IN THIN MnBI FILMS
PROEFSCHRIFT
TER VERKRIJGING VAN DE GRAAD VAN DOCTOR
IN DE TECHNISCHE WETENSCHAPPEN AAN DE
TECHNISCHE HOGESCHOOL DELFT, OP GEZAG VAN
DE RECTOR MAGNIFICUS IR. H. B. BOEREMA,
HOOGLERAAR IN DE AFDELING DER
ELEKTROTECH-NIEK, VOOR EEN COMMISSIE AANGEWEZEN DOOR
HET COLLEGE VAN DEKANEN TE VERDEDIGEN OP
WOENSDAG 13 NOVEMBER 1974 TE 14.00 UUR
door „ . • PIETER DEKKER natuurkundig ingenieur geboren te Rotterdam BIBLIOTHEEK TU Delft P 1834 3161 C 565424
page
1. INTRODUCTION I
2. EXPERIMENTAL TECHNIQUES
2.1. General 4 2.2. Evaporation chamber 5
2.3. Thickness determination of MnBi films 6
2.4. Microscopic observations 11 2.5. Hysteresis loop recording 11
3. PREPARATION OF THIN MnBi FILMS
3.1 . General 16 3.2. The phase diagram of the Bi-Mn system 17
3.3. The crystal structure of MnBi 19 3.4. Formation process of MnBi films 22
3.4.1. Microstructures in MnBi films 24 3.4.1.1. Annealing procedure 24 3.4.1.2. Atomic Mn to Bi ratio 27 3.4.1.3. Evaporation rates 27 3.4.2. Electron diffraction and electron microscopy 29
4. PHENOMENOLOGY OF MAGNETIZATION REVERSAL
4.1 . General 32 4.2. Magnetization reversal in MnBi films 33
5. DOMAIN GROWTH
5.1. General 38 5.2. Domain growth immediately after nucleation 40
5.2.1. Nucleation 40 5.2.2. Theory of domain growth immediately after
nucleation 42 5.2.3. Boundaries of the model 48
5.2.4. Observations 50 5.2.5. Discussion 54
5.3.1 . General 57 5.3.2. Theory 59 5.3.3. Measurements and discussion 63
5.4. Approach to saturation 71 5.4.1. Introduction 71 5.4.2. Phenomenological theory of approach to saturation 73
6. DOMAIN WALLS
6.1. General 78 6.2. Domain walls in MnBi films 80
6.2.1. Domain wall energy in bulk MnBi 80 6.2.2. Domain wall energy in MnBi films 86
6.3. Experimental methods to determine y 93
7. COERCIVE FORCE
7.1. General 95 7.2. Determination of the mean distance between disturbances
in the film structure from the Rayleigh curve 101
7.2.1 . Theory 101 7.2.2. Measurements 103 7.3. Coercive force mechanisms 104
7.3.1. Theory 104 7.3.2. Measurements and discussion 106
7.4. Temperature dependence of H 108 7.5. Coercivity of MnBi films on glass 111
Acknowledgements 113 References 114 Summary 120 Samenvatting 123 Curriculum vitae 126
1. INTRODUCTION
When a paper entitled "Magnetic writing on thin films of MnBi" appeared in print^ in 1957, the time seemed to have arrived for the construction of a magneto-optic memory. Since the preferred magnetization direction of MnBi films is normal to the film plane, these films are extremely adaptable for the storage of information in small domains. Another fea-ture of MnBi is that it has large Faraday and Kerr effects which enable magneto-optic detection of these domains. The problem of the writing process, which had to be performed with the aid of small magnetic rods or needles, was partially solved one year later bv Maver^ who introduced the Curie point writing technique. In this technique needles were also emploved, but they were heated instead of magnetized. In a later publi-cation Mayer^ used electron-beams for heating the MnBi information spots. In 1968 Chen et al.^ took full advantage of the properties of laser light and heated micron sized snots of an t^nBi film above the Curie tem-perature by focusing a laser beam on them. The proposed magneto-optic memory offered a tremendous increase in packing density over conventional mass memories, fuch as disks and drums. It was believed that through use of high speed optical beam deflectors, random addressing, erasing and reading would become possible. Further investigations of the Curie point writing technique by Chen et al. and Lewicki^ resulted in refinements and understanding of the temperature profiles inside the film. On the basis of this knowledge, Aagard et al.^ introduced a small mechanically addressable magneto-optic memory. In this memory, reading was accomplish-ed by means of the Kerr-effect and writing was performaccomplish-ed by the Curie point technique.
Knowledge of MnBi films with relation to magnetic properties was en-larged through the contributions of Langlet et al.^, Unger et al.®, Lewicki et al.^ and Chen et al.**. Vlhereas Lewicki originally described the Curie point writing characteristics of the material, Unger and Langlet published essentially on preparation of MnBi films and phenome-nology of the magnetization reversal of MnBi films. Calculations con-cerning magnetization reversal of MnBi films were reported by Chen^".
Due to the lack of a theoretical treatment of hard magnetic films, a fully satisfactory description has not yet been given. In contrast to soft magnetic films which have been thoroughly investigated, bot ex-perimentally and theoretically, hard magnetic films have not been the subject of much research since no direct applications of the magnetiza-tion reversal were envisioned. Improvements in the preparamagnetiza-tion method of MnBi films by Unger et al.^^, Lewicki et al . ^^ and Dekker et al.^^ resulted in a decrease of the coercive force H of the films which
c
brought them closer to a treatment by accepted theories concerning soft uniaxial magnetic films and platelets e.g. Kooy and Enz , Bobeck , Thiele^^ and Cape and Lehman^'. The results of these theories are in agreement with observations on orthoferrites and garnets, but do not agree with experimental observations on soft (H - 50 Oe) MnBi films. In order to deduce a theory which is capable of explaining the specific behavior of MnBi films, a close experimental inspection of the magneti-zation reversal processes in these films is a first requisite.
Fortunately, the magneto-optic effects in MnBi - Faraday effect for transmitted light and Kerr effect for reflected light - are large. This guarantees a clear picture of the domain pattern at any point of the hys-teresis loop. Furthermore, the Faraday and Kerr effects form an excel-lent means for recording the hysteresis loop since at saturation the mag-netization is normal to the film surface, which means that there is a large signal difference between the two saturated states.
The description of the magnetization reversal processes in thin MnBi films will be divided into three parts. Materials preparation is the sub-ject of Chapter 3. Here investigations of the influence of the Mn to Bi ratio on the film structure are presented and compared to the results of Iwama et al.''^, Kusuda et al.-'^, Unger et al.^° and Gordon et al.^'. It is found that imperfect films are obtained by intentional miscontrol of the Mn to Bi ratio. These films, with induced imperfections such as Bi residuals, show very high coercive forces which have, presumably, to be ascribed to nucleation difficulties. Conversely, films with carefully adjusted Mn to Bi ratios have low coercive forces. Honda et al.^^ even reported MnBi films of approximately 0.4 ym thickness which behave like
soft uniaxial magnetic materials.
The analysis of the coercive force in MnBi films, which is the subiect of Chapter 7, will be preceded by a discussion in Chapter 6 of the domain wall surface energy density y. In soft uniaxial materials, y varies only
slightly with position of the wall and also during the entire proceeding of the magnetization process. This is not the case in hard uniaxial films The coercive force mechanism for instance, is caused by variations in y^^ Moreover, measurements by Unger et al.^ and calculations by Malek et al.^' Kittel^^ and Jedeloo et al.^S give rather diverging values of y. Vari-ations in y might be caused by imperfections in the film structure. For-mal theories which describe the behavior of wall displacement in a
spa-tially alternating field of force of statistically distributed wavelength and amplitude developed by Kronmiiller^^ and Pfeffer^® are applied in order to calculate the average distance between wall pinning centers directly from measurements of the initial magnetization curve.
