S. Y. CHUANG and B. G. H o w : Positron Annihilation in Alnico 331

phys. stat. sol. 20, 331 (1967)

Subject classification: 13; 11; 20; 21.1.1; 22.8

Department of Phy,eics, University of Manitoba, Winnipeg

Positron Annihilation in Alnico and (Lao.,Pbo,,)Mn08

BY S. Y. C H U A N ~ and B. G. Hoaa

A study of the angular correlation of annihilation photons from positrons annihilating in alnico and single crystals of the perovskite (La0.7Pb0.3)MnO, has been made. It is possible to account for the observed angular distributions by a simple-minded consideration of the physical properties of the two materials.

Eine Unterauchung der Winkelkorrelation der Positron-Vernichtungsstrahlung in Alnico und (Lao,7Pbo.3)Mn03 wird beschrieben. Die beobachtete Winkelverteilung kann durch eine einfache Betrachtung der physikalischen Eigenschaften der beiden Stoffe erkliirt werden.

1. Introduction Positrons entering a metal are thermalized [l] in a time short compared with

their average lifetime. The momentum of an annihilating positron-electron pair is therefore chiefly the momentum of the electron. The measurement of this momentum is easily done by observing the angle between the two annihila- tion gamma rays [2]. The positron mainly samples the most loosely bound electrons in the solid but also samples some of the core electrons. The problem of predicting the positron-electron annihilation possibilities for systems con- taining several different types of atoms has been undertaken in this work.

2. Experimental The angular distributions of the annihilation photons were obtained using

a standard parallel slit apparatus as shown in Fig. 1. This consisted of a source of positrons and a sample mounted between the fixed and the movable detector with appropriate collimating slits. The positron source was 10 millicuries of 22Na deposited from aqueous NaCl solution on the end of a 0.6 inch diameter plastic rod covered with mica of thickness 2 mg/cm2. The sample was mounted

Motor

U

Elovable detix%r Source ,Fired detector

C-- 265cm 265cm + Fig. 1. The angular correlation apparatus

332 S. Y. CHUANG and B. G . HOGG

as shown in Fig. 1 to receive the positrons. The slits subtended an angle of one milliradian at the sample.

In operation the apparatus accumulated 1000 coincidence events a t a given position after which the movable detector was driven automatically through an angle of 0.9 milliradian to a new position. A region of 18 milliradians on either side of the 180” line was scanned a number of times until about 20000 counts per position was accumulated.

3. Results and Discussion Fig. 2 shows our results for copper which are in agreement with those of

Stewart [3]. The experimental curve noted by the closed circles has been fitted with a parabola, corresponding to the free electrons [4], a t the low momentum region as indicated by the dotted curve A. The dashed curve B has been cal- culated on the basis of annihilation of 3d Cu electrons with a positron whose wavefunction is represented by a step function - being zero inside the ion core and constant outside the ion core. Similar calculations have been done by Ferrell [4]. The intersection of curves A and B then gives us a measure of the Fermi level for Cu which from these experiments is 7.1 eV.

3.1 Alnico

Considering the case of alnico I (12% Al, 20% Ni, 5% Co, 63% Fe), the contribution of aluminum t o the angular correlation curve is mainly due to the conduction electrons, since the probability for the core electrons of A1 to anni- hilate with a positron is small, even if compared with the d electrons in Fe, Ni, and Co. Moreover, the “conduction” electrons of A1 in alnico are not truly

9

Fig. 2. The angular correlation of photons from positrons annihilating in Cu. Curve (A) inverted parabola, curve (B) 3d-electrons, pF Permi momentum

Positron Annihilation in Alnico and ( La0.7PbO.3)MnO3 333

Alnim

Fig. 3. The angular correlation of photons from positrons annihilat- ing in alnico. Curve (A) Bd-elec- trons, cnrve (B) 4s-electrons, cnrve (C) inverted parabola, D intersection of curves (A) and (C) z4

“free” electrons since they are coupled with Fe, Ni, and Co. As seen from Fig. 3, the parabolic portion of the angular correlation curve continues only up to 3.5 milliradians, whereas in the case of pure A1 [3] there is a good fit of inverted parabola to the experimental curve up to the cutoff a t the angle corre3ponding to the Fermi momentum.

