Hyperfine Interactions 62(1990) 199-206

199

FERROMAGNETIC LAVES PHASE INTERMETALLICS DOPED WITH SP IMPURITIES: A MOSSBAUER STUDY OF Zr(Fe I .xSi)2 C.M. da SILVA Departamento de Fisica, UFSM, Santa Maria-RS, Brasil J.B. MARIMON da CUNHA, F.P. LIVI Instituto de Fisica, UFRGS, P.O. Box 15051, 91500 Porto Alegre-RS, Brasil and A.A. GOMES Instituto de Fisica, UFRGS/CBPF-RJ, Brasil Received 5 March 1990 (Revised 20 July 1990)

The effect of Si on the hyperfine parameters of the pseudobinary compounds Zr(Fe I _xSix) 2 is studied by M6ssbauer spectroscopy in the C15 phase (x _<0.17). In these pseudobinaries, two magnetic sites of the pure compound coexist with a third site associated with the impurities. The local effects in Zr(Fe,Si)2 are qualitatively discussed, together with the observed trends of the hyperfine parameters. A comparison with Zr(Fe, A1)2 compounds is also presented.

1.

Introduction

Ferromagnetic Laves phase psuedobinary compounds A(Fe,A1) 2, where A is yttrium or zirconium, have been extensively studied in the last few years [1]. These experimental studies were motivated by the possibility of observing simple dilution effects in these materials. In fact, the measured averaged magnetic moment of these systems turns out to decrease with increasing A1 content. However, these sp impurities introduce large perturbations in the electronic structure of these intermetallics and several phenomena are induced, for instance: (a) the crystal structure of the compound ZrFe 2 changes from cubic C15 (MgCu 2) to hexagonal C14 (MgZn2) around concentrations of 24% atomic substitution of Fe by A1 [2]; (b) a new magnetic phase of reentrant spin glass type was observed in YFe 2 compounds doped with AI [3]. Studies of hyperfine interactions show that the hyperfine magnetic fields and quadrupole interaction have a strong dependence on the local configurations around the Fe atoms, as observed with MOssbauer spectroscopy [4,5]. 9 J.C. Baltzer AG, Scientific Publishing Company

200

C.M. da Silva et al., Ferromagnetic Laves phase intermetallics

Although very close in the periodic table, Si and A1 impurities show distinct behaviour when diluted in ZrFe 2 intermetallic. In what concems the lattice parameters, it was observed that Si impurities, contrary to A1, tend to decrease its value with increasing Si concentration [6]. Also, the compounds Zr(Fe I _ S i x ) a exhibit a single cubic phase for impurity concentrations up to 17% atomic substitution of Fe [7]. However, the saturation magnetization as a function of Si concentration is quite similar to the corresponding results for the A1 pseudobinary. Thus, a microscopic measurement is worthwhile.

2.

Experimental

The samples were prepared in an arc furnace under argon atmosphere. The component raw materials were melted several times and the mass losses were verified to be smaller than 0.3%. The samples were annealed for 5 clays at 900 ~ The X~ray patterns of powdered samples showed only the presence of the C15 structure in the concentration range between x = 0.0 and 0.17. M0ssbauer measurements were performed using a conventional constant acceleration spectrometer. Experiments were made at liquid helium temperature, and a SVCo(Rh) source was used. The data were fitted using a least-squares procedure, assuming a superposition of Lorentzian lines, and the main parts of the fitting program were the same as those constructed by Shenoy [8]. The experimental data obtained from the as-cast samples are shown in fig. 1. For some samples, we verified that the spectra obtained after the annealing process almost coincides with those observed in as-cast alloys.

3.

Results

In the ZrFe z compound, four Fe atoms are arranged at the comers of a tetrahedra inside a diamond structure associated with Zr atoms. A convenient local symmetry axis is obtained connecting an iron site which is common to two tetrabedra with the centers of opposite triangles [9]. Consider the angle between the easy magnetization axis and the local symmetry axis: if the easy axis is [111], the angles are 70o32 ' for three iron atoms and 0 ~ for the remaining one; if the easy axis is [110], the angles are 90 ~ and 35016 ' for two different pairs of Fe atoms; and in the last case, the easy axis being [100], all angles are equal to 54o44 '. In the case of the pure compound ZrFe 2, the easy axis points in the direction [111] and thus two magnetically non-equivalent sites do exist [ll]. The pseudobinaries Zr(Fe~- Si)2, on the other hand, can be understood as having three possible Fe sites; the first two correspond to the pure compound, namely site I with 0 = 70o32 ' and site II with 0 = 0 ~ The third site (site III) is associated with any Fe atom that has at least one Si as nearest neighbour. The existence of a third site has already been observed in the case of A1 impurities [4]. For site III, it will become clear

C.M. da Silva et al., Ferromagnetic Laves phase intermetallics

Vxo

.9:5

1

201

- 98 1.