Chapters 4 and 5 will be devoted to the phenomenological and theoretical descriptions of the magnetization reversal process respectively. The in-fluence of film thickness on the magnetostatic energy is known from work on soft uniaxial films^** ^^ ^^. It appears that in extremely thin films the magnetostatic coupling between domains is too weak to influence the magnetization reversal. The shape of the hysteresis loop - i.e. the mag-netization reversal process - is distinctly influenced by variations in the Mn to Bi ratio. Hysteresis loops of films with an excess of Bi are adequately described by a model of single domain islands possessing statistically distributed nucleation fields, whereas in the case of an excess of Mn it can be shown that this statistical model cannot be used. Finally, it is observed that films with a certain constitution behave at low fields like soft uniaxial materials. It is shown that interpretation of measurements in this region with the aid of appropriate theories'"* ^^ leads to satisfactory results. At high fields the reversal process is governed by domain tip pinning.
2. EXPERIMENTAL TECHNIQUES
2.1 General
MnBi films are hard magnetic uniaxial films which can be manufactured on glass substrates as well as on mica substrates with the crystalline c-axis normal to the film surface. Due to the strong crystal anisotropy along the c-axis, the magnetization, M , inside domains is always normal to the film surface. The existence of closure domains in thin MnBi films has not been observed. They are not thought to exist because the uni-axial crystal anisotropy energy K is an order of magnitude larger than
2 . . .
the magnetostatic self energy 2irM . If the magnetization of thin MnBi films were to be reversed by uniform rotation of the spins, a field of 2K^/Mg - 36 kOe would be necessary at room temperature with
K = 12x10 erg/cm-^ and Mg = 625 G. Since it was found experimentally that the reversal takes place dominantly by domain wall motion, the satu-ration field is strongly reduced and amounts to a maximum value of 4TTMS . However, experiments on imperfect films reveal that sometimes, through nucleation problems, fields of twice the demagnetizing field of the satu-rated film have to be applied.
Hysteresis loops are recorded using the large magneto-optic effects of MnBi. The magnetization is determined relative to the saturation
magnet-ization with these techniques and the applied fields are obtained using an electromagnet with an axial hole drilled in its iron core.
Observation of domain patterns can be accomplished by Bitter techniques or magneto-optic techniques. Due to the small domain sizes ('\' 0.5 um) in MnBi films, the Bitter technique fails here and one depends on observations with the magneto-optic Kerr effe<it or the Faraday effect. Since the width of the domain walls in MnBi films is on the order of 100 A, observations of walls will be impossible with visible light unless structural defects in the film cause a variation in the exchange stiffness constant A or the uniaxial crystal anisotropy K^ which would result in wider walls.
MnBi films are fabricated in a vacuum chamber by separate deposition of Bi films and Mn films followed by a heat treatment. Although it seems possible to obtain MnBi films by a method of co-evaporation, the
sand-wich technique has been followed for the preparation of the films which were used in the experiments described here.
Thicknesses of the separate Bi and Mn films are measured with a gauged quartz crystal thin film monitor (Balzers QSG 201). The gauging was per-formed by comparing the monitor indication to results of measurements using the Tolanski method.
2.2. Evaporation chamber
The evaporation setup inside the vacuum bell jar (Balzers BA 360) is drawn schematically in Fig.l. Three evaporation sources, one for Bi (99.9995 % Balzers code 261598), one for Mn (puriss grade Balzers code 261627/S2) and the third one for SiO (99.8 X Balzers code 261516/S 3a"'^) , the former two consisting of a Tungsten crucible (Balzers W 490 032) and the latter of a Molybdenum boat (Balzers MO 490 111), were mounted at the bottom of the vacuum chamber in a star formation. Directly above the
oration sources, a substrate holder was mounted which could contain either freshly cleaved mica sheets or glass plates. The dimensions of these substrates did not exceed 50 mm x 50 mm x 2.5 mm. The substrate holder was provided with a heating element, thus enabling the substrate temper-ature to he adjusted from 20 C to 400 C. Since the evaporation of the Bi film and the Mn film takes place separately, a single quartz crystal thin film monitor for the control of the film thicknesses was mounted near the substrate holder. The distance of both substrate holder and monitor from the plane of the evaporation source star formation was ap-proximately 20 cm. The vacuum pumps provided a vacuum of better than
10 torr during the evaporation and annealing periods.
Deposition of SiO on the MnBi film serves two purposes. The first is to provide a protective coating against corrosion. The second plays a role when observations with the Kerr effect are made. The SiO layer enhances the contrast between the reflections of the magnetic domains when viewed through a top illuminating polarizing microscope if the SiO thickness is properly adjusted to the reflection coefficients of the film surfaces.
2.3. Thickness determination of MnBi films
The preparation of MnBi films usually reauires an excess of Mn atoms in order to assure completion of the diffusion process. The final total mechanical film thickness will, therefore, not represent the thickness of
the MnBi film i.e. the magnetic film thickness.
The mechanical thickness of an MnBi film can be determined by the Tolanski interferometric method. The Tolanski method is based on the appearance of interference fringes in monochromatic light between a mirror and the film when the mirror makes a small angle with the film. Extinction is obtained when the distance between the film and the mirror is (2n+l)X/4. A step in the thickness of the film is observed as a shift of the interference fringes (Fig.2). The height of the step is expressed in the shift d of the fringes by h = ^ (y) where D is the distance between two fringes at one side of the step.
Fig.2. Determination of meahaniaaZ film thickness by the Tolanski inter-ferometric method
method is based on the assumption that a Bi - Mn double layer of appro-priate composition completely transforms into MnBi. The second method is based on a magneto-optic technique and will be described later.
Since the atomic weights and the mass densities of both Bi and Mn are known, it is possible to calculate the required thickness of an Mn film which is able to completely transform a Bi film of a given thickness to MnBi. When the mass density of MnBi is further known, the thickness of the resulting MnBi film can be calculated as well.
The calculation is based on two equations:
P M n V ^ PBi^Bi (2.1)
V *Bi
in which p = density, h = thickness and A = atomic mass and the subscripts indicate which material is intended. The complete transformation of a given Bi film into MnBi requires an equal number of atoms of Mn and Bi according to eq.2. 1. Since h . is known, k, can be calculated and be
Dl ^T\
used further in a second equation to obtain the thickness h^ . of the resultant MnBi film.
PMn^In ^ P B i N i = PMnBi^1nBi ^2.2)
^4nBi
The value of p
PMnBi ^ i «"
(2.3)
MnBi can be obtained from literature on bulk MnBi. However, there is some doubt about the accuracy of the given values which vary between 8.0 and 9.0 since bulk MnBi crystals which are free of unreacted Bi inclusions have never been obtained^" ^' ^ 2 . Calculation of p„ _. on
MnBi the basis of the crystal structure of MnBi and the atomic masses of Mn and Bi is preferred here.
A unit cell of the MnBi crystal structure (Section 3.3) contains 6 Bi ions and 6 Mn ions. The volume of this cell can be expressed in terms of the lattice constants, a and c, of the hexagonal structure^''. The mass den-sity is found by dividing the sum of the atomic masses by the volume of
3
the unit cell. Thus, a value of p., _. = 8.6 e/cm is obtained. MnBi "
The other quantities in eq.2.3 are taken from the Handbook of Chemistry and Physics. It is found that the thickness of the MnBi film depends on the thickness of the initial Bi film as K , „. = 1.44 h„. and further that
Mn ^"^'- ^'• an atomic Mn to Bi ratio R(:s-r) = 1.0 is obtained when the thickness of
Dl
the initial Mn film is 0.35 h,
Mn Bi
It is emphasized here that this calculation does not agree with the physi-cal situation of evaporating an excess of Mn. This excess is however necessary to generate and sustain a concentration gradient which allows the diffusion process to proceed smoothly to completion. This will be further discussed in Section 3.4.1.2.
