Magnetic and anisotropy studies in amorphous Co80-xHo xB20 alloys

Journal of Magnetism and Magnetic Materials 270 (2004) 99–103

Magnetic and anisotropy studies in amorphous Co _80x Ho _x B ₂₀ alloys

S. Sayouri ^a, *, O. El Marrakechi ^a , M. Tlem @ ani ^a,b , A. Kaal ^a , H. Lassri ^c

a

Laboratoire de Physique Th eorique et Appliqu ! ee, Facult ! e des Sciences Dhar Mahraz, B.P. 1796, F ! es Atlas, Morocco "

b

Laboratoire de Physique de la Mati ere Condens " ee et de l’Environnement, E.N.S., F ! es-Bensouda, Morocco "

c

Laboratoire de Physique des Mat eriaux et de Micro ! electronique, Universit ! e Hassan II, Facult ! e des Sciences, B.P. 5366, A ! . ın Chock, Route d’El Jadida, km-8, Casablanca, Morocco

Received 30 May 2003; received in revised form 27 July 2003

Abstract

The magnetization of melt-spun amorphous Co

Ho

B

alloys with (0 o x o 12), under magnetic fields up to 20 T, has been studied and the results obtained were analyzed based on the random magnetic anisotropy model. Addition of Ho has been found to decrease exchange and to enhance anisotropy.

r 2003 Elsevier B.V. All rights reserved.

PACS: 75.30.Gw; 75.50.Kj

Keywords: Amorphous alloys; Magnetization; Exchange and anisotropy constants; Co–Ho–B

1. Introduction

Amorphous transition metal (TM) and rare- earth (RE) alloys have been extensively investi- gated from the practical and fundamental points of view. The first studies related to these alloys showed that they exhibited several properties:

giant coercivity at low temperature [1], magnetic bubbles [2], etc., which make them suitable for new magnetic devices applicability. Besides, amor- phous TM–RE alloys have revealed a great variety of magnetic structures and phase transitions.

From the point of view of theory, competing exchange interactions, random magnetic anisotro-

py (RMA), and nearest environment of magnetic ions (generated by the effects of disorder) play essential roles in the determination of the magnetic structure of these alloys. Under the assumption that magnetic order is created by random aniso- tropy in the presence of ferromagnetic exchange (RMA considered as small compared with ex- change), a phenomenological model has been established to study amorphous ferromagnetism [3–5]. The analysis of the approach of the magnetization to magnetic saturation, based on the latter model, permits the determination of several magnetic parameters, such as the local random anisotropy constant, the exchange field and the ferromagnetic correlation length. Re- cently, magnetization studies have been performed on amorphous Co

Ho

B

[6,7]. The aim of

*Corresponding author. Tel./fax: 212-55-73-33-49.

E-mail address: sayouril@caramail.com (S. Sayouri).

0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved.

doi:10.1016/j.jmmm.2003.08.004

this paper is to study magnetic and anisotropy properties of these alloys and compare these properties with those of other TM–RE alloys.

2. Experimental details

Amorphous Co

Ho

B

alloys with 0oxo12 were prepared by melt spinning techni- que using a single roller in an argon atmosphere.

The amorphous state of the samples was verified by X-ray diffraction. The compositions of the alloys were determined by electron probe micro- analysis. Magnetization measurements were per- formed at 4.2 K in applied fields up to 20 T (at the SNCI, Grenoble). The Curie temperature, T _c ; of the a-Co

Ho

B

alloys was determined from the thermomagnetic data.

3. Results and discussion 3.1. Magnetic studies

Fig. 1 shows the variation of the magnetization of the alloys, at 4 K, as a function of the applied field, and Fig. 2 shows the Ho concentration dependence of the alloy moment. The magnetiza- tion decreases rapidly, with increasing Ho content, indicating the anti-parallel alignment of MT and RE moments, and a compensation of the moments occurs for about x ¼ 8: The alloy moment can be written as [8]:

m _a ¼ ½ð80 xÞm _Co xm _Ho =100; ð1Þ where m _Co and m _Ho denote the magnetic moments of Co and Ho, respectively.

