Local environment effects in Y2Fe14B-based compounds

187

Journal of Magnetism and Magnetic Materials 97 (1991) 187-192 North-Holland

Local environment A. Kowalczyk

effects in Y,Fe,,B-based

compounds

and A. Szajek

Institute o/ Molecular Physics, Polish Academy

of Sciences, Smoluchowskiego

I7/19,

60 - I79 Pornair, Poland

Received 18 September 1990; in revised form 21 November 1990

The influence of the local environment on magnetic properties of Fe atoms in Y2(FexM, _-x)14B (M = Si, Cr) is analysed in terms of the Jaccarino-Walker model. Each of the six inequivalent positions of Fe atoms having a specific local environment is treated independently.

we replace Fe atoms by some nonmagnetic or magnetic ones then we change the local environments of the atoms. This fact leads to a modification of the exchange interactions and to a decrease of the magnetic moments. That is the reason for considering the influence of the local environment on iron magnetic moments. The simple model of Jaccarino and Walker [9] is used for this purpose. In the next sections we shall consider the Jaccarino-Walker model in a generalized form adapted to the system and we shall present a discussion of the results.

1. Introduction The ternary rare earth-iron-boron compounds are of great scientific and technological interest. The R,Fe,,B compounds crystallize in a tetragonal structure of P4Z/mnm-type [l]. The R atoms are distributed on two different crystallographic sites, the Fe atoms on six different positions and B is located on one type of site. The number of neighbouring Fe atoms, as well as the magnetic moments are dependent on the crystallographic positions of an iron atom (see table 1). The experimental results and theoretical calculations for the compound Y,Fe,,B at 4.2 K reveal that the values of the magnetic moments on different atomic sites are not the same [2-S]. The Fe moment has a maximum value for the j, sites which are surrounded by 12 Fe atoms [2-81. When

2. Model calculations We have used the Jaccarino-Walker [9] model to analyse the local environment of Fe atoms in

Table 1 The parameters used in formula (4) taken from refs. [3-81. I

Position

nt

N,

1 2 3 4 5 6

k, k, jr

16 16 8 8 4 4

9 10 12 9 8 9

j2 C

e

0304-8853/91/$03.50

a, (x = 1.0)

121

141

[51

161

[71

181

2.07 2.23 2.43 2.31 1.90 2.28

2.25 2.25 2.80 2.40 1.95 2.15

1.63 2.16 3.20 2.64 3.18 0.90

2.41 2.11 2.74 2.16 2.28 2.32

2.16 2.47 3.08 2.50 1.60 1.80

2.36 2.62 2.61 2.35 2.31 2.11

0 1991 - Elsevier Science Publishers B.V. (North-Holland)

A. Kowalczyk,

188

A. Szajek

/ L.ocal enuironmeni

Y,(Fe,M,_,),,B (M = Si, Cr). Jaccarino and Walker have shown that in some materials the formation of a local moment on the transition metal atom is critically dependent on the number and kind of its nearest neighbours [9]. Applying this model to Nb, _,Mo,Fe alloys the authors [9] find the iron atoms become magnetic with a moment of 2.2~~ when they have at least seven MO atoms as nearest neighbours. Various developments of the Jaccarino-Walker model have been used for the study of the onset of magnetism in binary alloys as for example in Cu-Ni and Ni-Pt alloys [lO,ll]. This model was also used for more complicated pseudobinary compounds Gd(Co, Ni,_,), (MgCu,-type structure) by Burzo et al. [12]. Elemans et al. [13] used this model for the Th(Fe,_,Ni,), system having the hexagonal CaCu, type structure. The iron and nickel atoms have two inequivalent crystallographic positions, 3(g) and 2(g), having the number of nearest neighbours equal to 8 and 9, respectively. Since the 3(g) site occurs with the largest fraction the authors have used in calculations the number of nearest neighbours equal to 8 in both cases. Our purpose was to separate the contributions from the inequivalent crystallographic positions. In terms of the Jaccarino-Walker model the decrease of magnetic moment with decreasing x can be ascribed to a loss of moment in those Fe atoms that have an insufficient number of Fe atoms as their nearest neighbours. For each concentration x the probability of Fe atoms having n Fe atoms as nearest neighbours, out of a maximum number of N, is given by P(x,n,N)

=

N!

n!( N - n)!

x”(1 -X)?

(1) it is possible to calculate, for each concentration x, the number of Fe atoms that are surrounded by at least j Fe atoms as nearest neighbours from n=N P’(x)

magnetic

moments

=

P(x,n,N).

c

(2)

n=, Since Fe atoms having less than j nearest Fe neighbours are assumed to have no magnetic moment, one would expect the following expression for the average moment resulting from Fe atoms

F(x) =xP,(x)p(x=

1).