(a)
(b)
(c)
The above described method of film thickness determination is rather cir-cumstantial and is unreliable to some degree, since in MnBi Mn atoms can also occupy interstitial positions. A method which does not depend on knowledge of the history of the film under investigation utilizes one of the large magneto-optic effects of MnBi.
If a beam of light in which the plane of polarization is parallel or per-pendicular to the plane of incidence illuminates the surface of a mag-netized crystal or thin film, the reflected and transmitted light will be, in general, elliptically polarized. This phenomenon is known as the Kerr effect when the light is reflected and as the Faraday effect when the light is transmitted. Depending on the direction of the magnetization with respect to the plane of incidence, three cases are distinguished which are illustrated in Fig.3.
In MnBi films the direction of magnetization is normal to the film plane
X=6328^
('I' An(^)-*Pol)=r*0F
(4>An(-) -*Pol) = 7 - Q p
<t'An(+)-<l>An(-)= 2 0 p
Fig.4. Measurement of the Faraday rotation angle 9
and, thus, only the polar effects will be observed. The degree of ellip-ticity in both polar Kerr effect and polar Faraday effect in MnBi is small and the effects can be regarded as a rotation of the plane of polarization of the light upon reflection and transmission respectively.
Faraday and Kerr rotation angles are measured in a setup which is schema-tically drawn in Fig.4.
After transmission of the saturated MnBi films (M normal to the film ^ s
surface) the plane of polarization of the light (HeNe laser, X - 6328 A) is rotated through an angle +6 or -9 depending on the orientation of
r r
the magnetization with respect to the direction of propagation of the light. The analyzer is set for extinction. The film is then saturated in the opposite direction and the analyzer is set to extinction a second time. The difference in extinction angles equals twice the Faraday rota-tion angle.
The procedure for the Kerr rotation measurement is essentially the same, except that a beam splitter is required for the separation of the inci-dent and reflected beams.
Both Faraday and Kerr rotation angles depend on the film thickness. For the characterization of MnBi films, it is useful to determine the Faraday rotation per unit thickness, the so-called specific Farady rotation Q„„.
r o
This quantity has been determined by Unger et al.^". In his experiments he used MnBi films of various compositions and thicknesses and found a maximum specific Faraday rotation (per unit mechanical thickness) of 6 = 110 deg/ym for MnBi films on mica with an atomic Mn to Bi ratio of 1 .0.
since the Faraday rotation is directly proportional to the film thickness in a perfect film, it can be expressed as 9 = ^'^pq , where h is the mechanical film thickness. In imperfect films, or in films which are coated with an excess of Mn, 8 will no longer be directly proportional
r
to h. As a r e s u l t measurement of 6 w i l l then g i v e information about t h e
r
magnetic film thickness, i.e. the effective thickness of the MnBi film by simply dividing 9„ by 9 .
r r o
This technique of film thickness determination was first suggested by Unger et al.^° and adopted by others as the most reliable technique for this purpose. It seems that many properties of MnBi films are related to 9 rather than to the mechanical thickness h.
r
It should be noted here that this method of film thickness determination is limited to films which are thinner than approximately 1500 A since light transmission through MnBi films becomes troublesome for larger thicknesses.
2.i. Microscopic observations
After preparation, the films are examined under a polarizing r'.icroscope. Unreacted areas are easily observed since the optical absorption of MnBi is significantly smaller than the optical absorption of the separate Bi and Mn films which constitute the MnBi film. An example is given in Fig.5 where a microphotograph of an imperfect MnBi film is presented. The
photo-Fig.S. Imperfect MnBi film. Bright areas: MnBi; dark areas: Bi + Mn unreacted
graph was taken with unpolarized light. If reflected light had been used (which is necessary when h > 1500 A ) , the MnBi regions would have been dark and the unreacted regions bright. For the observation of the domain pattern during magnetization the microscope can be mounted on an electro-magnet which provides a field normal to the film surface with a maximum value of 9 kOe. The core of the electromagnet is solid. Therefore obser-vations must be performed by employing the Kerr effect.
2.5. Hysteresis loop recording
to be oriented normal to the film surface, the polar Kerr and Faraday effect, which are - as Judy^^ showed - certainly in the case of MnBi the strongest among the magneto-optic effects, can be used with advantage for the recording of the hysteresis loops, provided the propagation of the light is also normal to the film surface. In a saturated MnBi film the specific Faraday and Kerr rotation angles are proportional to the satu-ration magnetization, i.e. 9 = F.M_ and 9 = K.Mg.
r b K b
Magnetization processes which could appear in MnBi films are wall dis-placement, buckling, curling and uniform rotation. Saturation fields as measured on MnBi films indicate that uniform rotation does not occur. Chen''' 3"* showed that magnetization reversal takes place essentially by wall motion.
After a domain is nucleated in an MnBi film, it forms a region of reversed magnetization surrounded by a domain wall. Growth of the domain and
even-tually further nucleations of new domains lead to an increase in area of the reversed magnetization.
The net magnetization of the film is the algebraic sum of the positively magnetized area and the negatively magnetized area multiplied by Mg. Hysteresis loops of magnetic materials are obtained by accumulation of the discrete magnetization reversal jumps over the applied field trajec-tory 0 < H < H , where H is the saturation field.
s s
The small discretedomain wall displacements in MnBi films are the well known Barkhausen jumps. These are easily accumulated using the Faraday effect or Kerr effect. A polarized light beam illuminating a part of the film surface is illustrated in Fig.6. The net magnetization M of these areas is found to be
M = M r x - (1-x) 1 = (2x-l)M (2.4)
s ^ -' s
where x is the part of the illuminated area that is positively magnetized to M and 1-x the part that is negatively magnetized to M . In the posi-tively magnetized domains the plane of polarization of the incident linearly polarized light is rotated through an angle +9 = 9 h and in
r r b
the negatively magnetized domains a rotation of -9 = 9 h is found in
r r b
the transmitted light (Faraday effect).
x.l\e-°'^cosH(t>*Qf)
(1-x)lje"°'W((t>-eF)
-pol.angle
MnBi
Fig. 6. Optical accumulation of Barkhausen jumps
The intensity I of the light at the rear of the analyzer is maximum when the polarizer-analyzer angle is TT/U and is given by
I^ = il. exp(-ah) (1 ± sin 29„)
L 1 r
(2.5)
where the superscripts + and - denote whether the magnetization of the traversed region of the film is positive or negative and a is the optical absorption coefficient. Since 6„ = hFM , (2.5) becomes - in the small angle approximation
-I = il^ exp(-ah) (1 ±2hFMg). (2.6)
The net magnetization of the film (eq. 2.4) is expressed in terms of a net intensity as
Ij. = il^ exp(-ah) + (2x-l)I^ exp(-ah)hFM^
= jl. exp(-ah) + I. exp(-ah)hFM. (2.7)
direct proportionality between the variation in I and the variation in M. The net intensity thus represents the accumulation of the Barkhausen j ump s.
The method described here has an averaging effect when the beam diameter is large compared to the domain width. However, this averaging effect is lost if the size of the illuminated spot is smaller than or comparable to the average domain width.
Experiments with the Faraday rotation hysteresigraph, comparing hystere-sis loops recorded with a 1 mm diameter laser beam (HeNe, Spectra Physics Stabilite Model 120, X = 6328 A) and with a 5 ym size focused spot of the same laser show (Fig.7) that the averaging effect of a large beam diameter has a distinct effect on the shape of the hysteresis loop.
(a) (b)
Fig.7. Influence of light beam diameter on hysteresis loop recording, (a) 2 mm diameter, (b) 6 vm focused
The experimental arrangement for the hysteresis loop recording is shown in Fig.8. The light emerging from a stabilized iodine-tungsten lamp or a HeNe laser is polarized by a polarizer and enters the MnBi film through an axial hole in the core of an electromagnet (H = 13 kOe) . After
" max
traversal of, or reflection at, the MnBi film, the light is incident on an analyzer. A phototransistor is mounted behind the analyzer for the de-tection of the intensity variations. The phototransistor signal is fed to the Y-channel of a flat bed recorder (Hewlett Packard 7004 A) and is
a measure of the magnetization of the film.
