Magnetic and random anisotropy studies in amorphous Fe76−xNixCr4B12Si8 (0⩽x⩽10)

Magnetic and random anisotropy studies in amorphous Fe \V Ni

V Cr B

Si

(0 ) x ) 10)

A. MoustamKde , R. Berraho , S. Sayouri *, A. Hassini

Laboratoire de Physique du Solide, Faculte& des Sciences, B.P. 1796, Fe%s Atlas, Morocco

Laboratoire de Physique des Mate&riaux et de Microe&lectronique, Universite& Hassan II, Faculte&des Sciences, B.P. 5366, An(n Chock, Route d'El Jadida km-8, Casablanca, Morocco

Received 16 October 1998; received in revised form 22 February 1999; accepted 30 March 1999

Abstract

We have studied the magnetization of melt spun amorphous Fe

\VNi VCr

B Si

alloys with (0)x)10) under magnetic"elds up to 1.45 MA/m, and have analyzed the results at 8 K, based on the random magnetic anisotropy model.

The presence of Cr seems to have a non-negligible e!ect on the local random anisotropy constantK

*and the exchange constantA. 1999 Elsevier Science B.V. All rights reserved.

Keywords: Magnetization; Random anisotropy; Fe}Ni}Cr}B}Si

1. Introduction

The investigation of iron-based amorphous alloys has revealed a number of properties that are of interest for theoretical studies and technical ap- plications. Amorphous alloys are very interesting for magnetic heads because of their magnetic soft- ness [1,2]. Considerable attention has been given to the e!ect of Cr and/or Ni addition on the magnetic, electrical and thermodynamic properties of Fe}Ni- based alloys [3}13]. In particular, Ni and Cr seem to be responsible for the decrease of the various magnetic characteristics (saturation moment, Curie temperature, exchange constant,2) of the alloys.

In order to understand the e!ects of disorder on magnetic phenomena, a great variety of amorphous magnetic alloys has been studied [14]. Of particu-

*Corresponding author.

lar interest have been the roles of competing ex- change interactions and random magnetic anisot- ropy (RMA) in determining the magnetic structure of the alloys. Theoretical research on magnetic or- der in disordered systems has thus concentrated on two di!erent approaches. The"rst one completely neglects the e!ects of random anisotropy assuming that magnetic order is created by random exchange only [15,16]. The second one assumes that mag- netic order is created by random anisotropy in the presence of ferromagnetic exchange [17]. A phe- nomenological model by Chudnovsky and Serota [18}20] based upon the latter approach has been used to derive all main properties of magnets with RMA small in comparison with exchange. In real- ity, the latter consideration can be applied to two groups of solids [19]. The "rst group includes amorphous alloys with concentration of magnetic atoms above the threshold for ferromagnetism. The second group includes polycrystalline ferromagnets

0921-4526/99/$ - see front matter 1999 Elsevier Science B.V. All rights reserved.

PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 0 1 6 6 - 0

consisting of very small monodomain crystallites.

The model by Chudnovsky and Serota has been used by several authors to interpret their results [21}24]. Amorphous alloys exhibit RMA due to topological disorder. In order to gather more in- formation about the magnetic properties and RMA of the Fe}Cr based amorphous doped with Ni, we have examined the concentration dependence of the magnetic moment per 3d atom, k, and have determined, adopting the RMA model, parameters such as the exchange constant, the local random anisotropy and the dimensionless parameterj(the ratio of RMA strength to exchange); the magnetic behavior of the random anisotropy being very sen- sitive to the value ofj.

2. Experimental details

Amorphous Fe\VNiVCrBSi (0)x)10) were obtained using a simple melt spinning tech- nique in pure argon atmosphere. The starting ma- terials were of the purity better than 4 N. The ribbon samples were about 3 mm wide and about 30}40lm thick. The amorphous state of the sam- ples was veri"ed by X-ray di!raction. The exact chemical composition of the samples was deter- mined by electron probe microanalysis. A vibrating sample magnetometer was used to carry out mag- netic measurements in "elds ranging from 0 to 1.45 MA/m at 8 K.

3. Results and discussion 3.1. Magnetic studies

Fig. 1 illustrates the magnetization M for four compositions (x"0, 1, 5, 10) at 8 K, as a function of external"eldH. Since the saturation had not been attained at 1.45 MA/m, the saturation magnetic mo- mentM

was determined atH

using theH\de- pendence [13,25]. Fig. 2 shows the concentration dependence of the magnetization M

at 8 K. The alloy momentkcan be deduced from the relation k"M

m

Nk , (1)

Fig. 1. Variation of the magnetization of Fe

\VNi VCr

Si B versus the applied"eld.

where N is Avogadro's constant, k the Bohr magneton, and m the molecular weight of the Fe\VNi

VCr B

Si

alloys. Fig. 3 shows the con- centration dependence ofkat 8 K. Thekvalue for x"0 (k"1.72k ) is smaller than that cal- culated in Fe

Si B

(k"1.93k ) [26]; the pres- ence of Cr has a destructive e!ect on ferromagnetic ordering present in these systems. Furthermore, the addition of Ni is known to decreaseklinearly in the range of Ni concentrations studied, as observed in similar compounds [26]. Concerning the mag- netic moment of Cr, con#icting values have been reported; in Ref. [27] a value of!4k has been assumed. This value of !4k could also "t the experimental data obtained by Krishnan et al. [5], who estimated this value inadequately taking into account the work of Hasegawa et al. [28] based on the coherent potential approximation leading to a value of 0.75k . Investigating the temperature dependence of the magnetic saturation polariza- tion, Macko et al. [11] have deduced a value of

!2.2k for the Cr moment, while the calcu- lations by Das and Majumdar [29], assuming that

Fig. 2. The Ni concentration dependence of the saturation mag- netic momentM

.

the decrease of the moment with the addition of Cr is due solely to the moment of Cr, led to the values

!1.5k ,!1.34k and!0.85k owing to three di!erent concentrations of Cr in the alloys studied.

