3108 IEEE TRANSACTIONS ON MAGIWITCS. VOL. 29. NO. 6. NOVEMBER 1993

Magnetic Moment Distribution at the Interface in Amorphous Ferrimagnetic Bilayers

G. Peral and J.L. Vicent Departamento de Fisica de Materiales.Facultad de Ciencias FiSicas.Universidad Complutense de Madrid. 28040 Madrid. Spain

J. M. Gonztilez Instituto de Ciencia de Materiales. CSIC. Serrano 144.28006 Madrid. Spain.

D. Givord hboratoire Louis N&l. CNRS. 166X Orenoble cedex. France.

Abstract. We have modelled, in the hmework o€ a mkmmag- netic approximation, the magnetization process of YCa, and GdCo, single layer f i b and of YCOJcdCo, bilayers (magnetic field applied perpendicular to the sur€ace of the €ilms). Our aim was the study of the influence of the interlayer exchange coupling in the magnetization proeess o€ bilayers. The results obtained from our model show an increase in the saturation fEH of each individual layer in a bilayer m compa- rison to the value of that field in the corresponding single films. Those result are in quantitative agreement with previous experimental data.

I. INTRODUCI-ION

Layered compositional structures can induce complex distributions of the magnetization which, in turn, originate novel and interestillg magnetization processes [ 1-31. In most of these samples this phenomenology is directly related to the occurrence of interlayer exchange coupling. The deve- lopment of realistic micromagnetic models describing the magnetization process of these films is very helpful to un- derstand in some detail the features involved in the interla- yer coupling. Regarding, more concretely, the amorphous RETM/RE'TM bilayers (where RE and TM are, respecti- vely, rare earth and transition metal elements) it is possible to find for some compositions (as, for instance, YCo jGdCo,) a macroscopic magnetization distribution which is often called "ferrimagnetic interlayer coupling" [2,3] (Le.: the magnetization of the YCo, layer point, at low applied fields, antiparallel to that of the GdCo, layer). In these samples, the particularities of the coupling are origina- ted by the following facts: a) the Gd and Co moments are coupled antiparallel [2] (Gd is a heavy rare earth), b) the to- tal magnetic moment of the GdCo, layer points along the Gd moment sense and c) the leading exchange interactions co- rrespond to the co-co pairs [4]. In a previous work [5], so- me of the authors have evidenced signifcant differences between the magnetization process of single layer YCo, and GdCo, films and those measured in the corresponding indi- vidual layers in a sandwiched structure. These differences were attributed to the occurrence of a Niel type wall at the interfacial regions. Manuscript d v d F & N ~ 15, 1993

Regarding this interpretation, we should point out that the description of the transition structure for the directions of the Co magnetic moments as a N k l wall is only appro- priate for fields of the order of the saturation field since, only in this range, the Co moments at both sides of the inter- face point antiparallel. Our goal has been the detailed exa- mination, using a micromagnetic model and covering the whole field range involved, of the influence of the magnetic moment structutes induced by exchange coupling on the magnetization process of layered films .

n. DESCRIPTION OF THE MODEL

The model was developed in the framework of the micro- magnetic approximation. Due to their dimensions, the beha- vior of the films can be well represented by that of a chain of Co magnetic moments perpendicular to the surface of the films (we considered, for instance, 400 moments to repre- sent the bilayer). This one sublattice description is based in the large antijmallel coupling between the Gd and Co mo- ments in the GdCo, layer (which is smaller only by a factor of 5 than the Co-Co exchange [6]). The total energy per unit area of the system, E,., (measured in a surface perpendicular to the chain of moments) included the following terms (whose explicit form is given for the case of a YCoJGdCo, bilayer): a) -PY energy, E,

E K = c i ~ E(1- sin2eisin2cpi) i-N

i-1 (1)

In this expression d is the interatomic Co-Co distance (2.5 A), the direction of the i-th magnetic moment is a function of two independent angles 8, and 'pi (e, is measured with res- pect to a direction perpendicular to the film surface and is zero when the magnetic moments point outwards that surfa- ce, cp, is measured with respect to a direction in the plane of the surface, see Fig. 1). We assumed [4] that a uniaxial in- plane magnetic anisotropy, described by the constant K = 8000 erg/cm3, was present in both layers (the local easy axes in the YCo, and GdCo, layers were considered to be parallel). b) Zeeman energy, E,

0018-9464/93$03.00 Q 1993 IEEE

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Here H is the applied magnetic field (similarly to the case of Hall effect measurements, the applied magnetic field poin- ted perpendicularly to the surface of the films , see Fig. l), M, =My- = 450Gauss [2] for 1 5 i 5 200 and M, = =

675 Gauss [a for 201 5 i 5 400. c) Exchange energy

i-N- I

i- 1 E- = [ i] c mi(ei,(Pi).mi+l(ei+l,(Pi+l) (3)

In this term A = 0.7 x lod ergcm-' is the exchange constant for the Co-Co interactions [2] (fmt neighbows considered only) and m,(e,, 9,) is a unit vector pointing parallel to the i-th mametic moment.