The field at the MnBi films is measured with a Hall probe and fed to a Gaussmeter (Boonton 3265) . The output of the Gaussmeter enters the X-channel of the recorder and is directly proportional to the field intens-ity.
S.L.
T t
^
Fig.8. Magneto-optio hysteresigraph: A^, A^: analyzers; P: polarizer; H: Hall probe; S: magnetic film; S.L.: stabilized light source; F, K: Faraday, Kerr effect vertical input of recorder; G: Gaussmeter; R: re-corder.
3. PREPARATION OF THIN MnBi FILMS
3.1. General
Thin MnBi films are obtained by successive evaporation of a Bi film and an Mn film onto a glass substrate or a freshly cleaved mica substrate followed by a heat treatment of several hours at temperatures between 160 °C and 300 °C.
The properties of MnBi films depend on several parameters such as the Mn to Bi ratio, the film thickness, the evaporation rates of both Bi and Mn films and the annealing temperature.
The influence of the Mn to Bi ratio has been investigated by Unger et al.^" for films on mica substrates and by Dekker'^ for films on glass substrates. It was found that the preparation of an MnBi film on glass requires a substantial excess of Mn, whereas on mica MnBi films are readily formed when the number of atoms in the initial Mn film equals the number of atoms in the initial Bi film. A detailed description of the formation process including the influence of the annealing temper-ature and the evaporation rate is given in Section 3.4.
The film thickness has a distinct effect on the coercive force of MnBi films. Unger et al.^ experimentally investigated whether a definite rela-tionship exists between the film thickness and the coercive force and found a reciprocal exponential function H = H exp(-a9„) describing a relationship between H and 9 rather than a reciprocal proportionality between H and the mechanical film thickness as Chen^"* had suggested. There is some doubt, however, about whether the definite relationship really exists, since it has been found that the influence of the heat treatment during film formation seems to overshadow the influence of the mechanical and magnetic film thickness on H in that it is possible to obtain films with equal mechanical thickness and equal Faraday rotation but different coercive forces. A more detailed discussion of this problem will be delayed until Chapter 7, where the coercive force mechanism is described. For the moment it is important to remember that when two films are obtained with equal thicknesses and equal Faraday rotation angles, the structure of the lower H film is more perfect than that of the higher
H film. In the present chapter this knowledge will be used solely as a means to judge the degree of film imperfection.
It appears that thin MnBi films are more readily formed than bulk MnBi crystals. Understanding the formation process requires some knowledge of the phase diagram of the Bi-Mn system. Due to intensive investigations on the preparation of bulk MnBi by many authors between 1904, when Heusler^^ discovered that alloys of bismuth and manganese showed ferromagnetic pro-perties and 1957, when it became clear that bulk MnBi can not be used as a permanent magnet material because of its deterioration in atmospheric circumstances, this phase diagram has been quite well established. Parallel to the development of the phase diagram, the crystal structure of MnBi was studied and some interesting crystallographic properties of MnBi were discovered. The most important of these properties was the
occurrence of MnBi in two crystallographic phases. The first is stable at temperatures below 360 C (further denoted as "low temperature phase" Itp) and the second is stable at temperatures above 360 C ('high temper-ature phase" h t p ) . The ht-phase decomposes into molten Bi and aMn at 445 C. Through quenching a crystal or thin film of MnBi from above 360 C to room temperature by quickly cooling it in water, the high temper-ature phase can be frozen. This makes it possible to study both phases at room temperature. Both phases are ferromagnetic at this temperature but they possess different Curie points and different saturation magnetiza-tions. However, the quenched high temperature phase is not stable below 360 C and will relax to the low temperature phase. This relaxation has a relaxation time of two years at room temperature.
The magnetization of MnBi finds a strong easy axis along the crystallo-graphic c-axis of the hexagonal NiAs structure of the crystals. The
6 T
anisotropy constant is K = 12x10 erg/cm . Due to the preference of MnBi films to grow with the c-axis normal to the substrate - be it glass or mica or Q 1 i j oriented rock salt - the magnetization points normal to the surface in spite of the high demagnetization fields which occur. 3.2. The phase diagram of the Bi-Mn system
(Fig.9) of the Bi-Mn system in its final form and showed that the com-pound MnBi existed at the 21 weight per cent Mn line up to a temperature of 445 °C. Manufacturing bulk MnBi did not obey the laws of the phase diagram. Neither carefully adjusting the ratio of the Mn and Bi weights resulted in the entire transformation of all Bi and Mn into MnBi - free Bi and free Mn were always found in the final product - nor did an excess of Mn prevent the occurrence of free Bi. Seybolt's suggested explanation for this behavior was that fine grains of Mn were soon coated with a skin of MnBi through which neither Bi nor Mn could readily diffuse.
o o (b m a. E 10 12 U 16 18 20 22 24 »- Weight V. Mn
Fig. 9. Phase diagram of the Bi-Mn system. After Seybolt et al.^"^
and Sherwood^". The latter two authors were the first to get a preparation method for MnBi thin films in 1957'.
The method of Ellis et al . consisted of continuously dissolving Mn in liquid Bi at 500 °C (solubility of Mn 8 wt %, see Fig.9) and cooling to 300 °C (solubility of Mn 1.5 wt % ) . During this procedure MnBi crystallized The MnBi ingots contained 18 % free Bi. The average MnBi crystallite dia-meter was several tenths of a millidia-meter.
Another method, developed by Roberts^ was based on heating at 320 C for 25 hours a compressed powder mix of an adjusted Mn to Bi ratio. The treat-ment resulted in a 65.6 % yield of MnBi. The average diameter of the crys-tallites was 200 ym.
These data on bulk MnBi indicate that the formation of crystallites with dimensions on the order of 1 ym will be readily possible. Since thin films are not usually thicker than 1 ym, the diffusion of "^n through Bi can be expected to proceed to completion provided an excess of Mn atoms is pre-sent. This excess is necessary to sustain a concentration pressure and to avoid the occurrence of unreacted Bi in the final thin films . This Bi has a distinct effect on the coercive force in contrast to unreacted Mn as will be shown in Section 7.4. The process mentioned here is translated in
terms of the phase diagram as working beyond the 21 wt % Mn line. It would appear, however, that even more Mn is required when thin MnBi films are manufactured on glass.
3.3. The crystal structure of MnBi
As indicated in Section 3.1, two ferromagnetic crystallographic phases of MnBi exist. Although their crystal structure is very much alike, there are great differences in the magnetic properties of the two phases.
The crystal structure of MnBi resembles the hexagonal NiAs structure shown in Fig. 10. The structure consists basically of a close-packed hexagonal Bi-lattice the interstices of which are filled - although not all - with Mn ions. The Mn ions are surrounded by Bi ions and depending on the number of the surrounding Bi ions and their spatial order, octahedral, bipyramidal or tetrahedral, interstices can be distinguished.
filled in the Bi lattice are the octahedral sites. The lattice constants of Itp MnBi are c = 6.12 A and a = 4.29 A. The magnetic moments of the
o o
Mn ions are aligned along the hexagonal c-axis and the exchange integral is positive which means that the magnetic moments are parallel. The
• Mn
o Bi
Fig.10. Crystal structure of MnBi
magnetic moment per Mn ion was determined by Heikes^ and found to be approximately 4.0 \i„, where y is the elementary Bohr magneton. The
num-15 B
ber of 4 Bohr magnetons indicates that the Mn ions are trivalent. The Curie point of the low temperature phase cannot be measured because of the transition to the high temperature phase (htp MnBi) at 360 C which is accompanied by an abrupt loss of magnetization. The phase transition at 360 C was studied by Seybolt et al.^^, Roberts et a l . " , Andresen et al.?2 and Willis et al.^^. These investigations resulted in the conclusion that a 3 % c-axis contraction and a 1.5 % a-axis dilation forces an im-portant portion of the Mn ions to shift to bipyramidal sites in the Bi lattice where they apparently are not exchange coupled with neighboring Mn ions on octahedral sites. An antiferromagnetic exchange coupling cannot even be excluded. However, results obtained by neutron diffraction of quenched high temperature phase MnBi are in favor of the model without exchange coupling rather than the model with an antiferromagnetic coup-ling. Roberts found that 10 % of the Mn ions were shifted to bipyramidal
sites. If the magnetic moments of these ions are aligned antiparallel to the magnetic moments at the octahedral sites, a reduction in the net
mag-3+ .
netic moment per Mn ion of 20 % would have been the result. Then a moment of 3.2 y would have been measured. Measurements by Heikes^ showed
that a net magnetic moment of only 1.7 y„ occurs in auenched htp MnBi,
D
which requires, if the applied models were the same, a shift of
approxi-3+ . rio 3 +
mately 29 % of the Mn ions. Although Andresen et al.^ found a Mn shift of 15 % rather than 10 %, the high value of 29 % was never experi-mentally found.
