THE CURIE TEMPERATURE OF ASYMMETRICALLY MODULATED FINITE SUPERLATTICES WITH RANDOM IRREGULARITIES

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THE CURIE TEMPERATURE OF

ASYMMETRICALLY MODULATED FINITE

SUPERLATTICES WITH RANDOM

IRREGULARITIES

W. Maciejewski, A. Duda

To cite this version:

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JOURNAL DE PHYSIQUE

Colloque C8, Supplkment au no 12, Tome 49, decembre 1988

THE CURIE TEMPERATURE OF ASYMMETRICALLY MODULATED FINITE

SUPERLATTICES WITH RANDOM IRREGULARITIES

W. Maciejewski and A. Duda

Institute of Physics, A. Mickiewicz University, 60-769 Poznali, Poland

Abstract. - The effect of t h e asymmetry of modulation and the irregularities in the layer thicknesses on the Curie temperature of the finite magnetic superlattice is studied. It is found that the asymmetry modifies the dependence of

TC on the structural characteristics of superlattice. Moreover, the Curie temperature is sensitive t o the presence of the irregularities, especially in superlattices with modulation profiles dominated by weakly magnetized layers.

The Curie temperature of compositionally modulated magnetic films has been calculated recently [I-31 for simple models, assuming the ideal periodicity of superlattice and the symmetric type of compositional modulation. Our aim is to analyse the films more fre- quently used in the experimental measurements [4, 51, namely the films in which the magnetic modulation is asymmetric and the lattice periodicity is perturbed due to the technology.

We consider the film as a layered finite system of magnetic binary alloy of atoms with the spins

sA

and

sB,

and the exchange integrals JAA, JBB and JAB (where S* J**

>

sB.JBB). The concentration of atoms

I I I I I

5 10 15 2 0

I -

Fig. 1. - The influence of the modulation wavelength on the Curie temperature for different degrees of the modulation asymmetry. The S.C. structure and (001 surface

orientation is assumed (s* = 1,

sB

= 0.5, J*' = 2.0,

J~~ = 0.2, JAB = 0.65, r = 10);

8 = 6kTc { (zo

+

2al) [ J**s*

(sA

+

1)

+

+JBBsB

(sB

+

1) ]

is square-wave modulated and therefore, two types of homogeneous layers can be distinguished in each supercell of the film: a strongly magnetized layer, rich in atoms A and a weakly magnetized layer, rich in

atoms B. Each supercell has a constant thickness I

( E = m + - p t ; t = 1,2,

...,

r ) , wheremt andpt denotethe thicknesses of strongly and weakly magnetized layers,

and t labels the supercell. The thicknesses mt and pt characterize the degree of the modulation asymmetry.

Within the molecular field approximation, the Curie temperature is determined as the highest eigenvalue of some tridiagonal matrix [3]. Figures 1 and 2 present

typical results of our numerical analysis concerning the influence of the asymmetry of modulation on the value of Tc. We find that with respect to the degree of asymmetry, the curves plotted in the figure 1 can reproduce both the strong increase of Tc with 1, obtained in some experiments (see e.g. [5]), and very weak sensitivity of Tc on I reported e.g. in [4]. Moreover, the asymmetry

of modulation can appreciably modify the dependence of Tc on the modulation amplitude (A), (see Fig. 2).

I I I

03 0.2 0.3 0.L 0.5

A-

Fig. 2. - The influence of the modulation amplitude on the Curie temperature for different degrees of the modulation asymmetry (the parameters are as in Fig. 1).

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C8 - 1688 JOURNAL DE PHYSIQUE

In particular, for the extremal asymmetry correspond- thicknesses. The thicknesses mt and pt fluctuate ing to the case where the strongly magnetized layer is around the average values m and p, with the maxi- reduced to the single atomic plane (m = I ) , the Curie mum deviation of At equal to

temperature becomes a nonmonotonous function of the modulation amplitude, with the minimal value lower than the Curie temperature of the homogeneous film (i.e. for A = 0). This peculiar behaviour can be related to the destabilization of magnetic ordering, caused by the vanishing of correlation between atomic planes en- riched in atoms A.

The next two figures illustrate the effects origi- nated in the perturbation of the superlattice periodicity, caused by some irregularities in the thicknesses of both types of layers. Figure 3 corresponds to the

case where the film contains one perturbed supercell with the thicknesses of its constituent layers equal to m' and whereas the thicknesses of all other layers are established to be m and p. The relative deviation of the thicknesses of the perturbed layers is described by the following parameter:

A = [ ( m l - m )

+

(P-P')]

/

1. ₍₁₎

Fig. 3. - The influence of the perturbation of one supercell on the Curie temperature for different values of the modu- lation wavelength (the parameters are as in Fig. 1). It is apparent that for A

>

0, the Curie temperature increases with increasing A, especially for superlattices with short wavelengths of modulation. Moreover, we find that the profile of the function Tc (A) does not depend on the position of the perturbed supercell in the film.

Finally, figure 4 concerns the closest-to-reality case where all layers of the film have randomly perturbed

6 = maxi {At). (2)

The results shown in figure 4 imply that the influence of the random irregularities on the Curie temperature is different in the two cases: for m

>

p, the value of

Tc

is practically insensitive to the parameter 6, whereas for m

<

p it strongly increases with increasing 6. Therefore, the irregularities in the layer thicknesses affect the Curie temperature mainly for superlattices with modulation profiles dominated by the weakly magnetized layers.

Fig. 4. - The Curie temperature as a function of the max- imum deviation of randomly disturbed thicknesses of all layers for different degrees of the modulation asymmetry (the paremeters are as in Fig. 1).

Acknowledgment

This work was sponsored by the Project 01.08 of the University of Lodz.

[I] Ma, H. R. and Tsai, C. H., Solid State Commun.

55 (1985) 499.

[2] Sy, H. K., Phys. Lett. A 120 (1987) 203. [3] Maciejewski, W. and Duda, A., Solid State Com-

mun. 64 (1987) 557.

[4] Kwo, J., Gyorgy, E. M., Mcwhan, D. B., Hong, M., Disalvo, F. J., Vettier, C. and Bower, J. E.,

Phys. Rev. Lett. 55 (1985) 1402.