POSITRON ANNIHILATION IN MAGNETIZED IRON

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POSITRON ANNIHILATION IN MAGNETIZED IRON

P. Mijnarends, M. Höfelt

To cite this version:

P. Mijnarends, M. Höfelt. POSITRON ANNIHILATION IN MAGNETIZED IRON. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-284-C1-286. �10.1051/jphyscol:1971196�. �jpa-00214523�

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JOURNAL DE PHYSIQUE Colloque C I, supplkment au no 2-3, Tome 32, FPurier Mars 1971, page C 1 - 284

PO SITRON ANNIHILATION IN MAGNETIZED IRON

P. E. MIJNARENDS and M. H. H, HOFELT (*) Reactor Centrum Nederland, Petten (N. H.), the Netherlands

RBsum6. - Nous donnons ici des resultats de mesures de la correlation angulaire des gammas Bmis lors de l'annihilation des positrons dans des monocristaux de fer magnktique. La distribution de la densit6 de spin, vue par le positron, a Bte obtenue jusqu'au terme I = 6 et est comparb avec des calculs existants de structure de bande. Les caracteristiques de la distribution de la quantite de mouvement, attribuees d'habitude a une polarisation negative des electrons de conduction, sont interprktees en termes de Ia polarisation d'echange des fonctions d'onde 3 d.

Abstract. - Results are reported of 2 y angular correlation measurements in magnetized iron single crystals. The spin density distribution, as seen by the positron, has been obtained up to the I = 6 term and is compared with existing band structure calculations. The features in the momentum distribution, customarily ascribed to a negative conduction electron polarization, are interpreted in terms of the exchange polarization of the 3 d wave functions.

Positrons emitted by a radioactive source possess a longitudinal polarization, which is retained during thermalization in a solid. If the electrons in a ferro- magfietic metal are aligned by a strong magnetic field, annihilations with the unpaired electrons will take place from the singlet or the triplet state, depending on whether the field is parallel ( + ) or antipara!lel ( - ) to the momentum of the positron beam. The different selection rules for annihilations from these states cause the two-quantum angular correlation to depend on the field direction. This enables one to study the momentum distribution of the unpaired electrons by measuring the angular correlations N+ (8) and N- (8) [1].

A detailed interpretation of the available expe- rimental data [2-41 has proved difficult because of two reasons. In thz independent particle model the difference momentum density Ap(p) = p+(p) - p-@) is given by

= C [f+(n, k) 1 A+(n, k, PI l 2 -

k,n

- f-(n, k) I A-(n, k, P) l2 1, ⁽¹⁾

where

Ak(n, k, p) = 1 e-"-' $::)(r) cp(r) ddr (2) denotes the annihilation probability of an electron with spin ( i ). The occupation function f,(n, k) equals 1 if the state k in band n is occupied, and 0 otherwise, while $ and cp represent the electron and positron wave functions, respectively. Since A,(3 d) behaves quite differently from A,(cond.), Ap(p) is very sensitive to the actual form of the wave functions.

Secondly, the measured angular correlations consist of the weighted areas of slices through momentum space, which has the effect of smearing out details in Ap(p). As shown by Mijnarends [5], this problem can to a considerable extent be overcome by inverting the angular correlation data coliected on a number of oriented single crystals. Therefore, a set of accurate measurements was -performed on single crystals of

(*) Present address : Philips Research Laboratories, N. V. Phi- lips' Gloeilampenfabrieken, Eindhoven, the Netherlands.

iron, and the resulting angular correlations were inverted to display Ap(p). In this way it is expected that the results will be more amenable to theoretical interpretation. In the present paper preliminary results are given and an attempt is made to relate these to the band structure of iron.

From the analysis given by Berko [I] it follows that the difference and sum angular correlations are not directly proportional to the difference and sum momentum densities Ap(p) and pto,(p), respectively.

Instead, they are given by

where

AR(P) ⁼CP,[AP(P) + Pe,, ~ t o t ( ~ ) I

Here P, denotes the polarization of the positron beam and Peff is the effective total electron polarization as seen by the positron. Since P, and P,,, are not known separately one considers the ratio

Q(P> AR(@IRtot@) = P , 7 [ ( A ~ ( ~ ) l ~ t o t ( ~ ) ) + P e f ~ ] .

