Magnetic study in amorphous Fe67Y33 alloy

Magnetic study in amorphous Fe 67 Y 33 alloy

A. Hassini, A. Bouhdada, H. Lassri, and R. Krishnan

Citation: Journal of Applied Physics 90, 5253 (2001); doi: 10.1063/1.1412570 View online: http://dx.doi.org/10.1063/1.1412570

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constant K

has been extracted. A and K

are found to decrease with increasing temperature.

Experimental data show that the ferromagnetic correlation R

increases with increasing temperature.

© 2001 American Institute of Physics.

DOI: 10.1063/1.1412570

I. INTRODUCTION

Amorphous Fe ₁₀₀

Y

alloys represent a very interesting class of materials to study the influence of the structural dis- order on the basic magnetic properties. ^1–5 In particular, the transition-metal spin value, the exchange interaction, and the band structure are strongly changed as compared to their crystalline counterparts. It was hence interesting to see the influence of amorphous structure on the magnetic properties of Fe ₁₀₀

Y

alloys. Large magnetovolume effects such as a spontaneous volume magnetostriction and a forced volume magnetostriction were observed in those alloys. ⁶ The weak ferromagnetic moment and/or the occurrence of antiferro- magnetic interactions between Fe moments reveal important contributions of the local environment to Fe moments and to their magnetism.

Amorphous Fe ₁₀₀

Y

alloys have been known to show reentrant spin glass. ⁷ The magnetic properties are different depending on samples made by sputtering or melt-spinning methods. Samples made by the sputtering method show only the transition from paramagnetic to spin glass, ² but those made by the melt-spinning method show the transition of paramagnetic–ferromagnetic–reentrant spin glass for the samples with x ⬍ 40 and only the transition from the para- magnetic to spin glass for the samples with x ⬎ 50. ⁵ The de- gree of disorder depends on the the degree of the quenching speed, that is to say, on the difference of the methods of making specimens. The quenching speed in sputtering is higher than in melt spinning. Therefore, the change of mag- netic phases can be thought to occur corresponding to the degree of atomic disorder depending on the quenching speed.

Any technological process of preparation of amorphous sol- ids inevitably induces some coherent anisotropy K

. This K

can transform the correlated spin glass into a long-range fer

romagnetically ordered state similar to that in crystalline fer- romagnets.

Strong crystalline electric field interactions lead to a quenching of the orbital moment in cubic 3d metals. Under lower symmetry, 3d anisotropy may be large, as observed in compound Y ₂ Fe ₁₇ . ⁸ In amorphous systems, where the local symmetry is intrinsically low, a large magnetocrystalline an- isotropy is expected at the atomic scale. The random distri- bution of local principal axes suppresses this property at the macroscopic scale for ferromagnetic alloys. However, the fluctuations of the magnetization occur at a microscopic scale. In this case the local anisotropy may be deduced from the analysis of the approach to saturation magnetization.

The fact that Y is nonmagnetic also helps us to under- stand the results. In this work we describe the results of our studies in an amorphous Fe ₆₇ Y ₃₃ alloy prepared by the melt- spinning method and we will show that both the random magnetic anisotropy and the exchange interactions play an important role in the magnetic properties of the amorphous Fe ₆₇ Y ₃₃ alloy.

II. EXPERIMENTAL DETAILS

The amorphous Fe ₆₇ Y ₃₃ alloy was prepared by the melt- spinning technique in an argon atmosphere. The starting ma- terials were of purity better than 4 N. Argon ejection pressure of 2–5 kPa and a substrate speed of 35 m/s were employed.

The melt ejecting tubes were made of quartz glass with an ejecting orifice of about 0.4 mm in diameter. The ribbon samples were about 30 ␮ m thick with different widths vary- ing from about 2 to 4 mm. X-ray diffraction was used to verify the amorphous structure. Figure 1 shows the x-ray diffraction pattern of the melt-spun alloy. As can be seen from the figure, noncrystalline lines can be observed, but only a very broad peak around 2 ␪ ⫽ 40°. The exact chemical composition of the samples was determined by electron probe microanalysis. The magnetization was measured by the extraction method with applied field up to 100 kOe and in the temperature range 4.2–300 K.

a兲

Author to whom correspondence should be addressed; electronic mail:

[email protected]

b兲

Also at: Laboratoire de Magne´tisme et d’Optique de l’Universite´ de Ver- sailles, CNRS, URA 1531, 45 Avenue des Etats-Unis, 78035 Versailles cedex, France.

