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SOME RECENT ACHIEVEMENTS IN MAGNETIC THIN FILMS
L. Valenta
To cite this version:
L. Valenta. SOME RECENT ACHIEVEMENTS IN MAGNETIC THIN FILMS. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-15-C1-18. �10.1051/jphyscol:1971104�. �jpa-00213906�
SOME RECENT ACHIEVEMENTS I N MAGNETIC THIN FILMS
by L. VALENTA
Department of Theoretical Physics, Faculty of Mathematics and Physics of the Charles University, Prague, Czechoslovakia
R6sum6. - On presente ici un rksume bref de quelques r6cents succts, qui concernent la thkorie quantique des 61ec- trons dans les couches minces, l'anisotropie magnktique, dkformation du rkseau sur la surface de la couche mince, la thkorie et les mesures d'aimantation spontanke des couches ultra-minces, les sous-r8seaux dans les couches minces, le ((pinning 1) et la diffusion dans les couches minces.
Abstract. - A brief survey is given of some recent achievements concerning quantum theory of electrons in films, magnetic anisotropy, lattice distortion at the surface of films, theory and measurements of the spontaneous magnetiza- tion of ultra thin films, sublattices in films, pinning and diffusion in thin films.
In this review we will briefly sketch some of the present problems specific for magnetic thin films and the recent progress which has been achieved in attempts to clarify them.
I. A thin film is not only a small thin magnet but, first of all, a thin solid body. If its thickness is
-
10atomic layers or less it becomes a physically new subject and we are facing the problem to find its electronic structure and other properties. This problem has recently been and attacked by B.R. Cooper and A. J. Bennett [I] who have developped a theory of a fcc ultra thin film consisting of only a few atomic layers of d-band metal atoms. They used the tight binding approximation continuing the work prepared in the papers by E. T. Goodwin 121 and L. Kiinne [3].
The reason for the new properties of such ultra thin films is the contribution of the surface states whose participation in the physical properties of the specimen becomes comparable with that of usual states of the bulk material.
The appearance of the surface states depends, among others, on the crystallographic orientation of the nor- mal to the plane of the surface. It is also known that their appearance is enabled if we admit the existence of different constants (as the exchange and Coulomb integrals) in the surface layer.
One of the consequencies of the change of the density of electrons near the surface of the film is the appearance of the surface anisotropy which appears in more atomic layers than only one. Bennett and Cooper [4] have demonstrated it on a < 100 > Ni film using a simplified model for the d-levels to get at least a qualitative picture of the situation. The magnetic anisotropy has been introduced by means of a spin-orbit coupling term analogously to Brooks' theory of bulk materials. The numerical results are shown in figure 1. We see that the values of the surface anisotropy obtained are comparable with those obtai- ned by Nee1 [5]. It may also be seen that this new surface anisotropy varies with thickness in very thin films.
Reading the papers [l] and [4] we may see that the results have been obtained admitting some rather crude simplifications. Nevertheless, they seem to signal a new important direction of research.
11. As to the model used in [I] and [4] and, up to now, almost in all theoretical work, let us remark
FIG. 1. -Variation of the anisotropy energy per unit area with film thickness N for fixed film width Nz = N4 = 100.
Ksl and Ks2 are respectively the results of two methods of cal- culation. The short-dashed curve indicates the envelope of values for even N, and the long-cashed curve, the envelope for
odd N (after Bennett and Cooper [4]).
that there are some experimental and theoretical rea- sons to believe that a spontaneous distortion of the crystal lattice at the surface is to be expected. This distortion must also lead to surface effects which could be comparable with those discussed above. In such a situation a further step seems to be necessary, namely, a modification of the previous theory in the sense that we should find the equilibrium position of the atoms corresponding to the minimum (free) energy of the system. Unfortunately, this has not been done up to now. (Let us remark that an attempt to evaluate the lattice distortion, starting from another point of view, has been made by Corciovei et al. [6].)
