Magnetic and Mössbauer studies of amorphous Fe72-xYxHo8B20 alloys

j R journal of

N magnetism

and

magnetic materials

ELSEVIER Jourual of Magnetism and Magnetic Materials 163 (1996) 353-359

Magnetic and MiSssbauer studies of amorphous F e 7 2 _ x Y x H O 8 B 2 0

alloys

R. Krishnan a , * L. Driouch a H. Lassri b, y . D u m o n d a A n t o n y Ajan c

S.N. Shringi c, Shiva Prasad c

a Laboratoire de Magn£tisme et d'Optique de Versailles, B&iment Fermat, 45 avenue des Etats-Unis, C.N.R.S. F-78035 Versailles, France b Facult£ des Sciences Ain Chok, Hay Yassemina lI, Rue 19 No. 5, 20150 Casablanca, Morocco

c Physics Department, Indian Institute o f Technology, Bombay 400076, India

Received 18 October 1995; revised 17 April 1996

Abstract , !

We have carried out magnetic and M~ssbauer studies of amorphous Fe72_xYxHo8B20 alloys. The Fe moment decreases with the addition of Y and a magnetic compensation occurs at 4 K for x = 16. The temperature and field dependences of the magnetization have been interpreted using the mean field theory and Chudnovsky's model, respectively. These analyses yield some interesting parameters such as the random anisotropy, the exchange interactions JFe-Fe, JFe-Ho, etc. The M~ssbauer studies show that the average hyperfine field decreases linearly with the addition of Y, in accordance with the decrease in the Fe moment.

Keywords:

Amorphous systems - alloys; Rare earth-transition metal alloys; Mtissbaner spectroscopy; Magnetization; Mean field theory ; Exchange integral

1. Introduction

A m o r p h o u s alloys based on rare earths (R) and transition metals ( T M ) and metalloids (B), such as T M - R and T M - R - B , show interesting magnetic properties and have been studied in the p a s t b y a n u m b e r o f authors [1-3]. One o f the fascinating behaviours in such alloys arises from the r a n d o m anisotropy which is the result o f the topological disorder present in these materials. S o m e theoretical m o d e l s have been d e v e l o p e d to calculate the r a n d o m anisotropy and related parameters from the analysis

* Corresponding author.

o f the approach to magnetic saturation [4,5]. A n o t h e r interesting p h e n o m e n o n is the effect o f high m a g - netic fields. W h e n the field is high enough, the antiferromagnetic coupling between the rare earth and transition metal moments starts to b r e a k down and o n e observes a remarkable increase in the m a g - netization. This b e h a v i o u r can be explained in terms o f a m o d e l originally p r o p o s e d for rare earth garnets [6], which was subsequently applied to intermetallic c o m p o u n d s b y V e r h o e f et al: [7], and later b y us to amorphous alloys [8].

In essence, a s the applied field B is increased, first teChnical saturation is reached, and with further increases i n B, a critical field Bcr 1 is reached at which the antiferromagnetic c o u p l i n g starts to' b r e a k d o w n and the magnetization begins to increase al- 0304-8853/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved.

PH

S0304-8853(96)00347-2

354

most linearly. The inverse of the slope which is the

molecular field coefficient (nRT) is related to Bor 1 by the relation

Therefore, when the alloy composition is close to the Compensa- tion of the moments, then Bcr ~ is very small, of the order of 1 or 2 T. As the applied field B is further increased, there is second critical field

which the rare earth and transition metal moments are aligned parallel to each other and one has a forced ferromagnetic structure. This critical field is equal to

+ MR I and is normally very high because one of the terms now is the sum of moments of TM and R. For the type of alloys discussed here, this critical field Bcr 2 is generally above 30 T or so. In order to decrease Bcr z, it is necessary to decrease the transition metal sub-network moment as much as possible.

In an attempt to find such alloys we examined the amorphous Fe72_xYxHOsB20 system. We chose Ho as the rare earth metal and fixed its content at 8%

because our earlier studies showed that this concen- tration was appropriate to observe

conveniently [9]. The idea of substituting Y for Fe is to bring down the Fe sub-network moment. It was also inter- esting to study the effects of non-magnetic Y on the properties, such as the Fe moment, the hyperfine field, etc. Our preliminary studies [10] under high magnetic fields showed however that while B~r ~ decreased as expected from the model, B~r 2 was still above 35 T, which is the upper limit of the field available. This aspect will not be discussed in this paper; rather, we will describe the results of our magnetization and MiSssbauer studies. We have ana- lyzed the thermal variation of magnetization in terms of the mean field model and the approach to mag- netic saturation using Chudnovsky's model, and have obtained several parameters such as the random ani- sotropy, exchange integrals, etc. We then discuss the M~Sssbauer studies.

