Magnetic coupling in amorphous Co–Er films

Magnetic coupling in amorphous Co–Er films

J. Benjelloun, H. Lassri, L. Driouch, R. Krishnan, M. Omri, and M. Ayadi

Citation: Journal of Applied Physics 85, 1675 (1999); doi: 10.1063/1.369305 View online: http://dx.doi.org/10.1063/1.369305

View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/85/3?ver=pdfcov Published by the AIP Publishing

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Magnetic coupling in amorphous Co–Er films

J. Benjelloun and H. Lassri

Laboratoire de Physique des Mate´riaux et de Micro-e´lectronique, Universite´ Hassan II, Faculte´ des Sciences Ain Chock, B.P. 5366, Route d’El Jadida, km-8, Casablanca, Morocco L. Driouch and R. Krishnan

Laboratoire de Magne´tisme et d’Optique de l’Universite´ de Versailles, Batiment Fermat, 45, Avenue des Etats-Unis 78035 Versailles cedex, France

M. Omri and M. Ayadi

Laboratoire de Physique des Mate´riaux et de Micro-e´lectronique, Universite´ Hassan II, Faculte´ des Sciences Ain Chock, B.P. 5366, Route d’El Jadida, km-8, Casablanca, Morocco

~ Received 26 May 1998; accepted for publication 27 October 1998 !

Amorphous Co

Er

thin films have been prepared by rf sputtering and their magnetic properties have been studied. The mean field theory has been used to explain the temperature dependence of the magnetization. High-field magnetization studies performed at 4.2 K in magnetic fields up to 5.5 T on amorphous Co

Er

alloys have revealed, for samples with stoichiometry close to that of a compensated ferrimagnet, a magnetic behavior that is characteristic of a noncollinear magnetic structure of the Er and Co sublattices. From the noncollinear regime the exchange interactions between the Co and Er magnetic sublattices have been accurately evaluated. © 1999 American Institute of Physics. @ S0021-8979 ~ 99 ! 07803-2 #

I. INTRODUCTION

Amorphous rare-earth-transition-metal ~ R-T ! alloy films have been studied intensively for a number of years as eras- able optical disk memory media.

Amorphous R-T alloys represent a very interesting class of materials to study the influence of the structural disorder on the basic magnetic properties. In particular, the transition-metal spin value, the exchange interaction, and the band structure are strongly changed as compared to their crystalline counterparts. The field dependence of the magnetization of certain rare-earth based alloys, both crystalline and amorphous, shows interest- ing behavior when the applied field is sufficiently strong to break the antiferromagnetic coupling.

Based on a model proposed by Verhoef et al.

for the crystalline alloys several interesting magnetic parameters, such as the molecular field coefficient, the exchange field, etc., can be calculated. It has been shown by us that such a model is also valid for amor- phous alloys with random anisotropy.

In this work, we describe the results of our studies in amorphous Co

Er

alloys prepared by rf sputtering and discuss them in the con- text of conclusions published in the literature.

II. EXPERIMENTAL DETAILS

The amorphous Co

Er

films, with 6 , X , 23, were sputter deposited from a composite target using rf diode sys- tem. The starting vacuum was 10

Torr. The sputter gas was argon of 5 N purity. Water cooled glass substrates were used. The rf power was in the range 80–100 W and the argon pressure was fixed at 6 3 10

Torr. The film thickness was held at about 2500 Å. The magnetization was measured us- ing SQUID under fields up to 5.5 T and in the temperature range of 4.2–300 K.

III. RESULTS AND DISCUSSION

Results of the magnetization measurements are shown in Figs. 1 and 2 for the amorphous Co

Er

alloys. For all the compositions except for X 5 17.5 and 17.9, the magneti- zation shows a technical saturation and a small high-field susceptibility as shown in Fig. 1. However, for the two com- positions specified above, at the critical field H

, the anti- ferromagnetic coupling becomes unstable and is broken. For H . H

, a discontinuity in the slope of the magnetization curve is clearly seen and the field H

at which this occurs depends on the Er content. There is a clear correlation be- tween the value of the spontaneous magnetization ( m

) and the value of the transition field H

. Before discussing the high-field behavior, values for the Er and Co sublattice mag- netizations and the Er and Co atomic moments will be evalu- ated.

A. Magnetic moments

In Fig. 3, experimental results for the spontaneous mag- netization ~ expressed in Bohr magnetons m

) at 4.2 K are shown as a function of the Er concentration. The spontane- ous magnetization of the Co

Er

alloys rapidly de- creases showing an almost linear behavior. This rapid de- crease is associated with the antiferromagnetic coupling of the Co and Er moments. For lower values of the Er concen- tration, the resultant magnetization is directed along the Co magnetization, whereas for higher Er concentrations, the Er magnetization prevails. A compensation of the magnetization occurs for X 5 18.