Fe, Ni, and Co also contribute conduction electrons to the alnico as well as Al. All “conduction” electrons (better called outermost electrons) will behave the same way as far as the positron is concerned. These electrons all behave like 4s- electrons, and the total angular correlation curve can be considered to be com- posed of two parts : a contribution by all the electrons in the 4s-band and a con- tribution due to the 3d-band in Fe, Ni, and Co. (We are neglecting small con- tributions due to the core electrons.) Since the 3d-wavefunctions of Fe, Ni, and Co are much alike, we merely use one 3d-wavefunction to calculate the overlap with the positron wavefunction. When the contribution due to the 3d-electrons (curve A in Fig. 3) is subtracted from the experimental curve (Fig. 3, dotted curve) the rest of the curve fits well t o one calculated from 4s hydrogen-like wavefunctions (curve B). If we extend the inverted parabola, curve C in Fig. 3, to meet the d-electron distribution as we did in copper, then the cutoff point is a t 5.9 milliradians (corresponding to 8.8eV). This we call the free Fermi energy for alnico, if there is such a thing for this alloy. The calculated Fermi energy of A1 based on the electron gas model assuming 3 conduction electrons per atom is 11.5 eV and the Fermi energies for Fe, Ni, and Co based on 0.7 con- duction electron per atom are in the range of 5 to 6 eV. When these four kinds of atoms are mixed and reach equilibrium, the Fermi levels will be the same and in the region between 5 t o 11.5 eV. This is consistent with our value of 8.8 eV from positron data.

3.2 tLao.7Pbo.8)Mn08 The ionic crystals LaMnO, and PbMnO, are antiferromagnetic semiconductors.

Mixed crystals of LaMn0,-PbMnO, containing up to 30% of PbMnO, are ferro- magnetic with perovskite structure and exhibit a conductivity of lo2 Sz-l cm-l a t this concentration. The properties of ferromagnetism and conductivity in (Lao.,Pbo.3)Mn0, are accounted for by the “double exchange process” [5].

334 S. Y. CHUANG and B. G. HWG

Experiments on the alkali halides have indicated that, the 2-photon angular correlation are almost independent of the positive ions [6] that is, they are only dependent on the negative ions. Theoretically then this is interpreted to mean that in an ionic crystal the positron wave function is concentrated about the negative ions and therefore the positions are most likely to annihilate with the outermost electrons of the negative ions. In the (Lao.7Pbo.3)Mn0, crystals the positive ions La+++, Pb++, Mn+++, and Mn++++ are expected to make little or no contribution to the angular correlations. Most of the positrons are concen- trated at the site of the 0-- ions and annihilate with the 2s- and 2p-like elec- trons of the 0-- ions.

The experimental angular correlation curves are shown in Fig. 4. They can be fitted quite well t o the function [3]

where 5 = f - p and “a” is the 0-- radius which has been taken as 1.4 A and

p is the momentum of the annihilating pair. The first term, C, (1 + E2) e+’, is plotted as curve A in Fig. 4 and corresponds to the 2p-electrons, while the second term, C, e- f corresponds to the 2s-like electrons annihilating with the positrons.

The sum of curves A and B fits the experimental curve except a t the higher momentum region where the calculated curve drops faster than the experimental one. This discrepancy might be removed by considering annihilations with the 3d-electrons of the transition elements or with core electrons of the oxygen or some combination of these possibilities. Unfortunately, the discrepancy is so small that no clear cut picture can be presented.

We can, however, say that positron annihilation with the 3d-electrons which is responsible for the ferromagnetic properties is not significant. An experiment was performed on the perovskite crystal in which angular correlation curves were run with the magnetization vector first in the direction of the positron beam entering the sample and then opposite t o the direction. Similar experiments [7,8] on Fe and Ni showed a considerable polarization effect, while for the perov- skite crystal considered here the angular distribution were independent of the orientation of the crystal in the magnetic field. This leads us to conclude that there are virtually no positions annihilating with the magnetic 3d-electrons in (LaO.7PbO.S)MnO,*

6

Fig. 4. The angular correlation of photon8 from positrons Annihilating in (La..,Pb..,)YnO,. Curve(A) 2p-elec-

trons, curve (B) 2s-electrons

Positron Annihilation in Alnico and (La0.7Pb0.3)Mn03 335

Acknowledgements

We wish t o thank Prof. A. H. Morrish for arranging with Dr. J. W. Nielson of Airton for the growing of the (Lao.7Pbo.3)Mn03 crystals. The financial support of the National Research Council of Canada and the American Chemical So- ciety Petroleum Research Fund is gratefully acknowledged.

References [l] G. E. LEE WHITINQ, Phys. Rev. 97, 1557 (1958). [2] P. R. WALLACE, Solid State Phys. 10, 22 (1960). [3] A. T. STEWART, Canad. J. Phys. 36, 168 (1967). [a] R. A. FEFCRELL, Rev. mod. Phys. 28,308 (1956). [5] C. ZENER, Phys. Rev. 82, 403 (1951). [6] A. T. STEWART and N. K. POPE, Phys. Rev. 120, 2033 (1960). [7] P. E. MIQNARENDS and L. HAMBRO, Phys. Letters 10, 272 (1964). [8] S. BER~O and J. ZUCKERMAN, Phys. Rev. IRtters 13, 339 (1964).

(Received December 16, 1966)