SYSTEMATIC BEHAVIOUR OF 61Ni, 59Co AND 57Fe HYPERFINE FIELDS IN SOME CLOSE-PACKED ALLOYS

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SYSTEMATIC BEHAVIOUR OF 61Ni, 59Co AND

57Fe HYPERFINE FIELDS IN SOME

CLOSE-PACKED ALLOYS

J. Drijver, F. van der Woude

To cite this version:

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JOURNAL DE PHYSIQUE Colloque C6, supple'ment au no 12, Tome 37, De'cembre 1976, page C6-385

SYSTEMATIC BEHAVIOUR OF

61Ni, "Co AND "Fe

MYPERFINE FIELDS IN SOME CLOSE-PACKED ALLOYS

J. W. DRIJVER (*) and F. VAN DER WOUDE Solid State Physics Laboratory, Materials Science Center

University of Groningen, Groningen, The Netherlands

R6sum6. - Les champs hyperfins aux noyaux 6lNi, 59Co et 57Fe dans les alliages en empile- ment compacte de nickel, de cobalt et de fer entre eux et aussi avec des autres Blkments montrent une variation systematique et paraissent &re relies lineairement aux moments magnktiques a ses propres atomes et aux atomes voisins.

Abstract. -The hyperfine fields at 61Ni, 59Co and 57Fe nuclei in the close-packed binary alloys of nickel, cobalt and iron, with each other and with some other elements show a systematic variation and appear to be linearly related to the average magnetic moments on the neighbouring atoms.

1. Introduction. - From neutron-scattering experi- to the fields in the nickel metal. This demonstrates that ments it is well-known that in f. c. c. Ni-Fe alloys with the variation of H,, is not due to a moment change on

up to 40 at.

%

Fe, the Ni and Fe atomic moments at the parent atom but mainly to that on the neighbouring

0 K are nearly independent of composition and have atoms. Here we want to show that only atoms in the values of about 0.6 p, .and 2.8 pB respectively [I] immediate surroundings of the investigated nucleus (Fig. 1). These moments are also consistent with the contribute to H,,. To this end we compare literature values of low-temperature hyperfine fields in disordered

1

alloys with those in partially ordered Ni3Fe. We also try to explain the trends observed.

-

m 2. Data analysis.

-

With NMR experiments on 1

-

61Ni nuclei in Ni3Fe three well-resolved peaks have

V)

..-

2 : been detected [6]. This alloy develops

-

upon anneal-

E

ing below 770 K [7]

-

a superlattice with the L1,-

E _{structure (Fig. 2). The peaks were attributed to Ni}

1 ;

;.;

4 J ; $ i

.

A

.-

E

3 0 0.6 0.L 0.2 0

-

Fe,Concentrat~on

rFg

O B

FIG. 1. - Magnetic Foments. of Ni (lower series of points)

and Fe (upper ~eri'es of points) aioms in fci: Ni-Fe alloys, as

deterrrilned &ith neutron diffraction.

FIG. 2.

-

Unit cell of an A3B alloy with the Llz-structure. linear variation>'-of; the average alloy magnetization

with Fe coneentratio& 12j, which forms part of the Slater-Pauling'bzli&II But in the same composition range theel:hpp°.rI?ne fields

I

H,,

I

at 0 K increase l i n e a ~ l y ~ ~ i t k ~ t 8 h d I i r ~ concentration : by 80

%

at Ni nuclei f3,%l] and bpi20

%

at Fe nuclei [5] with respect

(9

present Atldress : Technical -Physics Dept., University

of Utrecht, Utrecht, The Netherlads.

nuclei which experience different hyperfine fields at

sites with 4 Fe nearest neighbours (n. n.)

-

as in the fully ordered alloy - and with 3 and 5 Fe nd n., out of a total of 12 n. n. In figure 3 H,, has been plotted against the average magnetic moment per n. n., m,.,.. Besides data for 61Ni fields in Ni [8] and Ni-Fe alloys [3,4,6], also data for Ni-Co and Ni-Cu alloys [4] and for fcc C, metal [9] have been included. For the

25

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J. W. DRIJVER AND F. VAN DER WOUDE

F C C ORD

C o

1

[Ni3Fe] [ N i l

I I I I I

FIG. 3.