.-~

k

Q.) k.J L L t_U

98

98

98

:l

98

%

, -40

o

40 v

I

, -4o

o

~.o

(mm/s)

Fig. 1. M6ssbauer spectra of Zr(Fe 1 _ S i )2" ( ~ experimental points; solid line shows the fitting results.

that it is not experimentally possible, within M0ssbauer spectroscopy, to determine simultaneously the EFG and the angle 0. Thus, it will be necessary to include additional hypotheses about the angle or the magnitude of the EFG. The Hamiltonian for the combined effect of magnetic hyperfine fields and quadrupolar interactions, when the magnetic effect is dominant, is given by perturbation theory [10]: H =-g#NHcfflz +

1

e2qQp2(cos O)[31z - I ( I - 1)]1[I(21- 1)],

(1)

where P2(cos 0) = 89 cos/0 - 1), 0 is the angle between Heft and EFG ( - q); the other symbols have their usual meaning. We suggest that in Si doped compounds, an impurity induced change on the local easy magnetization axis occurs. Since Si is a strongly perturbative impurity, in addition to the change in the easy magnetization axis one expects large modifications, at least in some hyperfine parameters. Our hypothesis is then of an impurity induced change of the local magnetization axis from [111] to [100] (cosZ0 = 1/3). This means that the electric quadrupole interaction vanishes, as predicted by expression (1). An

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C.M. da Silva et al., Ferromagnetic Laves phase intermetallics

example of impurity induced change of the local magnetization axis is provided by Zr(Fe, Co)2 [ 12]. The fitting procedure considered two possibilities for the Fe probes: (i) Fe with only Fe atoms around it: this structure implies two possibilities for the Fe sites; (ii) a third site with at least one Si atom around it. Sites I and II, with population ratio 3:1, show the combined effects of magnetic and quadrupolar interactions. In the description of the third site, two forms of distributions were used: for low concentrations (x < 0.08), a binary distribution has proved to be the most convenient, and for x > 0.10, because of the stronger disorder, a discrete distribution was adopted. For one concentration (x = 0.13), we verified that a Gaussian distribution yields almost the same parameters. Heff (kOe) X

200

X

X

9

X

9

a)

x

9

X 9

+

X

§ § §

150 0

O.

1/2 e2qO

(rnm/s)

,

i

~

•

b) O[ [S(mrUs) . -]

f L

O.

9

9

x

x

C~

3

L

.05

.

. i

0I

. 8

.

.

+

x

x

x

x

9

9

9

9

I

.lO

I

.13

I

.15

C

)

I.i~

.17 X

Fig. 2. Hyperfine parameters. (a) Magnetic hyperfine fields; (b) quadrupolar interaction; (c) isomer shift (relative to metallic Fe). (• site I, (o) site II, and (+) site III,

The results of this fitting procedure are presented in fig. 1, and the resulting hyperfine parameters are shown in fig. 2, as a function of Si concentration x.

4.

Local effects in Zr(Fe, Si)z: A qualitative discussion

4.1.

AVERAGED AND LOCAL EFFECTS IN PSEUDOBINARIES

In order to give a qualitative interpretation of the observed existence of three sites in these pseudobinaries, a rough description of neighbour effects and disorder

C.M. da Silva et al., Ferromagnetic Laves phase intermetallics

203

is necessary. If one intends to consider only averaged quantities such as, for example, the electronic specific heat, a simple effective medium description can be introduced to describe the effect of disorder. This effective medium is defined within the classical CPA approximation (for a recent reference, see [13]). Then, all averaged properties may be derived from the imaginary part of the resolvent g(e, x), defined in terms of the band structure e~, the concentration x and the energy e through:

with z=c+ir,

~5~0

and G(z, x) is the CPA self-energy, self-consistently obtained from the condition that the averaged scattering T matrix vanishes [13]. Since MOssbauer spectroscopy picks up local neighbouring configurations, these should be incorporated, extending the CPA description as done previously within the d-tight binding approximation [14]. A given MOssbauer Fe probe reflects the local configuration; this requires the associated local resolvent G, which extends the averaged resolvent to introduce local effects. The effective medium is perturbed by potentials V v describing the neighbourhood configurations, defined by a sphere of radius R C measuring the size of the locally perturbed region. The superscript v = Fe or Si identify the potentials corresponding to situations in which one Fe sphere centered in a given Fe probe is immersed in the effective medium or an immersed sphere with at least one Si around the center. In both cases and from the usual Born perturbation series, for the corrections to the averaged resolvent g(e, x) one obtains:

(2)

g, v(e, x) -- g(e, x) + g(e, x ) V Vg(e, x) + . . . . where v v =

ev -

o

e,x),

ev =

or

,

and or(e, x) is the effective medium self-energy, matrix notation being assumed. Site I, although involving only Fe neighbours, must also include the anisotropy potential responsible for the two magnetically non-equivalent sites in ZrFe 2 [9]. Perturbing gFC(e,x) by this potential, for the corresponding local resolvent one obtains: Gi(e,x)---g

.Fe

(e,x)+g

^Fe

70o32 ,~Fe

(e,x)Vanis

g

(e,x),

(3)

where, for a given angle 0, V a~n l S. = 6 ~ rr(e, x) is the potential introduced by the anisotropy. The parameter S ~ corresponds to the shifts in d sub-band centers

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C.M. da Silva et al., Ferromagnetic Laves phase intermetallics

describing the anisotropy effect [15], associated with the angle 0 with respect to the easy magnetization axis. In site II, the anisotropy potential is absent; then one has simply: ^Fe

(4)

Gii(e,x) = g (e,x).

For site III, in addition to the perturbation due to Si already included, one should take into account Vanls ~ with 0 = 54~ one obtains: Gitt(e,x)=g

4.2.

^Si

(e,x)+g

^Si

,~,54o44" ^Si,

(e,x)vam s

g re, x).

(5)

CONNECTION OF HYPERFINE PARAMETERS AND LOCAL EFFECTS

The hyperfine parameters are dependent on the local environment of the Fe sites; therefore, from (3), (4) and (5) it may be possible to have different values and concentration dependences for each of the hyperfine parameters. First of all, let us recall very simplified descriptions of the isomer shift (IS), quadrupolar interaction, and hyperfine magnetic field. Ingalls [16] suggested the following expression for the total amplitude of sstates at the nucleus:

[A I//s [2 = constant - O~dAnd -- O~pAnp + a A n 4 s ,

(6)

where a d, % and a > 0. Expression (6) shows, for example, that positive changes in d and p occupation numbers decrease the amplitude of s-states, the inverse occurring with the 4s occupation number. Although very simplified, expression (6) was able to qualitatively describe the trends observed in similar systems [9]. The quadrupolar interaction can be expressed in terms of d and p occupation numbers [17], and specific integrals involving the d and p states. Finally, the magnetic hyperfine field may be simply connected to the d, p and s magnetizations through [18] d

d

p

AHeff=-AcpAm-AcpAm

p

+AcepAm s.

(7)

Although aware that expressions (6) and (7) are extreme simplifications for the description of the hyperfine constants, we quote them to give a preliminary interpretation of the data.

C.M. da Silva et al., Ferromagnetic Laves phase intermetallics

205

4.2.1. Isomer shift In fig. 2(c), this parameter is shown to present two distinct behaviours. In the case of sites I and III, the IS is approximately concentration independent; site II, on the contrary, shows clear variation. In the above sketch of description, two distinct Fe sites are considered, both with only Fe atoms around it; only one of these include the anisotropy potential. These cases are incorporated in eqs. (3) and (4). These equations indicate the essential role of the anisotropy potential in compensating the effect of disorder included in gF~(e, x). A similar competition is shown in site III, where the combined effect of the Si impurity embedded in the sphere and the anisotropy potential provides the extra scattering that compensates the x dependence of ~ ( e , x). Note that without detailed calculations it is not possible to specify the role of s, p and d electrons in the above-mentioned compensation.

4.2.2. Quadrupole interaction As a consequence of our hypothesis of the role of Si in favouring the [100] local magnetization axis, we miss the experimental determination of the effect of Si impurities in changing the EFG. However, in sites I and II, the quantity q(x) is shown to decrease with Si concentration. Without a calculation including p and d electrons within the spirit of ref. [13], it is difficult to understand even qualitatively a change of the EFG with x.