If the disconnection model is adopted, the strong decrease in magnetic moment can be made plausible according to Roberts . When it is assumed that the exchange coupling of the shifted ion and its five nearest octa-hedral neighbors to the rest of the magnetic lattice is removed, a 10 ^ shift could be responsible for a decrease of roughly 60 % in magnetic moment. This would result in a net magnetic moment of 1.6 y„ which is close to Heikes' observed value. However, recent measurements of the re-duction of saturation magnetization of auenched htp films with respect to Itp films at room temperature by Unger'*^, Chen et al."* and Kempter"*" are in favor of a 15 % shift of octahedral Mn ions to bipyramidal sites where magnetic moments are aligned antiparallel to the remaining octa-hedral Mn ions, since the reduction amounts to only 30 % (Fig.11). Although several authors had suggested that the high temperature phase of MnBi was f errimagnetic, it was shown by Chen et al.'* that the high temperature phase has a Curie point at approximately 180 C and is ferro-magnetic. When quenching from above 360 C (the transition point), the high temperature phase is frozen. When the magnetization of a sample which has been treated in this way is measured as a function of temper-ature, - experiments which have been performed by Chen et al."*' and Unger " - it is found that the high temperature phase relaxes to the low temperature phase even at room temperature. The activation energy for this process is 1.08 eV according to Chen. The fast relaxation of the htp to the Itp phase (at 100 C relaxation time is 10 min.) makes it im-possible to measure the Curie temperature of the htp and one depends entirely on measurements of the susceptibility above 360 C in order to determine the Curie point of htp films. Unger reported that in thin MnBi films a mixed phase can also occur. This mixed phase could not be
identi-fied in a well established way. However, after heating the films above 360 C followed by slowly cooling to room temperature, the low temperature phase is always obtained.
A simple experimental check is found in a measurement of the saturation magnetization as a function of temperature. The quite distinct behavior of the two phases will immediately show up as illustrated in Fig.11 where the M (T) curves of both phases are represented.
low temperature phase
50 100 150 200 250 300 350 400 450 ^'Temperature'C
Fig. 11. Behavior of the magnetization of Itp MnBi and quenched htp MnBi as a function of temperature measured by use of Faraday rotation.
In the experiments which are reported in this work only MnBi films in the low temperature phase are considered.
3.4. Formation process of MnBi films
MnBi films are obtained bv annealing a double layer of Bi and Mn in vacuum. This process was developed by Williams et al.' who first evaporated an Mn film and then a Bi film onto a glass substrate. After annealing for
72 hours at temperatures in the range of 225 to 350 C, MnBi films were obtained. The MnBi films formed in this manner "have not been perfectly uniform and continuous. However areas approximately an inch square have formed with the c-axis oriented normal to the surface" (Williams'). The quality of the films was highly improved by Unger et al.^" who proposed interchanging the sequence of evaporation, i.e. depositing the Bi film prior to the Mn film. Films obtained by this method show a very high degree of perfection, and moreover, the annealing time could be reduced by at least a factor of three. In regard to the preferred orientation of the resultant MnBi films, it is believed that the deposition of the bismuth layer prior to the manganese layer plays a major role (Gordon et a l . ^ ' ) . The trigonal Bi lattice grows preferably with the basal plane parallel to the substrate surface, be it glass or mica, with the only difference that on mica the orientation of the hexagonal basal plane struc-ture is essentially single crystalline. Bi films formed on glass show no a-axis texture and are essentially polycrystalline.
The method followed for the preparation of the films which were used in the experiments of this work is adopted from Unger's work with slight changes in the annealing procedure.
Films with thicknesses in the range of 100 to 5000 A were prepared by successive evaporation of a Bi film and an Mn film followed by an anneal-ing procedure of approximately two hours at temperatures between 160 and 310 C. A protective layer of SiO (typical thickness 1000 A) was then evaporated onto the film when the MnBi film was cooled to below 50 C. The vacuum during the entire process was better than 10 torr. Films were judged on their quality by
a. Observation of the microstructure with visible light. b. Determination of H .
c c. Determination of 9„.
F d. X-ray diffraction.
e. Electron diffraction and electron microscopy.
The properties were expected and experimentally found to depend on Mn
1. The atomic Mn to Bi ratio R(=^) .
Dl
3. The annealing temperature and annealing time. 4. The substrate and the protective coating (SiO). 5. The film thickness.
3.4.1. Microstructures in thin MnBi films
Iwama et al.' showed that MnBi films manufactured on a glass substrate may consist of islands of MnBi separated by threadlike regions which probably consist of pure unreacted Bi. In situ observations by Unger et al.^" on the growth of MnBi films on a mica substrate show that intterup-tion of the annealing procedure for these films leads to an island-like structure also.
In order to investigate the influence of 1) the atomic Mn to Bi ratio, 2) the evaporation rates and 3) the annealing times and temperature on the occurrence of this microstructure three experiments were performed. These experiments were:
1. Variation of the annealing time and temperature while keeping constant
Mn Mn R(7-:-) and the evaporation rate of both Bi and Mn. R(^5-^) was chosen m
Bl bl
such a way that smooth MnBi films were obtained. Mn
2. Variation of R(:5-^) while keeping constant the separate Bi and Mn
evap-Dl
oration rates and applying the same annealing procedure to all films. 3. Variation of the evaporation rates while keeping constant the atomic
Mn to Bi ratio and leaving the annealing procedure unchanged. The initial thickness of the Bi films in these experiments was 420 A. An atomic Mn to Bi ratio of R(-5-r-) = 1 .0 was obtained when a 420 A thick
D l
Bi film was covered with a 150 A thick Mn film. The final thickness of the MnBi film (calculated) in this case was 605 A.
3.4.1.1. Annealing procedure
The influence of the annealing procedure was determined by annealing films with an initial composition of 420 8 Bi / 240 8 Mn ( Ri—^) = 1.6 ) on
Bl
glass and on mica in a vacuum at a heating rate of 8 C/min to 160 C. This temperature was sustained for 2 hours. After that period the film was allowed to cool slowly to room temperature. Then a coating of SiO (700 A) was deposited on it. The atomic Mn to Bi ratio was consciously chosen larger than 1.0 since the Bi-Mn phase diagram predicts that in
this case MnBi and free Mn will remain. Lewicki'^, Iwama'^, and Unger^" suggested that this Mn excess remains as a thin film or the MnBi films. Its influence on the film properties will be discussed later. After re-moval from the vacuum system, the MnBi films were examined under the optical microscope employing transmitted light. An example of this examination is given in Fig.12.
.?S»ffi«'P?f^S!!^
i?^P
%^
,'* ^' / *
Fig.12. Progress in the formation of an oriented MnBi film on alass. A> Tanneal = ISO C. B) Tanneal = 180 °C. C) Tanneal = '^10 °C.