From Fig. 2 and with the help of Eq. (1), the value of m _Co is calculated, for x ¼ 0; to be equal to 1.25 m

, which agrees well with the results pub- lished [9–11]. It is known that with the addition of RE metal, the MT moment decreases due to hybridization of the 5d and 3d orbitals. This decrease in Co moment can be considered as negligible for x o 5; as shown in the case of Er [9]

and Tm [12]. So, for x ¼ 3:6; the Co moment can be taken as 1.25 m

, and then m _Ho is calculated to be equal to 10.2 m

, which agrees with the

0 10 15 20

0 10 20 30 40 50

X=3.6 X=5.5 X=7.6 X=11.5

M (e.m.u/g)

H (T)

5

Fig. 1. Variation of the magnetization of amorphous Co

Ho

B

alloys, for different concentrations in Ho, as a function of the applied field.

0 2 4 6 8 10 12

µ

( µ

) µ

( µ

)

x

0.0 0.4 0.8 1.2

0.0 0.4 0.8 1.2

Fig. 2. Concentration dependencies of m

; the magnetic

moment of the a-Co

Ho

B

alloys ( m ), at 4 K, and, m

;

the magnetic moment of Co (’).

theoretical values (g

) of 10 m

and is close to the experimental value of 10.3 m

found in the literature [13]. This would indicate that the Ho spin structure is collinear on the first approxima- tion, and that the random anisotropy of Ho is rather small, although the ground state of trivalent Ho is

I 8 with a spin–orbit coupling. However, fields of about 3 T were necessary to saturate the samples which implies that some anisotropy is present, and therefore that the antiferromagnetic interaction between Co and Ho (J _Co2Ho ) is stronger than the random anisotropy. Such situa- tion has been observed for Fe–Ho–B alloys [14].

However, in amorphous Co–Er–B alloys the Er spin structure was found to be conical with a large average apex angle of about 82

, which was attributed to the strong random anisotropy of Er [9] and the antiferromagnetic interaction between Co and Er (J Co2Er ) which leads to a speromagnetic structure [15].

m _Co for other compositions may now be calculated based on the assumption that m _Ho is independent of x (Fig. 2).

3.2. Exchange constant

The exchange constant A can be calculated from the following expression [16]:

AðTÞ ¼ n HoHo J HoHo ½g _Tm 1 ² J _Ho ² ðT Þ ðx=100Þ ² =r HoHo þ ½n _CoHo þ n HoCo J CoHo ½g _Ho 1J _Ho ðT ÞS _Co ðTÞ ½xð80 xÞ=ð100Þ ² =r _HoCo þ n CoCo J CoCo S _Co ² ðT Þ

½ð80 xÞ=100 ² =r _CoCo ; ð2Þ

where n

is the maximum permissible number of atom pairs per unit volume extended to first neighbors (in our case, we take it to be 2), r

are the interatomic distances, which are taken to be;

r CoCo ¼ 0:25 nm, r CoHo ¼ 0:30 nm and r HoHo ¼ 0:35 nm, in accordance with the structural data of Harris et al. [17]. The temperature dependence of AðTÞ is essentially determined by the effective total momentum of an atom in sublattice i; J

ðTÞ:

J _Ho ðTÞ and J _Fe ðT Þ were assumed to be expressed by the Brillouin function:

J

ðT Þ ¼ J

ðg

m _B J

H

=k B TÞ; ð3Þ where g

and H

are the Land! e factor and the mean field at site i; respectively.

Values of J Co2Co and J Co2Ho deduced from this analysis (detailed elsewhere [7]) appear in Table 1.

From the same analysis, Idzikowski has deter- mined the values of exchange integrals relative to amorphous Co–Tb–B alloys [18]. The obtained values of J _Tb2Co are weaker than J _Co2Ho (This study), pointing out the strong effect of Ho compared with that of Tb. Reported values of J _Tb2Co and J _Co2Co [18] are also shown in Table 1.