In order to calculate the moment of Er ( m

), we fol- lowed the following procedure.

It is known that the Co mo- ment ( m

) diminishes when it is alloyed with a rare-earth

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0021-8979/99/85(3)/1675/4/$15.00 © 1999 American Institute of Physics

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metal due to the hybridization of the 3d and the 5d orbitals, but this effect is negligible for small concentrations. So we took m

5 1.72 m

obtained for the alloy with X 5 0 at 4.2 K, and assumed this to be the same in the alloy with X , 10.

Knowing the alloy moment ( m

) and using the relation;

m

~ T !5u M

~ T !2 M

~ T !u

5u~ 100 2 X ! m

~ T !2 X ^ m

~ T ! & u /100, ~ 1 !

we calculated ^ m

(4.2 K) & ^{to be 7} m

. This moment which is a projection along the applied field is smaller than the theoretical value (gJ m

) of 9 m

. This reduction could be attributed to the noncollinear and conical spin structure of Er. This phenomenon is the resultant of the strong random anisotropy of Er and the antiferromagnetic J

interactions which normally lead to a ‘‘sperimagnetic’’ structure.

Now Co moment for other alloys could be calculated based on the reasonable assumption that Er moment is independent of X.

The Co moment is found to decrease from a value of 1.72 m

for X 5 0 – 1.4 m

for X 5 22.5. The variation of the Co mo- ment with the Er concentration is shown in Fig. 4. The de- crease of the Co moment with the Er concentration can be understood as due to an increasing filling of the 3d spin-up band of the Co atom by the 6s

/5d conduction electrons of the Er atom. The cobalt moment, is found to have a power- law dependence on the Er concentration,

m

5 1.72 2 1.887 @ X/ ~ 100 2 X !#

~ 2 !

B. Temperature dependence of the magnetization The temperature dependence of the magnetization of the samples was studied and some typical results are shown in Fig. 5. For the samples with X , 18, it is seen that with in- creasing Er content as the temperature is lowered magneti- zation first shows a broad peak and then starts decreasing.

This decrease in the magnetization is due to an increase in the magnetization of the sublattice of Er. The magnetization compensation is seen clearly for X . 18. The compensation temperature is found to increase with increasing Er concen- tration as to be expected.

The sublattice magnetic moments of Co ( m

) and Er ( m

) were calculated using the mean field theory. According to Hasegawa et al.

and Mimura et al.,

the total spontane- ous magnetization m

can be approximated by the relation

~ 1 ! .

The sublattice magnetizations m

and m

are assumed to follow the Brillouin functions:

m

~ T !5 m

~ 0 K ! B

@ m

~ 0 K ! H

/k

T # , ~ 3a !

m

~ T !5 ^ m

~ 0 K ! & ^B

@ m

~ 0 K ! H

/k

T # , ~ 3b !

k

is the Boltzmann constant. The molecular fields H

and H

are given by

H

5 2J

Z

S

~ T ! /g

m

1 2J

Z

~ g

2 1 ! J

~ T ! /g

m

, ~ 4a !

FIG. 2. High field of the magnetization dependence for X517.5 and 17.9 at 4.2 K.

FIG. 3. Dependence of the spontaneous magnetizationmaat 4.2 K on the Er concentration X in amorphous Co1002XErXalloys.

FIG. 4. Dependence of the Co atom moment in amorphous Co1002XErX

alloys at 4.2 K on the Er concentration.

FIG. 1. Field dependence of the magnetization for Co1002XErX alloys at 4.2 K.

1676 J. Appl. Phys., Vol. 85, No. 3, 1 February 1999 Benjellounet al.

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H

5 2J

Z

~ g

2 1 ! S

~ T ! /g

m

1 2J

Z

~ g

2 1 !

J

~ T ! /g

m

, ~ 4b ! where J

, J

, and J

are the exchange integrals for CoCo, CoEr, and ErEr interactions, respectively, and Z

~ i, j 5 Co, Er ! is the number of nearest neighbors of the atom j for the atom i.

Using the m

values given in Fig. 4 and adjusting the exchange interactions J

and J

, the sublattice magne- tizations M

(T) and M

(T) and the total magnetization m

(T) 5 u M

(T) 2 M

(T) u can be calculated. From these fits the exchange interactions were extracted as a function of Er content ~ Table I ! . It is seen that J

increases and J

decreases, when the Er concentration increases. A similar increase in J

has been reported in intermetallic compounds and amorphous alloys also.