YCo layer Co moment

Co moment GdCo layer

Fig. I . Reference used to measure the orientation of the magnetic moments in our model. lke direction of the applied magnetic field and those of the

moments in both layers are also illustmted

We considered in this case that at the position of any magnetic moment in the chain an infinite plane, parallel to the film surface, was present. Inside these planes all the mo- ments were parallel and the plane can store a density of magnetic poles which will be proportional to the local value of the derivative of the magnetic moment orientation. Then, the dipolar energy was expressed by summing, over all the positions in the chain, the scalar products of the local mag- netization with the total field created by all other planes (for each plane this field is constant in modulus, proportional to the density of magnetic poles and directed perpendicularly to the surface of the film). The equilibrium configuration of the magnetic moments in the chain was evaluated, for a gi- ven value of the applied magnetic field, by minimizing with respect to the angles 8, and 9,. This was done numeri- cally using the steepest descent method.

m. RESULTS AND DISCUSSION

In Fig. 2 we present the moment distributions at the inter- facial region of a YCoJGdCo, bilayer evaluated for dif- ferent values of the applied field (since all the magnetic moment rotations occurred essentially in a plane only the angle 0, is plotted). These results evidence several in- teresting features. For instance, the minimum energy confi- guration of the chain of moments in zero applied field corresponds to parallelism between all the Co moments (that is the magnetization of the YCo, layer is antiparallel to that of the GdCo,). Upon application of a small field the torque acting on the moments at both sides of the interface origina- tes its rotation towards the field direction and the formation of a structure allowing the gradual transition for the direc- tions of the Co moments (the svucture is similar to a Niel type wall but here the angle formed by the Co moments at both sides of the wall is smaller than x for allfhe fields be- low saturation, see Fig. l).

f YCO,

2.00 u-

C 4 DISTANCE FROM THE INTERFACE (A) fig. 2 Field evolution of the distribution of Co moments at the interface as

evaluated from mr micromagnetic model of a YCoJGdCo, bilayer.

This structure is not symmetric with respect to the plane of the interface due to the different torques acting on the moments of the YCo, and GdCo, layers. For the same basic reason, the field evolution of the equilibrium configuration of moments is different at both sides of the interface. The consequences of these differences are illustrated in Fig. 3 where we present the field dependence of the width of the transition structure at the interface. In Fig. 3 it is possible to see how after an initial increase of the width two consecuti- ve maxima are reached. The fields for which these maxima occur coincide, to a good approximation, with the saturation field, H,, of YCo, and GdCo, single layer films as evaluated from the magnetization curves obtained from the equili- brium configurations of magnetic moments presented in Fig. 4. The equilibrium distributions of moments occurring in the bilayer at both maxima evidence that most of the moments (of the YCo, layer, in the case of the first maximum and of the GdCo, layer, in the case of the second one) reach para- llelism to the field direction at these fields. Since the trans- ition structure is basically originated by the balance between the exchange and Zeeman terms of the total energy and considering that for these particular distributions the total

3110

' 8 10600 . 20600 . 30 0 . 40bOO 50600 . 60-00 H 3 ! 0 e 1

Fig. 3. ~hiclare;s of the tlansition sttucmre for the directions ofthe co mo- ments present at the interfacial region of a YCoJGdCo, bilayer plotted as a

functim ofthe applied magnetic fEld.

energy of the system can not be lowered by further rotation of most of the moments towards the field direction, the sto- red exchange energy is distributed into a wider region which constitutes the origin of the increment of the thickness. For fields above the maxima the additional toque acting on the moments involved in the transition strucmre causes its pro- gressive decrease in width.

A WCo(indlrMual b p r in n bilayer lilm)

A YCo(dnqlr layor film)

ICo(rinql8 layor in a bilayer lilm)

O f ' 4000 . 8000 ' lZd00 . 16600 ' 20dOO H.,,dOe)

Fig. 4. Magnetization curves, evaluated by using the micromagnetic model, of single YCo, and GdC4 "s and of the YCo, and GdCo, individual la-

y- in a YCaJGdCo, bilayer.

The larger widths of the transition structure in the field range of the maxima are associatcd to a dimhution in the rate of increase of the component of the total magnetization parallel to the field direction and, therefore, to a significant increase of the field H, needed to saturate each individual layer .This quantity is used, if the anisotropy field H, of the sample is known, to obtain the saturation magnetization M, ftom Hall effect measurements through the relationship [7] H, - H, + 4xw. By comparing the magnetization curves shown in Fig. 4, it is possible to observe a difference (1 M ) B for both compositions) between the H, values calculated in single layers and individual layers in a bilayer. This

evaluation of the difference in the H, value agrees quantita- tively with previously reported [5] experimental results ob- tained in single layer YCo, and GdCo, films and in YCoJGdCoJYCo, sandwiches. These results are summari- zed in Table I.

TABLE I

Layer H, H, composition (single films) (individual layers in

sandwiches)

k G kOZ GdCo, 830 9.50

Y co, 5.80 6.80

IV. CONCLUSIONS

We have studied, by using a micromagnetic, model the magnetization processes of single layers of YCo, and GdCo, as well as that of a YCoJGdCo, bilayer. From our results, and basically due to the balance required between the ex- change and Zeeman terms of the total energy of the system, the occurrence of a transition structure for the directions of the Co moments at the interfacial region of the bilayers was shown. Furthermore, the calculation of the field evolution of that transition structure allowed us to quantify the increment of the saturation field originated, for the individual layers in the bilayer, by the interlayer coupling. This increment was in good quantitative agreement with previously published experimental results. From this comparison we can conclude that our one sublattice model was adequate to describe the magnetization process of the YCoJGdCo, bilayets and also, and more importantly, that in the evaluation, from Hall ef- fect data, , of the saturation magnetization of the individual layers in a layered structure an effective anisotropy term, re- lated to interfacial coupling should be included.

ACKNOWLEDGEMENT

G.P. and J.L.V. thank financial support from Doming0 Martinez Foundation.

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