(3)

In our case the situation is slightly more complicated because there are six inequivalent positions of Fe atoms in the systems and substitutional atoms M can also carry magnetic moments. The contribution to the average moment from different positions could be treated independently. The generalized formula for an average magnetic moment for the compound at the iron concentration x, when the impurities can have magnetic moments is

ji(x)

=

,gl w:eb

&

N’

xc

]=z,

+

NFe

x

cN’ ,=w,

(I)

= 1)

I1 N

.’

x’(l

- x>;“/-i

J

l-x

6 c ,=,

N

WYb

1

.’

[ J

x’(l

=

1)

-x)+‘,

(4)

where

The number N is determinated by the crystal structure of a given series of compounds. With eq.

Table 2 The experimental

effects in Y,Fe,,B

for the Y,(Fe,M,

[;I

=n!/(m!(n-m)!);

_x)14B (M = Si, Cr) systems

(14,151

P [p&Fe atom1 in the systems

Concentration 100.0

96.40

92.90

89.30

85.70

78.60

YdFG% -xh4B

2.20 2.20

2.08 2.14

1.98 2.08

1.89 2.04

1.77 1.98

1.83

YAFe,Cr,

-x)~4B

x [W]

A. Kowalczyk,

189

A. Szajek / L.ocal environment effects in Y,Fe,,B

denotes all six positions of atoms usually described as: k,, k,, j,, jZ, c, e; is the number of Fe atoms which occupy “r the I position; pp(“) is the magnetic moment of the Fe(M) atom in the I position for x = 1 (for the pure system Y,Fe(M),,B); is the number of nearest neighbours of Ni iron atoms in the I position; are the smallest numbers of Fe atoms sur=I)WI rounding the I position necessary to support a magnetic moment at the site; z, if the Fe atom is at the position I and w, when the magnetic atom M is there. is the total number of Fe atoms in the unit NFe cell ( NFe = 56). For the nonmagnetic M atoms the local moments #(x = 1) = 0 so the second term in eq. (4) vanishes. All the parameters are collected in table 1. The experimental values of magnetic moments for the systems [14,15] are listed in table 2. 1

3. Results and discussion In figs. l-3 and 4 we present results obtained for Y,(Fe,Si, _,&B and Y*(Fe,Cr, _*)i4B, respectively. The best fit was obtained for the parameters presented in table 3 using the Miissbauer data of Fruchart et al. [2]. The mean magnetic moment on iron atom from the Mossbauer measurements

Table 3 The fitting parameters z, and w, for results presented and 2 using formula (4) I

1 2 3 4 5 6

Position

k, k, A j2

c e

in figs. 1

YAFe,Cr, 17cr

-AB

z/

= ‘i‘a I/

z,

w,

z,

w,

0 0 10 7 0 7

0 0 0 0 0 0

4 6 6 4 4 4

5 6 6 2 2 2

6 4 6 3 3 3

4 3 4 2 2 2

YAFe, Si,_,) 14B

c-Cr = 0.6~~ ji Cr = 0.7/.l,

I

100

095

,

0.90

1

085

080

075

X

Fig. 1. Mean magnetic moment per Fe atom vs. concentration x of Y,(Fe,Si, _x),4B. Circles - experiment, line - theory.

2.204~~ is very close to that obtained from the magnetization measurements 2.2~~ [14]. The results presented in fig. 1 for Y,(Fe, Si,_,),,B show that the iron atoms in the k,, k, and c positions do not lose magnetic moments even when the Fe atom is completely surrounded by the nonmagnetic Si atoms. For the other positions ji, j, and c the smallest numbers of nearest neighbours of Fe atoms required to have magnetic moment are 10, 7 and 7, respectively. In the case of low concentrations of the impurities it should be considered which of the sites are preferentially occupied. The 85.7% and 78.6% for Si and Cr mean 2 and 3 atoms compared to 14 iron atoms in the formula Y,Fe,,B. It is possible that the positions with z, equal to zero are not preferred by the silicon atoms in the case of low concentration of impurities. The schematic representation of the crystal structure is presented in fig. 2 and the behaviour of iron moments in the particular sites in fig. 3. Unfortunately the experiment was not able to give a definite answer to the problem. Recent Mijssbauer measurements of Pringle et al. [16] gave, within the experimental uncertainty, several possibilities: a) the silicon randomly occupies all sites, b) the silicon randomly occupies all sites except the Sj, site, c) the silicon occupies only 16k, and 16k, sites in a random fashion, d) the silicon occupies preferentially the 16k, and 8j, sites.

190

A. Kowalczyk,

A. Szajek

/ Local environment

I

100

effects in Y,Fe,,B

I

095

090

I

085

1

X

080

075

Fig. 4. Mean magnetic moment per Fe atom vs. concentration x of Y,(Fe,Cr, _x),4B. Circles - experiment, line - theory. The curve A - Cr assumed as nonmagnetic, B - mean magnetic moment on Cr atom is 0.7)~~.

