 6 as an example.

anisotropy (acting

On

the homogenous magneti- -

_{FIG. 6.}

-

Lorentz micrograph of an EuS film 20

m

thick

zation) may be rotated in these films, but that only

taken at a temperature of 10 OK by Pfisterer, Fuchs and Tis-

the angular dependence of some small-field properties

cher [37].

that have sometimes been used to determine the ani- sotropy (small-field torque, initial susceptibility) depend on the direction of a saturating field previously applied.

The magnetic flux is expected to be closed within the sample if regarded in more detail than drawn in figure 5a [31], so that the configuration is in fact no more two-dimensional. For Ni-Fe films between 2.5 p and 10 p thick this has also been shown expe- rimentally [32].

2. PLANE MAGNETIZATION

FILMS. -

In films thinner than the threshold value mentioned in IV. 1, the magne- tization lies within the film plane throughout the domains. Here the only systematical inhomogeneity of the magnetization direction within a domain is the magnetization ripple caused by the crystallite orientation differences [33]. The ripple configuration is much less regular than the stripe configuration in stripe domain films. In contrast to the small-angle Bloch walls forming the stripe configuration, the ripple small-angle NCel walls are oriented perpen- dicular to the net magnetization of the domains.

The mean amplitude of the magnetization orientation

V. Conclusion.

-

Relatively large domains are observed in thin samples if the crystallites (or homo- geneously-oriented-crystallite regions) are either large compared to the magnetic wall thickness or small compared to the wall thickness. The magnetization within these domains lies homogeneously parallel to the sample plane (with a ripple structure resulting from inhomogeneities) if either the sample is especially thin (thinner than a value dependinn on the aniso- tropy'magnitude, for instance 0.6 pmfor (001) orien- ted nickel platelets) or if at least one easy axis is orien- ted parallel to the sample plane. The domains contain narrow stripes with alternating magnetization compo- nents perpendicular to the film plane if the sample plane contains no easy axis and the sample is thicker than the critical value depending on the magnetic anisotropy.

Very small domains, an isotropic behabiour within

the sample plane, and a relatively large coercivity

are observed for randomly oriented crystallites the

size of which is in the order of the magnetic domain

wall thickness.

C 1

-

⁴⁵⁶ E. FELDTKELLER

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