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THEORETICAL INVESTIGATIONS ON MAGNETIC
SURFACE ANISOTROPY
P. Bruno, J. Seiden
To cite this version:
JOURNAL DE PHYSIQUE
Colloque C8, Supplbment au no 12, Tome 49, d6cembre 1988
THEORETICAL INVESTIGATIONS ON MAGNETIC SURFACE ANISOTROPY
P. Bruno and J. SeidenInstitut d'EIectronique Fondamentale, CNRS UA 22, B6t. 220, Universite' Paris-Sud, F-91405 Orsay Cedex, Fmnce
Abstract.
-
In order to explain the magnetic surface anisotropy (MSA) observed on Au/Co/Au sandwiches, we make theoretical calculations, in the frame of band theory. We also study the effect of roughness and of lattice mismatch between the film and the substrate, and show that they can give significant contributions to the MSA.In a thin ferromagnetic film, the total magnetic anisotropy energy may be written:
where V is the volume, S the area, Q the angle between the magnetization M and the normal to the plane,
Kg and Ks respectively bulk and surface anisotropy
constants.
RRcent ferromagnetic resonance experiments in our Institute revealed the presence of a large magnetic sur- face anisotropy (MSA) in Au/Co/Au sandwiches [I].
We discuss here the physical origin of the MSA. Fol- lowing NCel [2], in a perfect film this can be generally attributed to the symmetry breaking at the surface. We call this mechanism "magnetocrystalline surface anisotropy" (MCSA) and study it within the frame of band theory.
We then try to take into account the effect of rough- ness of real interfaces, showing that: (i) it induces a "dipolar magnetic surface anisotropy" (DMSA), which is always positive; (ii) it generally reduces the MCSA. Finally we estimate the effect of the strains induced by the lattice mismatch between ferromagnetic film and show that they may induce a L'magnetoelastic sur- face anisotropy" (MESA).
1. Magnetocrystalline surface anisotropy
We present here some results of a tight-binding cal- culation of the MCSA; details are presented elsewhere PI.
We calculated the MCSA for fcc (001) and (111) monolayers, whereas previous calculations were re- stricted to (001) orientation [4]. The results, displayed in figure 1, emphasize a few points: (i) as in reference [4], the calculated MCSA's are much larger than ex- perimental MSA's [I, 51; (ii) the MCSA varies with the orientation; (iii) the MCSA varies with the atomic number 2, i.e. with the filling of the 3d band; (iv) the calculated result is rather close to the experimental MSA for Ni(ll1) [5], but very far for Co (111) (= hcp (0001)) [I]. This is probably due to the strong ideal- ization of the model (perfectly flat unsupported mono- layer), which is thus too far from the experiment.
Fig. 1. - Calculated MCSA's for fcc (001) (squares) and fcc (111) (triangles) monolayers. Closed symbols: transition metals; open symbols: hypothetical intermediate systems.
-.
- 5 -
2. Effects of interface roughness
Co I
.
t t Ni Fe fi 0 fcc (001) A tcc(r11)Real samples always present some roughness, and it is important to take this into account in the theoretical treatment. We characterize it by the roughness a (the average deviation from the ideally flat surface) and the correlation length
E
(the average lateral size of flat areas on the surface). For our Co films, a=
2A
and E-50 161.In order to study the effect of roughness on dipo- lar anisotropy, we have calculated [7] analytically the magnetostatic energy of a film with periodic roughness, within the continuous medium approximation. Apart from the usual dipolar anisotropy
and due t o the appearence of "magnetic charges" at the ends of terraces, the roughness produces an in- plane demagnetizing field, giving rise to an additional dipolar energy
C8 - 1646 JOURNAL D E PHYSIQUE
where
1
-
exp (-z J(2n+
1)'+
(2m+
1)2)X (4)
(2n+ 1)'(2m+ 1)2 d ( 2 n
+
1)2+
(2m+ 1)' It is proportional t o the area S, and thus is actually a "dipolar magnetic surface anisotropy" (DMSA), which is always positive. For our Co samples, its amount is below 0.1 erg.cmd2, but for samples with large rough- ness this DMSA may be much larger.We treat the effect of roughness on magnetocrys- talline surface anisotropy within the N6el's model [6]. In this model [2] the MCSA arises from the asym- metric environment of surface atoms as compared to bulk ones. When some in-plane neighbours are miss- ing (at the ends of terraces) this asymmetry is some- what reduced; thus, roughness reduces the MCSA by an amount:
OKslKs
--
-2a/(. ( 5 )For our Co samples this reduction should be less than 20 %
,
but according to this theory, MCSA is strongly affected by large roughness.3. Magnetoelastic coupling to the substrate
Preliminary RHEED experiments on our Co films (mismatch Au/Co: q z -14 %) suggest that one Co monolayer is pseudomorphic on Au, and that the strain decreases with increasing Co thickness [8].
The accomodation of a mismatch q = (ad - a,)
/
a, between the substrate lattice parameter a, and the deposit parameter ad results from the competition between: (i) the strain energy: E, = V (112) C E ~ ;(ii) the energy of interfacial dislocations [9]. We have introduced the energy of interfacial dislocations phe- nomenologically, through an effective dislocation line tension ,u [lo]. The minimization of the total energy is then straightforward, yielding the general features
of experimental observations [9]; (i) below a critical thickness
tc P / (adC 1771) ((3
the film is pseudomorphic. (ii) above t,, E = -qt,/t. Via the magnetostriction, there appears a strain- induced anisotropy, proportional to E . Above t,,
the anisotropy is thus a linear function of l/t, and we may talk of "magnetoelastic surface anisotropy" (MESA). For our Co films on Au, this MESA is about 0.7 erg.cm-2, very close to the experimental MSA.
Therefore, beside a possible MCSA, there is proba- bly in our Go films a contribution arising from MESA, the other mechanisms (DMSA and reduction of the MCSA by the roughness) being almost inoperant be- cause of the low roughness of these films.
Acknowledgments
We are grateful to Dr. J. P. Renard for suggesting these studies, to Drs. C. Chappert and P. Beauvil- lain for providing the experimental background and for helpfull discussions, and to Dr. D. Renard for commu- nicating us her unpublished RHEED results.
[I] Chappert, C., Le Dang, K., Beauvillain, P., Hur- dequint, H. and Renard, D., Phys. Rev. B 34
(1986) 3192.
[2] NBel, L., J. Phys. Rad. 15 (1954) 376. 131 Bruno, P., Phys. Rev. B (in press).
[4] Gay, J., Richter, R., Phys. Rev. Lett. 56 (1986) 2728.
[5] Gradmann, U., J. Magn. Magn. Muter. 54-57
(1986) 733.
[6] Bruno, P., J. Phys. F 18 (1988) 1291.
[7] Bruno, P., J. A p p l . Phys. 64 (1988) 3153. [8] Renard, D., (1988), private communication. [9] Matthews, J. W. and Crawford, J. L., Thin Solid
Films 5 (1970) 187.
[lo] Chappert, C. and Bruno, P., Intermag-MMM 88,