The exchange constant A was calculated from Eq. (2). The magnitude of A decreases gradually with increasing Ho content, in conformity with the variation of the Curie temperature (Table 2). The variation of the exchange constant, A; as a function of Ho concentration at 4 K (Fig. 3), follows the approximate relation:

Aðx _Ho Þ ¼ 0:127x _Ho þ 3:43: ð4Þ

3.3. Random anisotropy studies

The approach to saturation of the magnetic moment in random anisotropy magnets has been

Table 1

Values of J

and J

; [18] and of J

and J

(This study) deducted from mean field analysis

Co–Tb–B [18] This study

x

J

(10

J) J

(10

J) x

J

(10

J) J

(10

J)

2 9.3 0.14 3.6 10.90 1.46

4 9.7 0.53 5.5 10.24 1.42

6 10.1 0.787.6 11.35 1.61

811.4 0.8 1 11.5 12.14 1.71

studied by F ahnle and Kronm . uller . [19]. They showed the presence of a 1/ O H-term in the saturation magnetization. Chudnovsky and Serota [4,20] have proposed a phenomenological model to interpret the approach to saturation. From this model, for applied fields less than the exchange field H _ex ; the magnetic moment is expected to show a linear dependence on H

: The following equation and relations describe this situation [4,20]:

M ₀ M ¼ M ₀ 15

H _s H

1=2

; ð5Þ

H _s ¼ H _r ⁴

H _ex ³ ; ð6Þ

H ex ¼ 2A

M 0 R ² _a ; ð7Þ

where H r is the random anisotropy field, and R a

the length over which the local axes show a correlation; indeed, the anisotropy directions are assumed to be randomly distributed beyond the characteristic length scale R _a ; where atomic short- range order takes place. We assumed R _a ¼ 1:0 nm [21]. Plotting M as a function of H

(Fig. 4), one can deduce M ₀ ; the value of the magnetization extrapolated to H

; and H _s (from the slope).

Knowing M 0 and A; H ex and consequently H r can be determined. H r is related to the anisotropy

Table 2

Magnetic parameters relevant to the a–Co–Ho–B alloys

x

T

(K) A (10

J/m) K

(MJ/m

) H

(T) H

(T) H

(T) l R

( A) (

3.6 470 1.82 1.11 1.2 8.7 5.3 0.22 203

5.5 465 1.781.23 3 13.3 9.1 0.25 157

7.6 435 1.56 1.39 24 38.6 34.4 0.32 95

11.5 370 1.23 1.52 15 6.4 7.9 0.45 49

2 4 6 8 10 12

K

(MJ/m

) A

A (10

J/m)

X

0.0 0.5 1.0 2.0 2.5

1.5

K

0.5

0.0 1.0 2.0 3.0

2.5

1.5

Fig. 3. Variation of the exchange constant, A, and the anisotropy constant, K

as functions of Ho constant, of amorphous Co–Ho–B alloys.

1.0 0.8

0.6 0

25 50 75

x=11.5 x=7.6 x=5.5 x=3.6

M (e.m.u/g)

H^-0.5 (T^-0.5)

Fig. 4. H

dependence of the magnets at 4 K of amorphous

Co–Ho–B alloys.

constant by [4,20]:

H r ¼ 2K L

M ₀ : ð8Þ

Table 2 shows the various parameters obtained from the analysis of the data using the models described. The variation of the anisotropy con- stant, K _L ; as a function of Ho content (Fig. 3), can be well fitted to the following expression:

K _L ¼ 0:051x þ 0:950 ð9Þ

which indicates that addition of Ho enhances anisotropy in Co–Ho–B alloys.

It is known that the magnetic behaviour of the random anisotropy system changes drastically with the value of the dimensionless parameter:

l ¼ ð2=15Þ ¹⁼² ðR ² _a K _L =AÞ ¼ O ðR _a =R _f Þ; ð10Þ where R _f is the ferromagnetic correlation length.

For the compounds considered, l o 1 (R _f becomes greater than R _a ) (Table 2), indicating ferromagnetic behaviour with high exchange and weak anisotropy.

4. Conclusion

We have studied the magnetic and anisotropy properties of (Co,Ho) B alloys. The magnetic structure of Ho moments is collinear and Co and Ho moments couple antiferromagnetically. The magnetic moment of Co decreases with Ho concentration (x) and compensation occurs at about x ¼ 8: The anisotropy constant K _L of the a-(Co,Ho) B alloys increases with Ho content.

Finally, the anisotropy studies show that these alloys are weak anisotropy ferromagnets.

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