-

Hyperfine field Hhf at 6 1 Ni nuclei in several alloys, against the average magnetic moment on the nearest neighbours

-

mn.n. : Ni-Fe (+) ref .[3] ; Ni-Fe, Ni-Cu (@) and Ni-CO ( 0 ) ref. [4] ; Ni3Fe ( x ) ref. [6] ; Ni ( x ) ref. [8] ; Co ( 0 ) ref. [9].

-300

disordered Ni-Fe and Ni-Co alloys,

K.,.

is calculated from the average numbers of Ni, Co and Fe n. n. with moments of 0.6 p,, 1.7 p, -and 2.8 p, respectively. These moments are consistent with the Slater-Pauling curve and with neutron-diffraction data. In Ni-Cu alloys the decrease of the average moment is 1.1 pB per added Cu atom and this number ,is employed for the calculation of

K.,..

The solid line in figure 3 is drawn through the two points, corresponding to 61Ni

in pure nickel and in ordered Ni3Fe with 4 Fe n. n., and is given by :

Ni- Fe and Ni - C u

-

0 Co and Ni -Co . -

The other data closely conform to this relation up to

-

m

,.,.

= 1.5 pB, which corresponds to 40 at

%

Fe. In particular this is true for the fields, observed in Ni3Fe at the sites with 3 and 5 Fe n. n., so that clearly the magnetic moments in the second and more distant shells do not have a measurable contribution to Hhf.

The 57Fe fields, observed in Ni-Fe and other alloys, can be treated similarly. In ME spectra of partially ordered Ni3Fe the different contributions to Hh, are not resolved, but the lineshape can well be analysed by assuming a linear relationship between Hhf and the numbers of Fe atoms in the first and second shell around a central Fe atom [lo]. In this manner the contributions AHi to Hhf per Fe atom in shell i at 0 K were found to be :

AH, =

-

11.0 kOe and AH2 =

-

2.5 kOe

.

+ Ni-Fe

x Ni3Fe and Ni

On the other hand these contributions can be calculated from t h e average fields, observed in ordered and

-

0

S

-

_".. r I

I

-Io0-

disordered Ni,Fe 17, 101 and in nickel metal (Hucl, unpublished results). Then we obtain AH, =

-

11.0 kOe and AH2 = - 2.0 kOe, in fair agreement with the values above. In figure 4, Hh, has been plotted against

"

\

x+

'*

FIG. 4 . - Hyperfine field Haf at 57Fe nuclei in several alloys, against the effective average moment Zn.n.,-nn. on the nearest

neighbours. Ni-Fe (+) ref. [ S ] ; Ni3Fe ( x ) ref. [7] et [ l o ] ;

Ni ( x ) (Hucl unpublished) ; Co ( 0 ) ref. [ l l ] ; Ni3AI ( a )

ref. [12] ; Ni3Ga (*) ref. [13].

O 2:o 1.0 0

-

mn.n!p~)

-

the effective average moment per n. n., m

,.,.,

,,,.

This quantity is defined as the sum of %,,,. and the apparent moment of the second shell which is

where

k,.,.,.

is the average moment of th'k next- nearest neighbour shell with 6 atoms. The solid line in the figure is drawn through the three points corresponding to 57Fe in ordered and disordered Ni3Fe and in Ni metal, and is given by :

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SYSTEMATIC BEHAVIOUR OF 61Ni, 59Co AND 57Fe C6-387 with relation (2), when we take into account that

ppe = 2.03 pB [17] :

-

260 kOe and - 261 kOe for the observed and the calculated fields respectively Finally, we use data'of 59Co hyperfine fields in nickel-rich Ni-Co alloys [18]. Here a change of about

- 9.5 kOe per Co atom added in the first neighbouring shell, accounts fdr the satellite peaks observed in the more dilute alloys and also for the average field in the concentrated alloys. We obtain then in a nearest- neighbour-only model :

H,, =

-

58.8 - 8.6 x 12

K,,.

