Magnetic and anisotropy studies in amorphous Fe82−xHoxB18 alloys

Journal of Magnetism and Magnetic Materials 267 (2003) 1–6

Magnetic and anisotropy studies in amorphous Fe _82x Ho _x B ₁₈ 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 (LPTA), 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 (LPMCE), E.N.S., F ! es-Bensouda, Morocco "

c

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

Received 8 October 2002; received in revised form 27 March 2003

Abstract

The magnetization of melt-spun amorphous Fe

Ho

B

alloys with 0 p x p 16 under magnetic fields up to 1.8 T has been studied, and the results obtained are analyzed based on the random magnetic anisotropy model. The exchange A and the local random anisotropy K

have been found to decrease with Ho concentration.

r 2003 Elsevier Science B.V. All rights reserved.

Keywords: Amorphous alloys; Magnetization; Exchange and anisotropy constants; Fe–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 exhibit several properties: giant coercivity at low temperatures [1], magnetic bubbles [2], etc.

Moreover, contrary to their crystalline analogs, amorphous TM–RE alloys have revealed a great variety of magnetic structures and phase transi- tions and, due to their possible production over a

wide range of concentrations, they offer a unique possibility to smoothly modify their basic mag- netic parameters.

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.

Competing interactions can be present in dilute alloys and in concentrated alloys. In the first group, they result from the oscillating long-range behavior of the RKKY interactions and from the distribution of distances between magnetic impu- rities. In the second group, on the other hand, they give rise to short-range ferromagnetic and anti- ferromagnetic exchange [3,4]. In particular, amor- phous ferromagnets are those in which ferromag- netic exchange dominates while amorphous alloys

*Corresponding author. Faculty of Sciences, B.P. 5541 Sidi Brahim Physics, F ES 30000, Morocco. Tel.: +6-212-55-73-33- "

49; fax: +6-212-55-73-33-49.

E-mail address: sayouri1@caramail.com (S. Sayouri).

0304-8853/03/$ - see front matter r 2003 Elsevier Science B.V. All rights reserved.

doi:10.1016/S0304-8853(03)00293-2

for which the sign of the exchange interaction between neighboring spins is random exhibit spin- glass behavior. In addition to the exchange interaction, the magnetic anisotropy plays a major role in magnetic ordering in both crystalline and disordered systems. In amorphous ferromagnets, the direction of the anisotropy randomly fluctuates from one magnetic atom to another one [5]. If the anisotropy energy is larger than the exchange energy, then the orientation of any spin is determined by the direction of local anisotropy [6]. In the limit of weak random anisotropy, the exchange interaction favors long-range ferromag- netic order, so there must be ferromagnetic clusters of spins over short distances. At large distances, weak fluctuations in spin orientation, due to the local random anisotropy, destroy long-range order [7–9]. Theoretical considerations have been based on two assumptions, the first assuming that magnetic order is governed by random exchange only [10,11] and the second assuming that mag- netic order is created by random anisotropy in the presence of ferromagnetic exchange [5]. The latter consideration has been adopted to establish a phenomenological model [12–14] to study amorphous ferromagnetism. This model has been used to derive all the main properties of amorphous magnets with RMA being small in comparison with exchange [15–19]. This latter consideration can, in fact, be applied to two groups of solids [13]. The first group includes amorphous alloys with concentrations of magnetic atoms above the threshold for ferromagnetism, and the second one includes polycrystalline ferro- magnets consisting of very small monodomain crystallites.

Several important magnetic parameters, such as the local random anisotropy constant, the exchange field and the ferromagnetic correlation length, can be obtained by analyzing the approach of the magnetization to magnetic saturation on the basis of the model mentioned above, proposed by Chudnovsky and Serota [12–14].

In this paper, we study magnetic and anisotropy properties of amorphous Fe

Ho

B

alloys with the help of this model, and compare these properties with those of other TM–RE alloys.

2. Experiment details

Amorphous Fe

Ho

B

ribbons with 0 p x p 16 were prepared by the usual melt- spinning technique in an argon atmosphere [20].

X-ray diffraction was used to check the amor- phous state of the alloys. No Bragg peaks were observed during the characterization. The exact chemical composition of the ribbons was deter- mined by electron probe microanalysis. The magnetization was measured between 6 and 300 K using a vibrating sample magnetometer (VSM), in applied fields up to 1.8 T. The Curie temperature was determined using a VSM with a furnace.