5253

0021-8979/2001/90(10)/5253/4/$18.00 © 2001 American Institute of Physics

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III. RESULTS AND DISCUSSION A. Exchange constant

In such materials the mean field theories do not always explain local magnetic excitations. For an accurate descrip- tion of the low temperature behavior of magnetic properties the spin wave theory can be used. The spin wave energy can be expressed by

h ␻

q

/2 ␲ ⫽ E ₀ ⫹ Dq ² ⫹ Fq ⁴ ⫹ ...,

1

where E ₀ Ⰶ Dq ² is the effective energy arising from dipole–

dipole interactions, q is the wave vector of the spin wave, and D and F are spin wave stiffness constants. Thus, it would be of interest to examine the low temperature behavior of our system.

According to the spin wave theory, the temperature de- pendence of the magnetization of ferromagnets is given by

M

T

M

4.2 K

M

4.2 K

⫽ BT ^3/2 .

2

Equation

2

is a good approximation of low temperature magnetization in both crystalline and amorphous ferromagnets. ^9,10 The parameter B introduced in Eq.

2

is related to the spin wave stiffness constant D by the following relation:

B ⫽ 2.612 g ␮

M

4.2 K

^{4 k ␲}

^D

^{3/2 ,}

³

where g is the g factor (g _Fe ⫽ 2), k

is the Boltzmann’s con- stant, and ␮

is the Bohr magneton. Furthermore, the ex- change constant follows from the relation

A

T

A

4.2 K

^M

^{M 4.2 K}

^T

²

⫽ M

4.2 K

D

2g ␮

^{M M}

^{4.2 K}

^T

^{2 .}

⁴

The temperature dependence of magnetization M is shown in Fig. 2 where M (100 kOe) is plotted againt T ^3/2 . We have adjusted experimental data by using Eq.

2

which allowed us to find the B value of about 11.5 ⫻ 10

⁵ K

^3/2 . The coef- ficient is used to calculate the spin wave stiffness constant D and the exchange constant A, which are found to be equal to 55 meV Å ² and 13 ⫻ 10

⁸ erg/cm ³ , respectively, at 4.2 K.

B. Random anisotropy constant

The shape of the magnetization curve approaching satu- ration can be analyzed by the law of approach to saturation given by ^11–17

M

H

M ₀

^{1 ⫺}

^{H ⫹ H a}

^{1/2 ⫹ H ex}

^{1/2 ⫺}

^{H ⫹ H a}

^{1 ⫹ H ex}

⫺ a ₂

共

H ⫹ H

⫹ H _ex

²

^{⫹ ␹ hf H,}

⁵

where H is the magnetic field in kOe, M ₀ is the saturation magnetization in emu/g, H

is the coherent anisotropy field, H _ex is the exchange field, and ␹ hf is the high field suscepti- bility. The a coefficients depend upon the amount of various structural defects and intrinsic fluctuations. According to Kronmu¨ller, ¹⁴ the first term a _1/2 /(H ⫹ H

⫹ H _ex ) ^1/2 can arise from point-like defects, from intrinsic magnetostatic fluctua- tions, and from randomly distributed magnetic anisotropy.

The second, well known ‘‘classical’’ term a ₁ /(H ⫹ H

⫹ H _ex ) and third term a ₂ /(H ⫹ H

⫹ H _ex ) ² are attributed to the magnetoelastic interaction of quasidislocation dipoles.

The straightforward method for obtaining the coeffi- cients would be by fitting the experimental curve with this full expression. But because of the large amount of coeffi- cients involved, the fitting procedure gave ambiguous results, i.e., the experimental curve could be fitted with more than one combination of coefficients with the same accuracy.

Moreover in direct fit some coefficients turned out to be negative without physical meaning. Therefore some reduc- tion in the amount of the coefficient was desirable. The high field susceptibility term is very small and has a negligible effect on the measuring range and could be omitted. The magnetization curves for all samples are found to fit Eq.

5

well as shown in Fig. 3, and the values of the parameters M ₀ , a _1/2 , a ₁ , a ₂ and (H _ex ⫹ H

) obtained from the fitting at different temperatures are listed in Table I.

FIG. 1. X-ray diffraction pattern of the melt-spun Fe

Y

alloy.

FIG. 2. T

dependence of the quantity

⫺ M (4.2 K)兴/ M (4.2 K) for the amorphous Fe

Y

alloy.