In all these works, an antiparallel ordering of Cr magnetic moments with respect to the Fe and Ni ones has been assumed. In our case, to "t our experimental data (Fig. 3), we have assumed that the magnetic moments of Fe, Ni, and the number of electrons per atom donated to the transition metal (TM) d bands by Si and B atoms vary with TM composition [2]. The agreement between the ob- served data and the theoretical ones (solid curve Fig. 3) is very good (Table 2). We have found the value !2k for the Cr magnetic moment which agrees with that found in Ref. [11].

3.2. Random anisotropy studies

The approach to saturation of the magnetic mo- ment has been interpreted by ElsaKsser et al. [30]

Fig. 3. The variation of magnetic moment per atom 3d with Ni concentration.

and Chudnovsky et al. [19,31]. From these models [19,31], for applied "elds less than the exchange

"eldH, the magnetic moment is expected to show

a linear dependence onH\. From the slope, one can deduce the"eldHusing the equations [19,31]

M!M"M

15

H"H H

, (3)

whereHis the random anisotropy"eld. The local random anisotropy constantK

*is given by [19,31]

H"2K M*

, (4)

From the same model [19,31] one can also relate Hand the exchange constantAby the expression H" 2A

MR, (5)

Fig. 4. The Ni concentration dependence ofA.

Fig. 5. The Ni concentration dependence ofK

*. Table 1

Values ofAandK

*of Ref. [26] and those calculated from our experimental data

A(10\Jm\) K

*(MJm\) FeCr

Si B

28.6 2.64 FeSi

B

36 [26] 1.85 [26]

where R is the length over which the local axes show a correlation (typically 10 As) [26]. The ex- change constant can be obtained from the mean

"eld model proposed by Hasegawa [32] and from the Curie temperature using the relation proposed by Heiman et al. [33]

A" C2+k¹ S2+

4(S2+#1)r2+^}2+

, (6)

where C

2+ is the TM concentration and the in- teratomic distance r

2+^}2+ is taken as 2.5 As. We

found that the exchange constantAdecreases from 28.58;10\J/m to 26.61;10\J m\ when x increases from 0 to 10. It is known that the addition of Cr decreases¹

[9,11], itself related to A which is also in#uenced by this addition as observed in our case for x"0 compared to the value of A in Fe

Si B

[26] (Table 1).

The decrease of A follows the approximative law } 0.226x#29.8 which gives a value of 2;10\J m\for x"44 in agreement with the value 2.11;10\J m\ calculated in Ref. [11].

However, a few atomic percent of Cr seems to slightly enhanceK*as observed for the sample with x"0 (Table 1); therefore Cr contributes to the anisotropy of the system whereas Ni addition gen- erates the opposite e!ect, analogous to that ob- served in Fe}Ni-based compounds [26]. Figs.

4 and 5 show the concentration dependences of Aand K

*as functions ofx. It is known [31] that the magnetic behavior of the random anisotropy system changes drastically with the value of the

Table 2

The magnetic moment values calculated from our experimental data and those deduced using a model

x, Experimental data (ink) Model (ink)

0 1.72 1.73

0.5 1.71 1.72

1 1.70 1.71

2 1.69 1.69

3 1.67 1.67

5 1.64 1.64

10 1.55 1.54

Table 3

Experimental data relevant for the investigated samples x, M

(Am/kg) A(10\J/m) K

*(MJ/m)

0 160 28.58 2.64

0.5 159 28.50 2.63

1 158 28.35 2.61

2 157 28.21 2.60

3 155 28.03 2.57

5 152 27.70 2.53

10 144 26.61 2.42

dimensionless parameter j"

, (7)

where R

is the ferromagnetic correlation length.

For j(1 (weak anisotropy) R

becomes greater thanR. In our casejandR

are roughly constants in the range of concentrations studied (1R

2"

88 A,1j2"0.33) corresponding to a ferromagnetic system with high exchange and weak anisotropy.

Tables 1}3 summarise the results obtained from our experimental data.

4. Conclusion

We have examined the concentration depend- ence of the magnetic moment per atom 3d,k, and found that a value of!2k may be attributed to Cr assuming the variation not only of the magnetic moments of Fe and Ni but also of the number of

electrons per atom donated to the TM d bands by Si and B atoms. Adopting a model of random magnetic anisotropy, we have calculated the ex- change constantAand the local anisotropy energy K*. For the sample withx"0, the presence of Cr in#uences both A and K

*; it contributes to a de- crease of exchange and an enhancement of anisot- ropy. The evolution of these parameters forx'0 is similar to that observed in Fe}Ni-based com- pounds [26].

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