4.2.3. The hyperfine field Consider expression (7). Let us assume that mp is proportional to m , the proportionality constant being connected to the s and p degeneracy [9]. A classical assumption is to take m s and mp anti-parallel and proportional to m d. Within these hypotheses, A H f f is, according to (7), proportional to Amd. The same reasoning applies to averaged total bulk magnetization. Thus, the decrease of H ff can be associated with bulk magnetization measurements, which show similar behaviour [6].

5.

Final remarks

Firstly, this study exhibits the main features of the local environment effects in Zr(Fe 1 _ xSix)2: (a) up to a concentration x = 0.17, even in the presence of the strong impurity perturbation, the two magnetically non-equivalent sites of the pure compound can still be observed; (b) the origin of the third site is associated with the combination of Si impurity potential scattering together with anisotropy effects;

C.M. da Silva et al., Ferromagnetic Laves phase intermetallics

206

(c) the proportionality of the hyperfine field to the averaged magnetization is verified to be approximately valid. This contrasts with (Zr, Hf)Fe 2 compounds [9], where Her f is nearly concentration independent. Secondly, we compare the effect on a microscopic scale of Si and A1 in ZrFe 2. We have thus considered the results presented in refs. [4] and [19] and our own measurements. In the above references, only the averaged hyperfine parameters are shown; hence, we computed our averaged values from the data shown in fig. 2 using the populations of the sites extracted from the fitting. In both cases, results for the hyperfine field turn out to be very similar within the available precision for comparison of the data. The same occurs for the IS parameter. However, the EFG shows a clear difference. For 15% concentration of A1, the EFG is reduced to approximately 2/3 of the pure compound value. In the case of Si, 13% of impurities suffices to reduce the EFG to nearly zero. In view of this, we conclude that only very careful calculations of the electronic contributions to the hyperfine parameters can distinguish the physical mechanism determining the behaviour of Si or A1 impurities in ZrFe 2.

Acknowledgement The authors thank J.E. Schmidt for discussions and a critical reading of the manuscript. References [1] [2] [3] [4] [5] [6] [7] [8]

G. Hilscher, J. Magn. Magn. Mater. 27(1982)1. R. Gr6ssinger, G. Hilscher and G. Wiesinger, J. Magn. Magn. Mater. 23(1981)47. G. Hilscher, R. Gr6ssinger, V. Sechovsky and P. Nozar, J. Phys. F12(1982)1209. Y. Muraoka, M. Shiga and Y. Nakamura, Phys. Stat. Sol. A42(1977)369. M.J. Besnus, P. Bauer and J.M. G~.nin, J. Phys. F8(1978)191. S. Zamora, C.M. da Silva, J.E. Schmidt, F.P. Livi and A.A. Gomes, to be published. C.M. da Silva, F.P. Livi and A.A. Gomes, Solid State Commun. 64(1987)925. G.K. Shenoy, F.E. Wagner and G.M. Kalvius, MOssbauer Isomer Shift (North-Holland, Amsterdam, 1978). [9] L. Amaral, F.P. Livi and A.A. Gomes, J. Phys. F12(1982)2091. [10] S.K. Arif, D.St.P. Bunbury, G.J. Bowden and R.K. Day, J. Phys. F5(1975)1037. [11] G.K. Wertheim, V. Jaccarino and J.H. Wernick, Phys. Rev. A135(1964)151. [12] G. Wiesinger, A. Oppelt and K.H.J. Buschow, J. Magn. Magn. Mater. 22(1981)227. [13] J. Kudrnovsky and V. Drchal, Solid State State Commun. 70(1984)577; J. Kudrnovsky and J. Mazek, Phys. Rev. B31(1985)6424, and references therein. [14] F. Brouers, F. Gautier and J. van der Rest, J. Phys. F5(1975)975. [15] P. Bruno, Phys. Rev. B39(1989)865. [16] R. Ingalls, Phys. Rev. 155(1967)157. [17] H. PetIilli, Ph.D. Thesis IF-USP (1989), and to be published; L. Amaral, F.P. Livi and A.A. Gomes, An. Acad. Bras Cienc. 56(1984)17. [18] I.A. Campbell, J. Phys. C2(1969)1338. [19] G. Wiesinger, J. Magn. Magn. Mater. 25(1981)152.