0^ '^anneal = 2^0 °C.
The photographs of Fig.12 show bright and dark areas. The bright areas represent regions of MnBi in the film and the dark areas probably re-present unreacted Bi coated with unreacted Mn. Light absorption in the MnBi layer is smaller than in the double layer Bi/Mn of the same composite thickness. The optical absorption coefficients of Bi and Mn at a wave-length of 5000 8 are a^. = 6.94 x lO"'^ and a„ = 6.05 x lO"'^ cm"',
as the optical absorption coefficient of MnBi at 5000 A is a,, „. =
Ic: _i MnBi 4.0 X 10 cm . The existence of needles of MnBi and circular areas can
be observed in Fig.12.
The formation process can be followed further by annealing the film at temperatures above 160 C. This is achieved by placing the film in a furnace and increasing the temperature by approximately 10 C in 15 min. After every 10 C temperature rise, the film is removed from the furnace and microscopically inspected. T'le progress in the formation of the MnBi film is clearly observable. The circular areas grow at the expense of the matrix of unreacted Bi/Mn and MnBi needles until finally, at 240 C the entire film area consists of MnBi (probably with the Mn-excess as an over-laying film). The Faraday rotation of this film appears to be 9-, = 6.8
r
degrees, which means that the film has a magnetic thickness of
(6.8/l.l)x 100 A = 615 A since the specific Faraday rotation is 110 deg/ym. Approximately the same value, i.e. 605 A, is obtained when h^ . is cal-culated from the initial Bi film thickness assuming that only 150 A Mn
Mn
( R(:^-v-) = 1.0 ) takes part in the transformation of the Bi film into MnBi.
Bl
This observation is in favor of the suggestions of Lewicki, Iwama and Unger concerning the residual overlaying Mn film.
When the MnBi islands are still clearly separated, the coercive force is extremely high (typically between 5 kOe and 10 kOe). After reduction of the width of the separating areas, the coercive force decreases. When the film has been annealed at 240 C, the coercive force can still be reduced by bringing the film to 400 C for some time. This indicates that the transformation is not yet finished at 240 C.
Equally as important as the annealing procedure which provides for the diffusion are the annealing of the Bi film prior to the Mn deposition and the substrate temperature before Bi deposition.
Hermann et al.^^ showed that optimal epitaxy of Bi on mica is obtained at a substrate temperature of 70 C. At lower temperatures the a-axis orien-tation of the hexagonal structure of the basal plane of the trigonal Bi-lattice is less perfect. When Bi films of thicknesses larger than 3000 A are deposited, a different orientation of the lattice was found by Hermann. With respect to the large rhombohedral Bi unit cell (a = 6.54 X,
a = 87 34', 8 atoms per cell) the film is oriented with the (111) direc-tion normal to the substrate.
Duggal et al.'*'' investigated the properties of thin Bi films (h .<1000 A ) . They found thatBi films evaporated onto mica at 130 C are discontinuous
when h„.<600 A. Above h„.=700 A the films are continuous with both c and a Bl Bl
axes oriented throughout the film, the grain sizes are between 1 and 3 ym. As shown by Dekker et al.' , Bi films free of microscopically observable voids are obtained on mica for thicknesses down to 350 A vihen the sub-strate temperature does not exceed 70 C.
In order to obtain low coercive force MnBi films, the temperature of the Bi film prior to Mn deposition is held at 160 °C. When films prepared in this way are annealed at 270 C for two hours, the coercive force at room temperature is found to be independent of additional heat treatments even performed at temperatures around 400 C.
3.4.1.2. Atomic Mn to Bi ratio
The atomic Mn to Bi ratio before annealing is an important parameter in film preparation. Its influence is illustrated in Fig. 13.
Here a film with an initial composition of 420 A Bi / 150 A Mn ( R ( ^ ) = 1.0 ) deposited on glass was annealed using the same procedure as for the film of Fig.12. The photographs of Fig.13 show that the dark threadlike areas between the MnBi islands do not vanish in contrast to what was ob-served in the film of Fig.12. It was found, that in order to obtain con-tinuous films the Mn to Bi ratio must be larger than 1.6. On mica the situation is very different because here a ratio of 1.0 is already suf-ficient to obtain continuous films. These results are consistent with those of Chen et al.'*' who found that Bi to Mn volume ratios of 1.6 to 2.5 are required rather than a Bi to Mn volume ratio of 2.9, which is the stoichio-metric ratio.
3.4.1.3. Evaporation rates
THe evaporation rate of the Bi film in particular has a great influence on the properties of the MnBi films being formed.
Unger et al.^" showed that MnBi growth starts at Bi grain boundaries. It is therefore interesting to manufacture MnBi films starting with Bi films
•SJ.-J
M., '-"'
Fig.13. Growth of an MnBi film on glass from a Bi/Mn double film with atomic Mn to Bi ratio R(Mn/Bi) = 1.^0. Annealina temperatures: A) IPO °C, B) 180 "C, C) 195 °C, D) 210 °C, E) 220 °C, F) 240 °C, G) 250 °C, H) 270 °C
Fig.14. Influence of the Bi evaporation rate on film formation. Density of MnBi growth centers increases with increasing Bi evaporation rate. A) Bi evaporation rate 4.2 2/s. B) 7 %/s and C) 10 l/s.
with different grain sizes. The grain size of an evaporated film depends among other thingson the deposition rate of the material on the substrate.
Fig.14 shows how MnBi growth depends on the Bi deposition rate. The density of the MnBi crystal growth nucleation centers increases with the Bi deposition rate.
3.4.2. Electron diffraction and electron microscopy
The purpose of the observations with the electron microscope was to ob-tain information on the texture of the MnBi films and on the crystallite size.
To examine a thin film electron microscopically, the film must be removed from its substrate. It was found that MnBi films could hardly be removed from glass or mica. However, some small sized fragments were removed from several mica substrates. In most cases, very thin sheets of mica remained on the back of the films. The reflections in the diffraction patterns due to these mica residuals could be easily identified. The diffraction patterns of an MnBi film which was formed on mica by evaporating a Bi film of 400 A and an Mn film of 100 A respectively
( R(-r-r)< 1.0 ) and by annealing at 270 C for two hours is shown in
Bl
Fig.15. As the diffraction pattern shows, the area transmitted by the electron beam is essentially single crystalline. The samples that could be stripped off the substrate had diameters smaller than 150 ym. The entire surface of the samples was scanned and throughout this area the diffraction pattern remained unchanged. The crystallite size in the plane of the film will therefore be larger than 150 ym.
The diffraction pattern shows two strong MnBi reflections which are marked by arrows. These reflections are the same as those which were observed by Liu'*^ on MnBi films on glass substrates. The difference with Liu's obser-vations is that the specimen here is single crystalline whereas his sample was polycrystalline (crystallite size '^-1/3 ym) without an a-axis texture so that rings were observed rather than spots.
The MnBi reflections could be identified as the [l OO] and the ['''J ^^~ flections. The pattern is a 001 pattern, which means that the c-axis is normal to the surface, since the tilt was two degrees.
It was not possible to obtain electron microscopic pictures of the grain structure of the films. Replica techniques failed to give any information on relief in the film surface. When it is assumed that the crystallite size exceeds 150 ym, the replica results could be very easily explained
Mn
Bl
MrBi
Bl
Fig.15. a) Electron diffraction pattern of a thin MnBi/Bi film. Arrows indicate MnBi and Bi reflections, b) Model of film formation.
since at lowest magnification of the electron microscope (8000 x ) , an area of 12 cm (screen diameter) divided by 8000, or 15 ym is the maximum visible area.
The observations mentioned here are in contrast to those of Liu on MnBi films deposited on glass. This was to be expected since Bi films deposited on mica show a very strong c-axis and a-axis texture whereas Bi deposited on glass possesses a c-axis texture only and the orientation of the a-axis varies from crystallite to crystallite. Since the orientation of the Bi crystallites forms the basis for the final MnBi orientation, the Bi texture will determine the MnBi texture.