(kOe) ₍₃₎ the coefficients of which lie between the 6 1 ~ i and the 57Fe values.

3. Discussion.

-

The empirical relations. for H,, may be interpreted as follows. The constant term is the field Hhf(0) a t the investigated nuclei in an environ- ment with zero magnetic moment. Thus H,,(O) constitutes the contribution to the hyperfine field from the electron shell of the parent Ni, Co or Fe atom with a moment of 0.6 pB, 1.7 pB or 2.8 CL, respectively. Reduction of this moment results in a proportional decrease of Hhf(0), as we have seen in hcp Fe,Ge. Hhf(0) can be separated in a (positive) orbital field, HoRB, a (negative) core-polarization field Hcp and a (positive) field HcEps due to the self-polarization of the 4s conduction electrons by the 3d-spin at the same atom. In the case of 61Ni these contributions clearly cancel, so that changes in the nickel moment are not reflected in its hypedine field.

HoRB can be estimated from HoRB = 2

<

r3-,

>

pORB, where r,, is the 3d-shell radius and pORB the atomic orbital moment.

<

r3-,

>

values were taken from ref. [21], interpolating for the electronic configurations which are consistent with the spin moment. Spin and orbital moments were obtained from experimental g'-factors [21]. Substracting HoRB from Hhf(0) we obtain HspIN = Hcp

+

HcEps. In table I the relevant data for the calculation of HoRB are given together with the values HSPIN/~sPIN, the field values normalized to the spin moment on the parent atom.

The trend in Hsp,N/~spIN can be explained in two ways. Firstly, the 3d-radius shrinks when going from

Fe to Ni. Because the 3s and 4s shells are expected to change less (otherwise the lattice parameter would decrease also), the positive contribution from the outer s-electrons to Hcp becomes larger and thus decreases HspIN/pSp,, in absolute ,value.

On the other hand the ,self-polarization of the 4s- electrons by PSPIN may increase going'from Fe to Ni, leading in this way to a decreasing Hspm/pSp,. This is indicated by the behaviour .of the term in the empirical relations which is linear in m,.,.. The coefficients of these terms are given in the last column of,table I. We suggest that this contribution to Hh, arises from a negative spin-polarization of 4s conduction electrons on the parent atom, in response to the neighbowing magnetic moments. Figures 3 and 4 show that the kind of neighbouring atom is unimportant and that ohly the magnitude of the magnetic moment counts. This indicates that the mechanism is not of a simple Friedel type, but more resembles a short-ranged RKKY interaction with a spin polarization at the nucleus, which is determined by the 'kind of the parent atom. While this field is negative at n. n. histance, it is positive at the site of the considered magnetic moment, so that the trend in the last column of table I also explains the change in H ~ ~ I N / ~ ~ ~ J ~ .

The fields, observed in fcc Fe3Ge [17] and Fe,Ga [19], are 30 kOe smaller in absolute value than calculated on basis of the magnetic moments. But in these alloys a considerable electric-field gradient is observed at the Fe nuclear site, indicating a distortion of the atomic core 1171. When the spin polarization of the parent atom strongly deviates from a spherical distribution, the core-polarization constant may be affected and this may impede the empirical relations for H,, deduced above. On the other hand, the reported fields at Ni, Co and Fe nuclei in Pd and Ni-Pd alloys are strongly diverging from our relations [22]. An excessive unquenching of the orbital moment has been suggested 1221, leading to a large orbital field. It may be noted that the lattice parameter of Pd is 10

%

larger than that of the alloys considered by us, which vary within 1

%.

Therefore we think that our analysis is meaningful only in alloys with 12-coordination and with a nearly constant nearest-neighbour distance.

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Cij-388 J. W. DRIJVER AND F. VAN DER WOUDE

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