5254 J. Appl. Phys., Vol. 90, No. 10, 15 November 2001 Hassini et al.

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According to Chudnovsky’s model, ^{18 –20} the factors a _1/2 and a ₂ are related to the anisotropy field H

and the ex- change field H _ex by the relations

a _1/2 ⫽ H

²

15H _ex ^3/2

6

and

a ₂ ⫽ H

² 15 ⫽ 1

15

^{2K M 0}

^{2 ,}

⁷

where K

is the random local anisotropy.

From the same model, H _ex can be expressed as

H _ex ⫽

^{a a 1/2 2}

^{2/3 ⫽ M 2A 0 R}

^{2 .}

⁸

Knowing all the parameters a _1/2 , a ₂ , and M ₀ , one can evaluate H _ex , H

, and K

. It is seen that for our alloy, the random local anisotropy constant K

is 10 ⁷ erg/cm ³ at 4.2 K, which is larger than that of elemental Fe

K ⫽ 5.7

⫻ 10 ⁵ erg/cm ³ at 4.2 K

. This fact implies that the Fe orbital moment is incompletely quenched in the alloy. 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. ²¹ The value for K

deduced by us us- ing Chudnovsky’s model is in agreement with the value of the local magnetic anisotropy calculated by Fa¨hnle using a

semiempirical Hartree–Fock perturbation approach for the local spin-orbit coupling operator. ²² The temperature depen- dence of the anisotropy constant of Fe ₆₇ Y ₃₃ , presented in Fig. 4, shows reductions in K

with increasing temperature from 4.2 to 250 K.

From the H _ex and A mentioned above, it is possible to calculate the important structural parameter R

. From Chud- novsky’s model ²⁰ we can write

R

⫽

^{M 2A 0 H ex}

^{1/2 ,}

⁹

where we calculated R

⫽ 10 Å. One finds in transition metal rich alloys, generally, that R

is about 10 Å. The length R

is found to be practically independent of temperature. The an- isotropy directions are assumed to be randomly distributed beyond the characteristic length scale R

where atomic short range order takes place.

Finally, from H _ex and H

and with the help of the rela- tion

␭⫽冉

^{15 2}

^1/2

^{H H ex}

^⫽

^{15 2}

^1/2

^K

^{A R}

²

^,

¹⁰

the dimensionless parameter

was calculated.

plays an important role in distinguishing between the cases of strong anisotropy

1

and weak anisotropy

1

. It is found that in our alloy

1, which corresponds to a ferromagnet system with weak random anisotropy.

Experimental data show that the ferromagnetic correla- tion R

increases with increasing temperature

Fig. 5

. This behavior of R

can be understood in terms of the temperature dependence of variables on which R

depends according to

R

⫽ R

␭

² ⫽

^{15 2}

^{K A}

²

^{R 1}

^{3 .}

¹¹

IV. CONCLUSIONS

We have prepared the amorphous Fe ₆₇ Y ₃₃ alloy by the melt spinning technique and carried out the magnetization study. We have studied the magnetization of our amorphous

FIG. 3. Field dependence of the magnetization of amorphous Fe

Y

alloy at different temperatures.

FIG. 4. Temperature dependence of the local random anisotropy.

TABLE I. The values of saturation magnetization M

, factors a

, a

, a

and field (H

⫹ H

) for the amorphous Fe

Y

alloy at different tempera- tures.

T (K) M

(emu/g) a

(kOe

) a

(kOe) a

(kOe

) H

⫹ H

(kOe)

4.2 90 0.47 64 7 41

100 85 0.36 58 8 39

150 79 0.28 52 10 38

200 77 0.20 33 17 35

250 70 0.09 17 23 30

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alloy in terms of the spin wave theory, which allowed us to determine the spin wave stiffness constants D and the ex- change constant A. We have analyzed the high field magne- tization curve of the amorphous Fe ₆₇ Y ₃₃ alloy in the frame- work of the model of Chudnovsky et al. The results show several features

exchange field, random anisotropy field, ferromagnetic correlation length

all consistent with each other and in agreement with theoretical predictions. The Fe moment and the random local anisotropy decrease with in- creasing temperature. The exchange field is higher than that of the random anisotropy field, which corresponds to a fer- romagnetic system with weak anisotropy.

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5256 J. Appl. Phys., Vol. 90, No. 10, 15 November 2001 Hassini et al.

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