2. Experimental details

The amorphous Fe72_xYxHo8B20 alloys with 0 <

x < 20 were prepared by single-roller melt-spinning technique under an inert atmosphere. The amorphous state was verified by X-ray diffraction and the com- position was determined by electron probe micro-

analysis. The magnetization was measured in the range 4 - 3 0 0 K, using a vibrating sample magne- tometer (VSM) under applied fields up to 2 T. The high-field data for H < 10 T were taken from our earlier work [10]. The Curie temperature (T c) was also determined using a VSM. The room-temperature and the 80 K MBssbauer spectra were taken in standard transmission geometry, using a 57Co(Rh) source. The low-temperature data were taken by cooling the sample in a liquid N 2 cryostat. A natural Fe absorber was used for the calibration.

3. Results and discussion 3.1. M a g n e t i c m o m e n t

We first consider the magnetization at H = 2 T.

Fig. 1 shows the Y concentration dependence of the magnetization ( M ) at 4 K, which decreases almost linearly with increasing x. Compensation is reached for x close to 16. This decrease in M arises to a large extent from the decrease in Fe sub-network magnetization due to the substitution of Fe by Y.

Besides, the hybridization between 3d orbitals of Fe and those of 4d of Y also leads to a decrease in the Fe moment /XFe, which can be calculated as follows.

The alloy moment (/x A) is given by the relation

~[L A = I ~Fo(72 - x) - ~Ho(8)1/100. (1) If we take /XHo = 10 /z B, as found in our earlier work [9], then we can calculate the value of /xFe from the experimentally determined value of /x A by

80

.9

60 40 20

0 [ I I I

0 5 10 15 20 25

X (Y)

Fig. 1. Y concentration dependence of the magnetization at 4 K.

R. Krishnan et al. / Journal of Magnetism and Magnetic Materials 163 (1996) 353-359 355

.=_

E o

2.5 ~ - i i i

/

2 1.5 1 0.5 0

0 5 10 15 20

x(Y)

Fig. 2. Y concentration dependence of/xFe at 4 K.

25

using Eq. (1). Fig. 2 shows the appreciable decrease in ]'£Fe with increasing Y content due to hybridiza- tion effects, as mentioned earlier.

3.2. Temperature dependence of the magnetization We studied the thermal variation of the magneti- zation for all the samples; as an example, Fig. 3 shows the result for x = 4.6. There is a sharp de- crease in M for T < 200 K due to the strong in- crease in the Ho moment, which opposes that of Fe.

We have analyzed these results using the mean field theory, as proposed by Hasegawa [11], which has been utilized by several authors in the past and is well documented. We recall the model briefly below.

The molecular fields Hno and

of the Ho and Fe sub-networks, respectively, can be written as HHo(T)

-- H + 2JSo_FeZHo_Fe ( gHo -- 1)SFe(T) /gno IZB + 2 JHo-HoZHo-Ho( gHo -- 1) 2

×].o(T)/g.o (2)

H F e ( T )

= H + 2JFe_FeZFe_FeSF¢(T )

/gFe tZS + 2JFe--HoZF~--Uo( gHo -- 1) Jno(T)

IgFo (3)

where the symbols have their usual meanings, and H is the applied field. The coordination number Z is generally taken as 12 for amorphous alloys.

We can further write the sub-network magnetiza- tion in terms of the Brillouin function, as follows:

SFe(T)

= SFe(0 K) Bs( gFe/ZB) SFe(0 K) HF~ ( r ) / ( k r ) ,

(4) ].o(r)

= Jno(0 K) Bj ( gno PCB) JHo( 0 K) Hno ( T ) / ( k T ) .

(5)

We made the reasonable assumption that SF~ is temperature independent in the range 4 - 8 0 K, in accordance with our earlier work on similar alloys but with Er [12]. This already enables us to obtain the temperature dependence of the Ho sub-network from Eq. (1). We also took the theoretical values for gFe, gHo, and for SFe, SHo we used the experimental values at 4 K. Using the above equations we made a theoretical fit by iteration of the temperature depen- dence of the magnetization, using JF~-Fe, JFe-no and ]no-no as adjustable parameters. This adopted standard has been used by many authors before. Fig.

3 shows the results for the composition with x = 4.6;

it can be seen that the calculated curve agrees well with the experimental points. Table 1 shows the various parameters obtained for the three composi- tions studied. The exchange integrals do not vary significantly with the addition of Y.

The Curie temperature can be related to the ex-

1.5

7.0

0.5

,~ o.o

- 0 . 5

- 1 . 0

- 1 . 5

MHo

Fig. 3. Temperature dependence of the magnetization of Fe67.4Y4.6 H08 B20 alloy.