Unger et al.^'-' investigated MnBi films on mica by electron diffraction and found that both the c-axis and the a-axis are oriented throughout the film, with the c-axis pointing normal to the surface. The electron micrographs of the MnBi films showed grain sizes of approximately 0.3 ym.
4. PHENOMENOLOGY OF MAGNETIZATION REVERSAL
4.1. General
The concept of magnetic domains was originated with Pierre Weiss. He postulated that in a ferromagnetic material spontaneous magnetization always exists, but that its direction is different in different regions, the so-called domains.
Indirect experimental evidence for the existence of domains was found in the occurrence of the Barkhausen effect, i.e. when an applied field is continuously increased, discontinuous jumps in the magnetization of the magnetic body occur. These Barkhausen jumps were thought to originate with a rotation or reversal of the domain magnetization as a whole in the direction of the applied field, but later another reason was found in that the magnetic domains which are magnetized in the direction of the applied field - or have a component in that direction - grow at the expense of the domains with opposite magnetization. This domain growth is accomplished by a reversible or irreversible shift of the domain boundaries, the so-called domain walls, which separate the various domains.
Direct proof of the existence of domains is given by microscopic obser-vations employing the Faraday effect or the magneto-optic Kerr effect
(Sections 2.3 and 2.4).
The domain configuration of a magnetic body is determined by the reauire-ment of minimum total free energy. Several energy terms contribute to the
total free energy.
- The magneto crystalline anisotropy is the origin of a number of prefer-red orientations (easy axes) of the atomic magnetic moments. In case of uniaxial anisotropy a contribution to the total free energy density of
2 . 4 . 6
the form K,sin (f) + K„sin (t + K_sin * + is found where K. , K_, etc. are the anisotropy constants of the material and ij is the angle between the local orientation of the magnetization and the easy axis. - The exchange energy expresses that in a ferromagnetic material adjacent
contri-bution Aifif. will occur. A is the exchange stiffness constant and ij). . the angle between the neighboring moments.
- An energy contribution arises due to a distribution of free magnetic poles in the body. This magnetostatic self energy density is expressed as jH.M where M is the local magnetization and H, is the field which results from the free pole distribution (demagnetizing field). - Stresses in the material cause stress anisotropy energy terms. These
anisotropy terms are conveniently described as a uniaxial anisotropy 3 . . .
with anisotropy constant y Xa; Xis the magnetostriction coefficient and a the applied stress.
Since the magnetic moments are parallel inside the domains, there is no exchange energy contribution caused by the domains themselves. However, in the domain walls the magnetization rotates in a continuous manner from the direction of magnetization in one domain to the direction of magneti-zation in an adjacent domain. Therefore, a small angle exists between neighboring magnetic tr.oments in the wall. This gives rise to an exchange energy term. Also, the orientations of the magnetic moments inside the wall deviate from the easy axes and thus the vjall will contribute to the magneto crystalline anisotropy.
The energy stored in the domain walls is usually expressed as a domain wall surface energy density, i.e. the free energy contribution of a wall divided by its width. In calculations the domain walls are considered infinitely thin, carrying a surface energy density y.
4.2. Magnetization reversal in MnBi films
In a uniaxial material like MnBi, only two preferred directions of spon-taneous magnetization exist, along the crystalline c-axis and antiparallel to each other. In oriented MnBi films the easy axis is perpendicular to the film surface.
In MnBi films which are magnetically saturated (single domain) along the c-axis, a demagnetizing field 47rM = 8 kOe exists.
Whereas in NiFe films this field would easily be able to force the magne-tization to rotate from the direction normal to the surface to a direction in the film plane, - thus reducing the demagnetizing energy - it can"ot
force this rotation in MnBi films because of the large magneto crystal-line anisotropy.
If (}i denotes the angle between the magnetization M and the easy axis, the energy per unit volume of a single domain film in an applied field H , which is perpendicular to the film plane and which tends to reverse M, is given by (if is restricted to f0,iij):
E = K.sin (f + K„sin (fi + H M cosit) + ^H.M cos()i
1 t- 3. S Q o
(4.1)
w i t h H, = 4irM cose)). H i g h e r o r d e r a n i s o t r o p y t e r m s a r e n e g l e c t e d . The 2 2 s y s t e m i s a t s t a b l e e q u i l i b r i u m when (3E/3())) = 0 and (3 E/3<j) )> 0 and
2 2 a t u n s t a b l e e q u i l i b r i u m when (3E/3<^) = 0 and (3 E/3(t) ) < 0 .
~ = (2K, - 4TTM ^) s i n * cos<ti + 4K s i n (fi cos(ti - H M sin(}i = 0 ( 4 . 2 ) o (p 1 5 Z 3. S
which has a solution at sin* = 0.
2
• ^ =(2K, - 47TM ^) ( c o s ^ * - sin^<t>) + 12K„sin'^(|) cos (f
4 K . s i n H M cos(l); ( 4 . 3 ) At sine)) = 0 ( 4 . 3 ) r e d u c e s t o 3 ^ 34.^
^h
$ = 0 2K, - 4TTM - H M 1 s a s 2K, - 4TTM + H M 1 s a s ( 4 . 4 )which are negative when H > 77—' - 4ITM 2Kl / M
. M s 0 s < - r r - ' + 4ITM M s IT S ( 4 . 5 )
the film plane, an applied field which opposes M is unable to rotate the magnetization of the film in a uniform way out of the direction along
2K1
the c-axis unless its magnitude is larger than | — ' - 4TTM | , which is approximately 32 kOe in MnBi.
A further result of the calculations is that the demagnetizing field of the perpendicularly saturated film will neither influence the direction nor the magnitude of the magnetization.
sat
1 2 3 4 5 5
H ( k O e ) *•\
1.0
M.: I
J.
T
1 2 3 4 5 6
H(^e:
Fig.16. Typical hysteresis curves of MnPi films
The hysteresis curve of a thin MnBi film should show a nucleation field at H^ = (2K/M^ - 4ITM ) = 32 kOe. However, reported hysteresis curves of MnBi films on glass as well as on mica never show nucleation fields
larger than 10 kOe and observations reveal that H can be negative (See Fig.16). Moreover, MnBi films saturate in the easy direction at fields that are comparable to 4TIM . Therefore, it is improbable that the magne-tization reversal process of MnBi films is due to uniform rotation. The typical hysteresis loops of MnBi films presented in Fig.16 are characterized by a nucleation field H of low magnitude, which may be either positive or negative, i.e. parallel to M or opposing M respec-tively, by the coercive force H and by the saturation field H where
c sat M reaches M .
The small magnitude of the nucleation field is typical of a domain wall nucleation process. Microscopic observations immediately after nucleation reveal that labyrinths of reversed domains sprout into the film in order to demagnetize it. This means that at nucleation domain walls are indeed formed.
The process is illustrated in Fig.17. When the applied field, which is initially parallel to M of the saturated film, is decreased, nucleation occurs at H = H . Further decrease of H results in growth of the
re-a n re-a versed domain until at H = H the net magnetization is zero.
Fig.17. ^Magnetization reversal in an fMBi film with negative nucleation field.
In general several types of domain walls are possible. In cubic materials walls exist between domains whose magnetizations make angles of 72 , 90 ,
109 and 180 i;ith each other. The first three types are known as 90 walls, the fourth type as 180 walls. These various types of walls find their origin in the magneto crystalline anisotropy of cubic materials. In hexagonal materials - including MnBi - with a single easy axis, it is improbable that 90 walls will occur, since the magnetizations in the domains are preferably oriented opposite each other. Only when closure
domains occur at the surface of the film could a 90 wall be present. How-ever, it was shown by Kittel^^ that such closure domains will not exist
2
in uniaxial materials when K >> 2TrM . Since this relationship is fulfilled in MnBi,any domain wall in MnBi films will be a 180 wall and domain mag-netizations are always antiparallel to each other.