111. The theory of films must be, in principle, the same as that of bulk materials. However it must be applied to situations which are quite different from that in massive specimens. It is necessary, therefore, to have a more precise information on the actual state of the film, especially on the 5-10 atomic layers near the surface. Unfortunately, this information remains still very unsatisfactory.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971104
C 1 - 1 6 L. VALENTA Despite of this situation the experimental as well as the theoretical work goes on. In theory a lot of results have been accumulated and are being produced in hope that the accepted model assumptions will either be confirmed in future, or will prove to be good enough. (Nevertheless, it is not quite certain, that such expectations will be fullfilled.) E. g. if we accept the existence and mathematical form of magnetic anisotropy, we may gbtain curves of spontaneous magnetization decreasing or increasing towards the surface or interface in multilayered films as demons- trated recently e. g. in a paper by Corciovei and Vamanu [7].
Ferchmin and Puszkarski [8] (see Fig. 2) have demonstrated on a film, consisting of only 10 atomic layers that for some range of the values of the aniso- tropy constants the magnetization may even have a locally nonmonotonous behaviour.
FIG. 2. - Variation of the local spontaneous magnetization MI across the film vs film thickness (I is the number of atomic layers) in dependence on the anisotropy parameter A. Mo is the magnetization a t T = 0, M is the average magnetization of the sample (after Ferchmin and Puszkarski [s]).
The most conclusive test of such theories may probably be given by experiments on ultra thin films.
Despite of the importance of such experiments only a few people have found interest or, may be, currage to do them. One of the singular points in this field are the experiments by Gradmann and his coworkers who report on measurements of films till to two- dimensional ones. As an example we give here the figure 3 taken from Gradmann and Miiller's paper [9] dealing with epitaxially evaporated Co films.
It is a pity that there is a lack of experiments of this kind in other laboratories. Gradmann's results may be either confirmed or modified, but if the discus- sion would approve these results, they would become of fundamental importance because they contain some quite hard statements against the present theory, or, more exactly speaking, against the theory of some special model.
We see again the necessity of a more precise know- ledge of the measured film. Because of the possible lattice distortion, surface roughness, discontinuities, inhomogenities etc. it is not excluded, or, maybe, probable, that both, theory and experiment, treat
FIG. 3. - Spontaneous magnetization vs temperature for cobalt films in dependence on the thickness DM (number of atomic
layers) (after Gradmann and Miiller [9]).
quite different subjects. It means that an agreement or disagreement of experiment with theory needs not necessarilly be accepted as an final answer to the problem.
IV. Many of the problems mentioned above are intimately connected with the magnetic anisotropy which seems to be still not investigated enough as to the various forms we may meet. E. g. recently Abaku- mov has discovered a new anisotropy phenomenon [lo] which he calls a (< decaying anisotropy >>. This anisotropy may be reversibly induced or eliminated regulating temperature. Abakumov connects its appea- rance with the contamination of the films through the residual atmosphere during deposition.
An other interesting observation has been reported by Soohoo [ l l ] who was able to demonstrate that in permalloy films deposited in magnetic fields H 5 10-I Oe the anisotropy gradually disappears with H -+ 0.
V. Let us say a few words to the concept of magne- tic sublattices which has been applied so successfully to ferrimagnetism and antiferromagnetism by Pro- fessor Niel.
If we take as a sublattice those atoms of the same kind which are in the same physical situation we may use the concept of sublattices for some reasonable situations also in films (see e. g. [12], [13], [14], [15]).
A recent application of a molecular field calculation with the generalized notion of sublattices has been made by Sukiennicki [I61 who has used it in an inves- tigation of the distribution of the spontaneous magne- tization in the neighbourhood of the interface between two adjacent ferromagnetic films in a coupled layer.
Since the molecular field calculations performed up to now have been made without inclusion of any anisotropy, which may easily be done, an improvement of such calculations may be expected. The crucial point
again is what kind and magnitude of the anisotropy should be used.