356 R. Krishnan et al. / Journal of Magnetism and Magnetic Materials 163 (1996) 353-359 Table 1

Some fundamental parameters of Fe72_~Y~HosB20 alloys Y content JFe-Fe Jve-no T c (exp) T c (calc) x (10 -22 J) (10 -22 J) (K) (K)

4.6 5.5 2.2 480 500

10 6.0 2.2 393 385

15.2 6.6 2.4 300 287

change integral JF~-F~ using the mean field theory [13]. Neglecting JHo-Ho, we can then write

3 k T c = 2ZF~_F~Jr~_FeSF~( SF~ + 1). ( 6 ) So we calculated T c, knowing J F ~ - w obtained ear- lier and c o m p a r e d with the experimental values.

Table 1 shows that the agreement is satisfactory.

3.3. Random anisotropy

W e now describe the analysis o f the field depen- dence o f the magnetization under the f r a m e w o r k o f C h u d n o v s k y ' s m o d e l [4,5]. S o m e parts o f this sec- tion will be reported elsewhere, so we discuss this topic only very briefly for the sake o f completeness.

Two field regimes can be distinguished: (1) ap- plied fields smaller than the exchange field Hap p <

Hex, and (2) applied fields higher than the exchange field Hap p > H~x. The field dependence o f M for these two cases are as follows:

( Mo -- M ) / M o = ( 1 / 1 5 ) ( H s / H a p p )

for Hap p < Hex, ( 7 )

and

( Mo - M ) / M o = ( 1 / 1 5 ) [ H r / ( Happ -k Hex)] 2

for Hap p > H~x. ( 8 )

In Eq. (7) the slope H s = H4/H~3x, where H r is r a n d o m anisotropy field, which is related to the local r a n d o m anisotropy constant by the relation H r = 2 K ] / M o. F r o m the same m o d e l one can also relate Hex and the exchange constant A by the expression Hex = 2A/MoR2a, where R a is the length over which the local s y m m e t r y axes show a correlation. W h e n the local anisotropy field is smaller than the ex- change field, then one can relate the correlation

80

60

40-

20-

~ : ~ ° ° 0

O m i L i

4.6

10

0 i

0.2 0.4 0.'6 0.8

H-0.5( 102 Oe-0.5)

1.0

Fig. 4.

dependence of the magnetization M at 4 K for three samples with x = 0, 4.6 and 10.

length o f the ferromagnetic exchange Rf b y the relation

Rf = ( 1 5 / 2 ) ( A / K 1 ) 2 R~- 3. ( 9 ) The exchange constant A can be obtained from the m e a n field m o d e l p r o p o s e d by H a s e g a w a [11], and from the Curie temperature using the relation pro- p o s e d by H e i m a n et al. [13]. C o m b i n i n g the above models, we can extract several interesting fundamen- tal magnetic parameters, as described below.

To interpret our results we have used the first case which is appropriate. Fig. 4 shows the ( H ) - 1 / 2 dependence o f M for three compositions. The slight deviation from the linear dependence observed for the high-field region arises from the instability o f the antiferromagnetic coupling, as mentioned earlier [10].

Table 2 shows the various parameters obtained from the data analysis using the m o d e l s described. It is

Table 2

Exchange field, random anisotropy and other parameters at 4 K from Chudnovsky's model

Y content A (10 -s He× H r K, (10 7 Rf x erg/cm) (T) (T) erg/cm 3 ) (A)

0 453 12.5 4.3 0.9 833

4.6 273 22.3 5.7 0.8 578

10 161 15.6 13.8 1.1 153

R. Krishnan et al. / Journal of Magnetism and Magnetic Materials 163 (1996) 353-359

357 seen that for the alloy with x = 0, the r a n d o m local

anisotropy constant is 0.9 × 107 e r g / c m 3, which is about one-fifth o f w h a t we found for F e - E r - B - S i alloys for a similar Er concentration [14]. This indi- cates that the contribution to the anisotropy from H o is smaller than that from Er. It is also seen that Rf decreases strongly with decreasing F e content, which is to be expected, because the n u m b e r magnetic atoms are decreased.

3.4. Mi~ssbauer studies

A t r o o m temperature, only the s a m p l e s with x = 4.6 and 10 showed a six-line pattern, and the others with x = 13.7,15.2 and 20 showed a paramagnetic doublet M S s s b a u e r spectrum because the T c < 300 K. A t 80 K, o f course all the samples showed broad

O

:to! q

1°° 1 ~ " ~

°'1

98 97

x = 1 5 . 2 O

m

] " t x_-l.,

k,~ 9 8 :r2,~ . . . j~" : "

g 7 l g g 6 3 0 3 8 g 12

V e l o c i t y ( r a m / s )

Fig. 5. MSssbauer spectra at 300 K, for the samples with x = 4.6, I0, 13.7, 15.2 and 20, and the hyperfine distribution for samples with x = 4.5 and 10.