3. Results and discussion

3.1. Magnetic moments at low temperature

The concentration dependence of the magnetic moment of the a-Fe–Ho–B alloys at 6 K is shown in Fig. 1. The magnetization decreases rapidly with

0 4 8 12 16

0.4 0.8 1.2 1.6

Ho

Ho Fe Fe

x

(at. %)

0.5 1.0 1.5 2.0 Fe_82-xHo_xB₁₈

µ Fe ( µ B ) µ a ( µ B )

Fig. 1. Concentration dependence of m

and m

; the magnetic

moments of the a-(Fe, Ho)B alloys and Fe, respectively.

increasing Ho content, indicating the anti-parallel alignment of the TM and the RE moments. The alloy moment m _a can be written as [21]

m _a ¼ jð82 xÞm _Fe xm _Ho j=100; ð1Þ where m _Fe and m _Ho denote the magnetic moments of Fe and Ho, respectively. The magnetic moment, m _Ho ; of Ho can be calculated as follows [21]. For small concentrations (x p 4) of Ho, the moment of Fe is not significantly perturbed. So, taking the value of m _Fe ¼ 2:06 m _B obtained for the alloy with x ¼ 0 and substituting in Eq. (1), it is possible to determine m _Ho for x ¼ 4; whose value of 10:5 m _B agrees well with the theoretical value of gJm _B : Using the value of m _Fe ; m _Ho can be calculated for other compositions richer in Ho. It was found that m _Fe decreases from 2:06 m _B to 1:83 m _B when the Ho concentration increases from 0 to 14. This decrease in m _Fe is mainly attributed to the hybridization of the 5d and 3d orbitals.

3.2. Exchange constant

The exchange constant A can be calculated from the following expression [22]:

AðT Þ

¼ n HoHo J HoHo ½g _Tm 1 ² J _Ho ² ðT Þðx=100Þ ² =r HoHo

þ ½n _FeHo þ n _HoFe J _FeHo ½g _Ho 1J _Ho ðT ÞS _Fe ðTÞ ½xð82 xÞ=ð100Þ ² =r _HoFe

þ n FeFe J FeFe S ² _Fe ðTÞ½ð82 xÞ=100 ² =r FeFe ; 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 given by r _FeFe ¼ 0:25 nm, r _FeHo ¼ 0:30 nm and r _HoHo ¼ 0:35 nm, in accordance with the structural data of Harris et al. [23]. The temperature dependence of AðT Þ is essentially determined by the effective total momentum of an atom in sublattice i; J

ðTÞ:

J Ho ðTÞ and J Fe ðTÞ were assumed to be expressed by the Brillouin function

J

ðTÞ ¼ J

ðg

m _B J

H

=k _B TÞ; ð3Þ where g

and H

are the g

factor and the mean field at site i; respectively.

Using the values of J _FeFe and J _FeHo obtained in a previous study (Table 1) [24] and neglecting J Ho2Ho ; the exchange constant A was calculated from Eq. (2). The variation of A as a function of temperature is shown in Fig. 2. The magnitude of A decreases gradually with increasing Ho content, in conformity with the variation of the Curie temperature (Table 1). The variation of the exchange constant, A; as a function of Ho concentration at 10 K, follows the approximate relation:

Aðx _Ho Þ ¼ 0:127x _Ho þ 3:43: ð4Þ

0 200 400 600

0 1 2 3

T (K) A ( 1 0

J.m

)

x=16.2 x=13.7 x=10 x=7.6 x=4

Fig. 2. Temperature dependence of the exchange constant of amorphous Fe

Ho

B

alloys.

Table 1

Values of exchange integrals, and the Curie temperature of the a-Fe

Ho

B

alloys [24]

Alloys J

(10

J) J

(10

J) T

( 7 5 K)

Fe

Ho

B

5.8 1.30 600

Fe

Ho

B

5.66 1.08 520

Fe

Ho

B

4.70 1.14 490

Fe

Ho

B

4.69 1.17 430

Fe

Ho

B

4.14 1.22 380

The same behavior has been observed for amor- phous (Fe, Tm) alloys [18], for which A varies in conformity with the approximate equation Aðx _Tm Þ ¼ 0:126x _Tm þ 3:74: ð5Þ In both cases, A decreases, as a function of Ho and Tm concentrations, with the same slope (Fig. 3).