If we accept the idea of a film composed of a set of parallel atomic layers treated as sublattices we must expect that the spin waves in the film should contain both the acoustical and optical modes and some transient forms between them. This has been demonstrated explicitly in the past (see e. g. [17]) but in fact, it is now commonly being implicitly involved in the diagonalization procedure used in the spin-wave theory of thin films (see e. g. [7]).
The existence of such modes may independently be tested by computer calculation without any use of sublattices and the results confirm the previous ones as will be reported in more detail elsewhere [18], [19].
An other example of the use of the sublattice model may be found in the recent paper by Szczeniowski and Wojtczak [20].
VI. The lack of detailed information on the surface a t present gives rise to assumptions which may be quite controversial.
Let us take as an example the problem of pinning.
There is a lot of papers confirming or denying the existence of fully free or fully pinned spins at the surface and some mechanisms for effective pinning have been proposed. Unfortunately, none of them has brought the definitive solution u p to now.
To demonstrate the situation let us briefly mention two recent papers partly dealing with almost the same subject. The first of them is the paper by Okochi [21], the other one by Bajorek and Wilts [22]. Both have investigated permalloy films with 81 Ni-19 Fe (B. + W.j
and 83 Ni-17 Fe before evaporation (0.) in the fields t o 13 kOe, at the frequencies of 1-8 GHz (B. + W.) and 9.4 GHz O.), at room temperature. The films were 30-9 000 k (B. + W.) and 2 590 A (0.) thick and were prepared in a vacuum of 1 . 1 0 ~ ~ torr (B. + W.) and torr or lower (0.).
The theoretical basis used by the interpretation of the experimental results was in principal the same fenomenological theory. The apparent differencies are possibly in preparation in vacuum, in neglecting (B. + W.) or admitting (0.) eddy currents and in thick- ness measurements (by means of a 30 Hz hysteresis loop tracer calibrated with samples measured with a Tolanski multiple beam interferometer (B. + W.)).
Moreover, B. $. W. respected the surface roughness using the Schlomann correction for demagnetizing fields.
Now, as may be seen on figure 4 taken from [21], Okochi shows that his results obey the quadratic law for the resonance fields vs square of the mode number if we accept the assumption of completely pinned spins at the surface (Kittel's model) for the field inten- sities H above 4 nM and the field orthogonal to the film.
Contrary to this result, Bajorek and Wilts assert that they have explained for the first time uniquely the resonance spectra for both H parallel and perpen- dicular to the film by the excitation of unpinned spin wave modes. As one of the supporting arguments for this statement may be used their Table I demonstrat- ing clearly the preference of the unpinned case if they compare the product of the square of the thickness
FIG. 4. - Resonance field vs the square of the mode number P for a permalloy film of thickness 2 590 A in fields above
4~ M, HI film (after Okochi [21]).
of the film times the slope of the experimental curves for the applied static magnetic field vs mode number.
This situation demonstrates a challengeing dilemma in this field. Several times in the history of the problem it seemed that we have approached the solution of the problem of pinning. Nevertheless, it seems, that we have not yet reached it again.
In addition to the previous results, let us mention here some results obtained recently numerically for a one-dimensional Heisenberg model in the spin wave approximation for 40 and 60 atoms by Valenta, Vamanu and Havlasovd [19]. Their computed data show that chains with a rather strong positive or negative uniaxial anisotropy at the ends and interfaces a ) may have no pinned spins at the ends for both positive and negative surface anisotropy constant, b) some modes
Product of the square of the thickness of the film L2 and the slope of experimental curves for the applied static magnetic field us mode number for pinned and unpinned mode assignments (after Bajorek and Wilts 1221).
Pinned case Unpinned case
Film Slope x L2 Slope x L~
Thickness x lo-' G.cm2 x lo-' G.cm2
(A) - - -
845 1 714 2 585 3 500 1 424 3 240 5 180 6 990
C 1 - 18 L. VALENTA show effective pinning which is mode number depen- dent and the roles of the pinned parts may be mutually interchanged. c) Sometimes the spin-waves appear, due t o effective pinning only on a part of the whole chain.