The Co–Er interactions de- pend critically on 3d – 5d hybridization according to Brooks et al.

Therefore the increase in J

would indicate an in- crease in the 3d – 5d hybridization when the Co concentra- tion relative to Er is decreased. The result of the calculation is shown in Fig. 5 where the calculated solid line agrees well with the experimental points.

C. High-field magnetization process

In the magnetization curve experimentally observed for the amorphous Co

Er

and Co

Er

alloys, there is a clear magnetic transition that separates two regions in the applied field scale. The differential susceptibility character- izing these two states is by at least one order of magnitude different. In Co

Er

, for instance, the differential suscep- tibility evaluated up to 3.5 T amounts to 0.006 m

/T, whereas after the transition to 0.0197 m

/T. Such a transition is not expected in systems with a sperimagnetic structure for

which a continuous and gradual approach to saturation, as- sociated with an increasing fan angle of the sperimagnetic structure, is expected. On the other hand, these magnetiza- tion curves resemble the curve of a ferrimagnetic compound.

In Fig. 2 one can see that for field higher than a critical value, the magnetization rises steeply and linearly. The above results could be analyzed in term of the existing model proposed by Verhoef et al.

as described below.

The molecular field coefficient n

is obtained as pro- posed by the model for the ferrimagnetic compounds from the slope of the magnetization curve,

d m

/dH 5 ~ n

!

. ~ 5 ! The critical field H

where the straight part of the magne- tization curve starts is given by the product of the resultant alloy moment m

and the molecular field coefficient n

,

H

5 n

u M

2 M

u . ~ 6 ! At sufficiently high fields, the second critical field is ex- pected when the Er and Co moments are aligned parallel and one should observe a plateau. This second critical field is given by the relation:

H

5 n

~ M

1 M

! . ~ 7 ! The exchange interaction J

~ the exchange parameter ap- pearing in a nearest-neighbor Heisenberg-type Hamiltonian ! can be obtained by the equation

J

5 n

g

m

2

N

/ ~ g

2 1 ! Z

, ~ 8 !

where N

is the number of 3d atoms per unit of mass and g

is the Lande´ factor. We find that the J

values derived from high-field magnetization measurements in agreement with J

values obtainable from an analysis of the tempera- ture dependence of the magnetization.

The magnetic phase diagram presented in Fig. 6 shows the dependence of the internal magnetic structure of these ferrimagnetic alloys on external fields. The concentration de- pendence of the lower critical field H

, above which a noncollinear magnetic structure appears, resembles very much the concentration dependence of the spontaneous mag- netization. The upper critical field H

, at which the forced ferromagnetic state is attained, is not observable in the avail- able field range.

IV. CONCLUSIONS

The magnetic properties of Co

Er

films were in- vestigated with respect to their compositional and tempera- ture dependence. The spontaneous magnetization was ana-

FIG. 5. Temperature dependence of the spontaneous magnetization for Co1002XErX alloys. The solid lines were calculated from the mean-field theory.

TABLE I. Magnetic characteristics at 4.2 K of amorphous Co1002XErXalloys.

X MCo(mB) MEr(mB) JCoCo(10²¹⁶erg) JCoEr(10²¹⁶erg) nCoEr(T/mB)

6.3 1.54 0.44 120 22.5 48.5

9.3 1.48 0.65 100 24 51.8

13 1.37 0.91 84 25 53.9

19.2 1.22 1.34 78 25.5 55

22.5 1.09 1.57 77 26 56

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lyzed in terms of the mean field theory. The Co moment and the exchange interactions J

and J

were evaluated.

We have observed in high magnetic fields a magnetic transition for some amorphous Co

Er

alloys that occurs in the field range up to 5.5 T for systems with low net mag- netizations. The occurrence of the transition can be under- stood within a model of two magnetic sublattices, formed by

the rare-earth and 3d transition-metal moments, as the for- mation of a noncollinear ferrimagnetic-like structure in high magnetic fields.

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FIG. 6. Magnetic phase diagram for amorphous Co1002XErXalloys at 4.2 K.

The full lines show the lower H₁^critand upper H₂^critcritical fields calculated within the two-sublattice model. CFI—collinear ferrimagnet, NCFI- noncollinear ferrimagnet, CFF—collinear field-forced ferromagnet.

1678 J. Appl. Phys., Vol. 85, No. 3, 1 February 1999 Benjellounet al.

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