-12-g-6-8 0 8 6 9 12

V e l o c i t y ( r a m / s )

Fig. 6. M5ssbauer spectra at 80 K, for the samples with x = 4.5, 10, 13.7, 15.2 and 20.

patterns. Fig. 5 shows the r o o m - t e m p e r a t u r e M g s s b a u e r spectra for samples with x = 4.6, 10, 13.7, 15.2 and 20 at 300 K and the corresponding hyperfine field distribution for x = 4.6 and 10 as typical examples. Even though the samples with x = 13.7 and 15.2 are still magnetic at r o o m tempera- ture, we do not observe the six-line pattern for these because o f the large line widths involved. Fig. 6 shows the spectra and the hyperfine field distribu- tions taken at 80 K for all the samples studied.

The hyperfine parameters were obtained using the

W i n d o w ' s technique. The hyperfine field Hma x = 400

kG, where

goes to zero, was used in the

fitting procedure. The isomer shifts, line widths, and

the intensity ratio o f the second to the third lines

were o p t i m i z e d to give a m i n i m u m X 2. A line width

o f 0.35 m m / s , which is greater than the natural line

width o f F e (0.26 m m / s ) , has been used to take care

o f the quadrupole splitting (QS) distribution, which

was otherwise neglected in the analysis. The average

hyperfine field values are not found to be influenced

b y the choice o f line width. This was taken as

confirmation o f the correctness o f the given field

358 R. Krishnan et al. / Journal of Magnetism and Magnetic Materials 163 (1996) 353-359 Table 3

Hyperfine parameters for amorphous Fe72_xYxHosB20 alloys at 300 and 80 K

X Hay Hpeak IS QS b X 2

(kG) (kG) ( m m / s ) ( r a m / s ) At 300 K

4.6 145 160 0.008

10.0 69 76 - 0.002

13.7 - - -0.0446

15.2 - - - 0 . 0 4 4 6

20.0 - - - 0.0446

A t 8 0 K

4.6 196 210 - 0 . 0 3 10.0 161 139 - 0 . 0 5 13.7 144 149 - 0.03 15.2 124 63 - 0 . 0 4 20 100 57 - 0 . 0 3

- 2.6 1.035

- 4.0 0.921

0.60 2.103

0.62 1.285

0.62 2.136

2.0 1.056 1.0 i .045 1.1 0.886 0.5 0.959 0.12 0.881

values. The hyperfine parameters obtained at 300 and 80 K are given in Table 3.

The intensity ratio b = 2 is obtained if there is a random distribution of magnetic moments. However, when the samples are in ribbon form, different val- ues of b have been reported [15]. These are different from b = 2 because of various local anisotropies. It is only when M~Sssbaner spectra are taken on essen- tially powdered samples that b = 2 is justified [16].

Keller [15] has shown that even though the P(H)

may be distorted because of a poor choice of b, the value of Hay is independent of the choice of b.

Hence we expect Hay to be reliable.

200 ~ ~ a t 80K

~ " 150 ~ ~ ~ ~ ~ ~ > a t 300K

100

x

Fig. 7. Y concentration dependence of the average hyperfine field Hav at 300 and 80 K.

The variation of the average hyperfine field (Hav) with increasing Y concentration is shown in Fig. 7. It can be seen that H,v diminishes almost linearly with increasing Y content, and the rate of decrease of the hyperfine field in kG can be represented by the relation H , v = 2 2 2 . 3 - 6 . 1 1 x , where x is the Y concentration. This decrease is attributed to the de- crease in the Fe sub-network magnetization that arises from the hybridization of 3d orbitals of Fe with the 4d ones of Y, as pointed out earlier. Bara et al. [14]

reported M~issbauer studies on the amorphous YxFes0_xB20 system (without the addition of Ho as in our case) and found that the decrease in the hyperfine field with the addition of Y corresponds to a slope of 6.65 k G / % Y , which is slightly higher than our value. Although they did not specify which model they used to fit the spectra to obtain the distribution of hyperfine parameters, our results are still comparable. For x = 0, we found H~v = 225 kG, which is 55 kG lower than the value reported by Bara et al. [14], due to the presence of an additional 8% of Ho in our case.

4. Conclusions

We have prepared amorphous Fe72_xYxHO8B20 alloys by melt spinning and carried out magnetiza- tion and Mtissbauer studies. The magnetic compensa- tion occurs for x = 16%. The Fe moment decreases with increasing Y content. The various exchange integrals have been calculated using the mean field theory. The random local anisotropy of H 0 is close to 1 × 107 e r g / c m 3. The exchange field is higher than that of the random anisotropy field. The ferro- magnetic exchange correlation length decreases strongly with the addition of Y. The average hyper- fine field shows a linear decrease with Y and is in accordance with the decrease in the Fe moment due to hybridization effects.

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