And finally, d) some of the first resonance peaks, observable in this model, may be almost identical for both positive and negative surface anisotropy and the difference between them appears with higher modes.
If such experience proves t o be transferable t o real films it could help to clear u p some observed discre- pancies.
VII. The linear model gives a rather easy possibility t o investigate what happens if we admit the violation of a regular arrangement of binary crystals by diffu- sion. This has been studied by Valenta, Vamanu and Havlasova [18], [19]. What is apparent is the sensitivity of the spin wave resonance on the changes
caused by diffusion. I t may be seen that even a few diffused atoms may change the number and magnitude of the peaks, observable according t o this model.
Though it is not quite clear at present what changes are to be expected for threedimensional samples, it seems, that diffusion may be a source of uncertainly in the interpretation of observed resonance data in some cases.
Let us remark at the end, that in this short survey only some of the recent achievements in magnetic films have been mentioned and it remains t o apologize t o the authors of the many unmentioned important papers.
The background of this report was the author's, feeling that the further progress in films and small particles depends strongly on a better understanding of surface phenomena in particular and on the pro- gress in physics of thin or srnsll solids in general.
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1970, B 1, 4654.
r21 GOODWIN (E. T.). Proc. Cambridze Philos. Soc..
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1939, 35, 205 and 221 and 232. -
[3] KUNNE (L.), Czech. J. Phys., 1967, B 17, 894.
[4] BENNETT (A. J.) and COOPER (B. R.), to appear in Phys. Rev.
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[6] CORCIOVEI (A.), CROITORU (M.) and GRECU (D.), preprint, 1969, Institutul de Fizica Atomica, Bucharest.
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[8] FERCHMIN (A. B.), PUSZKARSKI (H.), preprint, 1970, to be published in the Proceedings of the IV.
Interriational Collo~uium on Magnetic Thin Films, Prague, September, 1970. -
[9] GRADMANN (U.) and MULLER (J.), preprint, 1969, submitted to publication in the Proceedings of the IV. International Colloquium on Magnetic Thin Films, Prague, September 1970.
[lo] ABAKUMOV (B. M.), preprint, 1970, to be presented at the IV. International Colloquium on magnetic Thin Films, Prague, September 1970.
[ I l l S o o ~ o o (R. F.), preprint, to be published in .the Proceedings of the IV. International Colloquium on Magnetic Thin Films, Prague, September 1970.
[12] VALENTA (L.), Izv. Akad. Nauk, ser. Jiz., 1957, XXI 879.
[I31 VALENTA (L.), Phys. Stat. Sol., 1962, 2, 112.
[14] S o o ~ c o (R. F.), Magnetic Thin Films, 1965, Harper
& Row, New York, Evanston and London, Sec. 6. 2 c).
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[I61 SUKIENNICKI (A.), preprint, 1969, to be published in the Proceedings of the IV. International Collo- quium on Magnetic Thin Films, Prague, Sep- tember 1970.
[17] VALENTA (L.) and WOJTCZAK (L.), 2. Natuvforschg., 1967, 22a, 620.
[I81 VALENTA (L.), VAMANU (D.) and HAVLASOVA (H.), paper presented at the international Conference on Magnetism, Grenoble, September 1970.
[19] VALENTA (L.), VAMAN~J (D.) and HAVLASOVA (H.), submitted to publication in the Proceedings of the IV. International Colloquium on Magnetic Thin Films, Prague, September 1970.
[20] SZCZENIOWSKI (S.), WOJTCZAK (L.), Acta Phys. Polo- nica, 1969, XXXVI, 241.
[21] OKOCHI (M.), J. Phys. Soc. Japan, 1970, 28, 897.
[22] BAJOREK (C. H.) and WILTS (C. H.), preprint, 1970, Calif. Inst. Technol.