Magnetization reversal by domain wall motion at the fields considered here is only possible when reversed domains are nucleated at small nucle-ation fields. According to Brown^ , nuclenucle-ation in undisturbed crystals requires applied fields which are in the same order of magnitude as the nucleation field for uniform rotation, i.e. H = K /M . For MnBi films
' n u s
this would be lowered by 4ITM and result in fields around 10 kOe, opposite to the direction of magnetization of the saturated film. In fact, MnBi films show nucleation fields which are much lower and which can even be zero or in the direction of magnetization of the saturated film. This phenomenon can be understood qualitatively by assuming that film imper-fections (pin holes, Bi-inclusions) are the origin of perturbations in the uniform magnetization distribution of the saturated film.
Two cases can be distinguished now. 1) The nucleation of a reversed domain at such a perturbation requires a field which is larger than the wall motion coercive force H or 2) the required field is smaller than
c
H . In the first case the nucleated domain will grow immediately and magnetization is reversed by one large Barkhausen jump. The hysteresis
loop will be practically rectangular (Fig.l6b).
In the second case, the nucleus dimension will be stabilized by the coer-cive force and magnetostatic fields which arise from its structure. In this case, the hysteresis loop will be a conti4;iuous function of the applied field (Fig.16a).
5. DOMAIN GROWTH
5.1. General
Domain growth in MnBi films has been a subject of much attention and interest in literature during the past decade and more specifically during the past few years. Qualitative descriptions have been given by Chen et al.'*, Unger et al.^, Honda et al.'*^ and Kusuda et al.'*^. The first quantitative approach was given bv Honda et al.^^ and Ono et al.^" wno presented straightforward theories describing the stability of Curie point written cylindrical domains in MnBi films. It was Honda et al. especially who recognized that Curie point written spots were limited in radius by stability requirements which had already been formulated by Thiele'°, Bobeck'^ and Koov and Enz for application to soft
(H < 47rM /lOO) uniaxial films and platelets with perpendicular easy axes. The considerations in the preceding chapter show that MnBi films are to be regarded as normal uniaxial films with perpendicular easy axes. It will be shown that, in spite of the large coercive forces in MnBi films, the above mentioned theories can be easily applied to MnBi films. However, sometimes the general theories fail. The saturation field H ^,
° sat
for instance cannot be calculated within an order of magnitude.
An interesting phenomenon is nucleation of magnetization reversal which will be treated in Section 5.2. It is generally accepted that nucleation occurs at film imperfections. Knowledge about the nature of imperfections in MnBi films is poor. Therefore, nucleation fields cannot be calculated. However, domain growth immediately after nucleation can be described by a theory which was presented by Dekker and Van den Berg^. The results of this theoretical treatment lead to suggestions of a model of nucleation of magnetization reversal in MnBi films. A further result of the theory, which is confirmed by observations, is the fact that the width of the domains which grow after nucleation is determined by the coercive force rather than by the equilibrium of magnetostatic forces.
Domain growth rear M = 0 is described in Section 5.3. It is shox-jn that domain growth near M = 0 follows essentially the theory which was developed by Kooy and Enz'^ . Their theory can be applied to thin uniaxial films with
perpendicular easy axes whose domain patterns at M = 0 resemble a peri-odic parallel stripe domain pattern. Fig.18 shows this to be the case in MnBi films which are thicker than 1200 A and have low coercive forces. However, it appears that the resemblance of the actual domain pattern to the periodic parallel stripe domain pattern alters with decreasing thick-ness. Therefore, in thin films deviations between theory and experiments can be expected. These deviations become more severe with decreasing film thickness.
Fig.18. Resemblance of domain pattern in a 1200 A thick f4nBi film with a periodic parallel stripe domain pattern.
A theory describing the approach to saturation will be presented in Section 5.4. This process cannot be described by periodic parallel stripe domain theory''* or theories concerning cylindrical reversed domains'^ '^. Unger° suggested that the magnetization curves show the typical form of approach to saturation where the increasing demagnetizing field opposes the reversal of the very last oppositely magnetized domains. However, theoretically''* '^ '^ it can be shown that no reversed domains should exist in MnBi films at fields where they are still observed. Observations show that near saturation stripe domains still exist. Furthermore, experi-mental observations show that dM/dH decreases with applied field H .
a a This is in contradiction to periodic parallel stripe domain theory too.
However, it is possible to give a modification of this theory, which is based on the assumption that domain wall pinning prevents the vanishing of the stripes at high fields. This modified theory, together with
assump-tions on the distribution of pinning centers leads to a plausible inter-pretation of the approach to saturation.
5.2. Domain grov;th immediately after nucleation 5.2.1. Nucleation
As was pointed out in Section 4.2, nucleation of magnetization reversal in MnBi films occurs at low applied fields. The nucleation field of a specific MnBi film depends on the magnitude of the applied field which saturated the film even when the saturating field exceeded 4-ITM and reversed domains should no longer exist. The phenomenon was observed in a pronounced form by Dekker et al.'^ for an MnBi film which was held at a temperature of 250 ''c.
At room temperature the influence of the saturating field on the nucle-ation field is less. As Fig.19 illustrates, an increase of H by a
Fig.19. Dependence of nucleation field on saturation field. 1) H . = 13 kOe] 2) H =
10 kOe, 3) H ^ = 6 kOe. ^'^^
' sat
factor of two leads to a change in H of only a few tens of oersteds. The dependence of H^ on H can be understood when it is assumed that many similar lattice defects are present at whose sites similar
magneti-perpendicular easy axes whose domain patterns at M = 0 resemble a peri-odic parallel stripe domain pattern. Fig.18 shows this to be the case in MnBi films which are thicker than 1200 X and have low coercive forces. However, it appears that the resemblance of the actual domain pattern to the periodic parallel stripe domain pattern alters with decreasing thick-ness. Therefore, in thin films deviations between theory and experiments can be expected. These deviations become more severe with decreasing film thickness.
i
I*
Fig.18. Resemblance of domain pattern in a 1200 A thick l'4nBi film with a periodic parallel stripe domain pattern.
A theory describing the approach to saturation will be presented in Section 5.4. This process cannot be described by periodic parallel stripe domain theory''* or theories concerning cylindrical reversed domains'^ '^. Unger^ suggested that the magnetization curves show the typical form of approach to saturation where the increasing demagnetizing field opposes the reversal of the very last oppositely magnetized domains. However, theoretically ^ it can be shown that no reversed domains should exist in MnBi films at fields where they are still observed. Observations show that near saturation stripe domains still exist. Furthermore, experi-mental observations show that dM/dH decreases with applied field H .
a a This is in contradiction to periodic parallel stripe domain theory too.
However, it is possible to give a modification of this theory, which is based on the assumption that domain wall pinning prevents the vanishing of the stripes at high fields. This modified theory, together with
assump-tions on the distribution of pinning centers leads to a plausible inter-pretation of the approach to saturation.
5.2. Domain growth immediately after nucleation 5.2.1. Nucleation
As was pointed out in Section 4.2, nucleation of magnetization reversal in MnBi films occurs at low applied fields. The nucleation field of a specific MnBi film depends on the magnitude of the applied field which saturated the film even when the saturating field exceeded 4ITM and reversed domains should no longer exist. The phenomenon was observed in a pronounced form by Dekker et a l . ^ for an MnBi film which was held at a temperature of 250 °C.
At room temperature the influence of the saturating field on the nucle-ation field is less. As Fig.19 illustrates, an increase of H by a
sat
Fig.19. Dependence of nucleation field on saturation field. 1) H + - 13 kOe', 2) H , =
10 kOe, 3) H ^ = 6 kOe. ^'^^ ' sat
factor of two leads to a change in H of only a few tens of oersteds. The dependence of H^ on H^^ can be understood when it is assumed that many similar lattice defects are present at whose sites similar