( 5 ) Apart from the scaling factor P,, this only differs from the corresponding ratio Qf(p) of the p's by the (small) additive constant PC,. The uncertainty in Peff therefore means an uncertainty in the zero level of Qr@), but does not effect its shape. Moreover, an estimate of P,,, may be obtained from a measu- rement of thc relative change in three-photon yield with field up and down. Measurements by Berko and Mills [6] yielded P, Peff = (- 53 f 9) x from which it follows that the zero level of Qf(p) will not be more than 0.6 - 1 % below that of Q(p).

Positrons emitted by a 50 mCi 2 2 ~ a source were focussed upon oriented siilgle crystals of iron by a 17 kG magnetic field, which at the same time served to magnetize the crystals. The angular correlations were measured with a conventional long slit instru-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971196

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POSITRON ANNIHILATION IN MAGNETIZED IRON C 1 - 285

ment [7] having an angular resolution of 1.1 x 85 mrad.

The crystal orientations are shown in figure 1. The fact that the [ill] direction is not represented is expected to have a less serious effect in b. c. c. Fe than in ar, f. c c. metal as Cu.

FIG. 1. - Stereographic plot of the sample orientations.

Figure 2 shows a contour plot of Q(p) in the (001) and (110) planes. Its most remarkable features are a thin positive shell surrounding the origin, containing peaks at - 3 mrad along the [loo] axes, a wide nega- tive region between 4 and - 10 mrad with deep minima along the [loo] axes, and a positive region with very high peaks (- 18 %) at 14.5 mrad, also along the same axes. The sum distribution Rto,(p), on the other hand, is only slightly anisotropic with bulges in the [I101 directions, small peaks on the [loo] axes at ^N2.5 mrad, and a shallow local minimum at the origin.

An attempt to relate these observations to Wakoh and Yamashita's (WY) [8] computation of the band structure of iron will be limited to the [I001 directions, since along these most detail is observed. As the direc- tional dependence of A(k, p) on p is the same as that

of $(r) on r, only states with A , symmetry will contribute in these directions. Furthermore, in the vicinity of r only s states can contribute, since A(3 d, k, p) vanishes as p2. The conduction band hybri- dizes with the 3 d band of A , symmetry. Consideration of WY's band structure diagram shows that along T H the latter band intersects the Fermi level at a point - 4 mrad from r f o r the majority spin direction, while the corresponding minority spin band lies enti- rely above the Fermi level. As a result there will be a small region with a net majority d and s-spin density at angles just below 4 mrad (say 3 mrad). This may explain the positive peaks found in that position.

The length of the (002) reciprocal lattice vector is 17 mrad. Subtracting this from the position of the peak at - 3 mrad, one arrives at the large peak found at 14.5 mrad. Thus, the latter is connected to the small peak by an Umklapp-process in which both 3 d and conduction electrons may take part. The large height of the secondary peak is explained by the small value at large momenta of R,,, in the denominator of Q@>.

The third feature of interest is the deep minimum around - 6.5 mrad. A similar minimum, although at slightly lower angles, was observed in a polycrystal by Berko et a]. [2], and interpreted by them in terms of a negative conduction electron polarization. Howe- ver, the strongly negative region observed in the present experiment extends all the way up to H, i. e.

far outside the s-like part of the Fermi surface. It seems unlikely therefore that any conduction electron spin density could account for it. Moreover, since in that part of k-space the 3 d states of A , symmetry of both spin orientations are full, the negative region can only be explained by assuming that A+ # A- owing to the exchange polarization of the 3 d wave functions. Computations of A+ and A - in order to investigate this point are in progress.

p in mrad

FIG. 2. - Contour diagram of the ratio Q(p) = AR(p)/Rtot (p) in the (001) and (110) planes. Indicated values in percents.

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C 1 - 286 P. E. MIJNARENDS AND M. H. H. HOFELT

References

[I] BERKO (S.), Positron Annihilation (Academic Press, [4] MIHALISIN (T. W.) and PARKS (R. D.), PkyS. Rev.

Inc., New York, 1967), p. 61. Letters, 1967, 18, 210.

[2] BERKO (S.) and ZUCKERMAN (J.), Phys. Rev. Letters, [5] MIJNARENDS (P. E.), Phys. Rev., 1967, 160, 512.

1964, 13, 339a. [67 BERKO (S.) and MILLS (A. P.), Bull. Am. Phys. Soc.

[3] MIJNARENDS (P. E.), Proceedings of the International 11, 1970, 15, 270.

Conference on Magnetism, Nottingham, 1964, [7] MIJNARENDS (P. E.), Phys. Rev., 1969, 178, 622.

p. 230. [8] WAKOH (S.) and YAMASHITA (J.), J. Phys. Soc. Japan, 1966, 21, 1712.