Fig. 2. The schematic representation of the crystal structure of Y*Fe,,B (for detail explanation see ref. [24]). Black circles indicate k,, k, and c sites not preferred by the Si atoms.

Moze et al. [17] have shown using high resolution neutron diffraction powder samples, that the impurities (Mn and Cr) preferred the Sj, site. Table 3 and fig. 4 present results for Y,(Fe, Cr,_,),,B. If we assume, following ref. [18], the nonmagnetic behaviour of chromium atoms pFr = 0 the curve A in fig. 4 lies very distincly below the experimental points although all parameters z, are equal to zero. The chromium atoms surrounding

133 100

0.96

092

0.88

x

082

Fig. 3. Magnetic moment per Fe atom vs. concentration x in particular sites for Y2(FeXSi, _-x),4B and the fitting parameters from the table 3.

the iron ones cause decreasing of the iron moments but not to zero. The theoretical moment is too low in comparison to the experimental data. It means that an additional term in eq. (4) is lacked, which could increase the magnetic moment. The above analysis indicates that the chromium atoms presumably carry a magnetic moment. In order to increase the total theoretical moment towards the experimental value the mean magnetic moment of chromium atoms should be parallel to the mean magnetic moment of the iron ones. It is a well known tendency of chromium magnetic moments to take antiparallel orientation to the iron moments. Although in some situations, e.g. in amorphous Fe,_,Cr,,Zr,, alloys [19], the chromium moments can be parallel to the iron ones. Fe-rich regions contain two different local coordination structures, which produce both ferromagnetic and antiferromagnetic states below T,.In Fe-Cr alloys (ref. [20] and references therein) the antiferromagnetic chromium induces such behaviour on iron impurities. In our case there are six inequivalent positions and the above analysis does not mean that all of the chromium atoms should have parallel polarization of magnetic moments. In Y,Fe,,B the interactions between iron atoms situated at distances d < 2.5OA are negative and at d > 2.50 A are positive [21]. So a part of the chromium moments could be antiparallel but the average resultant moment of all chromium

A. Kowalczyk,

A. Szajek

/ Local environmenteffects in Y2Fe,,B

atoms should give a positive contribution to the magnetization curve. Generally it is possible to take into account the magnetic moments of the impurities in eq. (4) but then we should know the chromium moments (py # 0) in pure Y,Cr,,B, such data are not available from experiment because this system does not crystallize in the tetragonal structure. Certainly analysis of all possible orientations and values of magnetic moments in the six different crystallographic positions is not possible. Under some simplifying assumptions we have decided to estimate the contribution of chromium atoms to the resultant moment: 1) all of the chromium moments are parallel to the iron ones, 2) the contribution of the chromium to the mean magnetic moment from a particular site is the same (has the same weight) like in the case of iron contribution in Y,Fe,,B [2]. We considered a mean magnetic moment on chromium atom between 0.2 and 0.8~~. The best fitting was obtained for the mean moment jI = 0.6 and 0.7~~ on the Cr atom. The value from this range is the most probable. The increasing of the mean magnetic moment of chromium causes the increasing of the fitting parameters z, and w,. A larger magnetic moment needs more of the iron atoms as nearest neighbours. The largest values of z, and w, were obtained for the j, site which has the maximum number of nearest neighbours equal to twelve. The fitting to the experimental results was made in very narrow range of concentration x: 85.7 and 78.6% for Si and Cr, respectively. It was not possible to get the homogeneous one-phase systems for higher concentrations [14]. This is a severe limitation because the fitting was possible in the range of concentration x where the magnetization curve is very flat and the differences between theoretical curves are very small. Therefore only for higher concentrations the fitting is more reliable because the change of z, and w, parameters causes larger changes (see for instance ref. [22], fig. 4 or ref. [23], fig. 1) and an additional difficulty is that the average magnetic moment is a superposition of moments from the six different iron positions.

191

4. Conclusions In this paper we have presented the calculations of the influence of the local environment on the magnetic properties of Fe atoms in Y,(Fe, M,_,),,B (M = Si, Cr) using the JaccarinoWalker model. The results lead to the following conclusions: For Si substitution the Fe atoms in the k,, k, and c positions do not lose magnetic moments even being completely surrounded by the substituted nonmagnetic atoms. Perhaps these positions are not preferred by Si atoms. The chromium atoms (all or perhaps only some of them) should have magnetic moments and the resultant mean magnetic moment should be parallel to the iron one (in some sites the polarizations of chromium atoms could perhaps be parallel and antiparallel). The estimated value of the mean magnetic moment is 0.6-0.7~s on the chromium atom (assuming the proportional distribution of moments like for the iron moments in Y,Fe,,B) in the same crystallographic position.

Acknowledgements The authors are grateful to Prof. J.A. Morkowski for the stimulating discussions and critical reading of the manuscript. This work was supported by the Polish Academy of Sciences under the Project No. CPBP 01.12 (A.S.) and RPBP 01.8 (A.K).

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