However, this decrease differs from that observed for (Fe, Gd)B alloys [25]; for these latter alloys, the variation of A follows the approximate law:

Aðx _Gd Þ ¼ 0:094x _Gd þ 4:536: ð6Þ The exchange decreases more rapidly in (Fe, Ho)B and (Fe, Tm)B alloys than in (Fe,Gd)B ones and Table 2 compares values of A for these alloys for similar RE concentrations.

3.3. Random anisotropy studies

The approach to saturation of the magnetic moment in random anisotropy magnets has been studied by F. ahnle and Kronm. uller [26]. They showed the presence of a 1= O H-term in the

saturation magnetization. Chudnovsky and Serota [13,27] 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 [13,27]:

M ₀ M ¼ M ₀ 15

H _s H

1=2

; ð7Þ

H _s ¼ H _r ⁴

H _ex ³ ; ð8Þ

0 5 10 15 20 25

1.5 2.0 2.5 3.0 3.5 4.0

4.5

Gd

Ho Tm

A ( 1 0

J/ m )

x

Fig. 3. Concentration dependence of the exchange constant, at low temperature, for (Fe, RE)B alloys, RE=Ho, Tm, Gd.

Table 2

Comparison of values of exchange and anisotropy constants of some (Fe-RE)B compounds

Composition A (10

J/m) K

(MJ/m

) Fe

Ho

B

(this study) 2.52 1.53

Fe

Tm

B

[18] 2.73 1.1

Fe

Gd

B

[25] 3.77 1.6

0.7 0.8 0.9 1.0

0 50 100 150

x=4

M (e.m.u / g)

H ^-0.5 (T ^-0.5)

x=8

x=10 x=16 x=14

Fig. 4. H

dependence of the magnetization at 6 K of

amorphous Fe

Ho

B

alloys.

H _ex ¼ 2A

M 0 R ² _a ; ð9Þ

where H r is the random anisotropy field and R a is 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 [28]. 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 constant by [13,27]:

H _r ¼ 2K _L M 0

: ð10Þ

Table 3 shows the various parameters obtained from the analysis of the data using the models described. It is seen that values of the random local anisotropy constant K L for small Ho content are larger than those of elemental Fe (K L ¼ 4:8 10 ⁴ J/m

at 300 K). This fact implies that the Fe orbital moment is incompletely quenched in the alloys. It is likely that a small but appreciable orbital moment of the relatively large Fe moment of the site is mainly responsible for the Fe sublattice anisotropy [29]. Els. asser et al.

[30] using electron theory, have reported a comparable value of K _L for amorphous Fe;

moreover, the estimated value of R _a (=1.0 nm, see Ref. [28]), used in our calculations, is supported by this agreement. The random local anisotropy of a-Fe–Ho–B alloys is smaller than that found for a-Fe–Er–B–Si alloys [17], which indicates that the contribution to the anisotropy from Ho is weaker than that from Er.

It is known that the magnetic behavior 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; ð11Þ where R f is the ferromagnetic correlation length.

For the compounds considered, lo1 (R f becomes greater than R _a ) (Table 3), indicating ferromag- netic behavior with high exchange and weak anisotropy.

4. Conclusion

We have studied the magnetic and anisotropy properties of (Fe, Ho)B alloys. The magnetic structure of Ho moments is collinear and Fe and Ho moments couple anti-ferromagnetically. The magnetic moment of Fe decreases with Ho concentration (x) and compensation occurs at about x ¼ 13: The variation of the exchange constant as a function of Ho concentration is similar to that of (Fe, Tm)B alloys, but is slightly different from that of (Fe, Gd)B alloys. The anisotropy constant K L of the a-(Fe, Ho)B alloys decreases with Ho content. Values of K L for the same concentration corresponding to (Fe, Ho)B, (Fe, Tm)B and (Fe, Gd)B are comparable (Table 2), but are smaller than those of (Fe, Er)BSi.

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

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Table 3

Magnetic parameters deduced from the approach to saturation for the a-Fe

Ho

B

alloys

Alloys M

(e.m.u/g) A (10

J/m) H

(T) H

(T) K

(MJ/m

) l R

Fe

Ho

B

128.7 2.96 6 3.5 1.56 0.19 270

Fe

Ho

B

67 2.52 11 6.5 1.53 0.22 202

Fe

Ho

B

39.5 2.03 15 9.7 1.34 0.24 171

Fe

Ho

B

12.8 1.64 37 27.4 1.21 0.27 136

Fe

Ho

B

34.6 1.45 12 8.6 1.03 0.26 146

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