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Magnetic compton profile measurement using circularly polarized gamma-rays from oriented 191mIr nuclei
Nuclear Instruments and Methods in Physics Research 221 (1984) 419-426 North-Holland, Amsterdam
419
MAGNETIC COMPTON PROFILE MEASUREMENT USING CIRCULARLY POLARIZED G A M M A - R A Y S F R O M O R I E N T E D 191mIr N U C L E I N. S A K A I , O. T E R A S H I M A a n d H. S E K I Z A W A
The Institute of Physical and Chemical Research, Wako, Saitama, 351, Japan Received 28 June 1983 Circularly polarized 129 keV y-rays from oriented 191mlrnuclei are used to measure the Compton profile of magnetic electrons in ferromagnetic iron. A high degree of circular polarization is obtained even at temperatures about 200 mK owing to the large hyperfine magnetic field at the Ir site in Fe metal. Utilization of a 40 mCi v-ray source, together with a 3He/4He dilution refrigerator and a solid state detector, is found to be effective in obtaining high statistical accuracy. Efficient geometrical arrangement of the apparatus is discussed based on the cross section of the spin-dependent Compton scattering. Experimental procedures, source preparation and data accumulation are described in detail.
1. Introduction
When monochromatic photons are Comptonscattered to a fixed direction, the observed energy spectrum of the scattered photons is Doppler-broadened because of the quantum mechanical motion of electrons in matter. This spectrum, the so-called Compton profile, provides information about the momentum distribution of electrons. Hitherto many Compton-profile measurements have revealed the momentum distribution of conduction electrons in various solids [1]. However, no direct information on the spin states of electrons in magnetic solids can be obtained by these ordinary unpolarized-photon Compton-profile measurements. When the incident photons are circularly polarized, the Compton-scattering cross section becomes dependent on the direction of the electron spins. Then, using circularly polarized photons, it is possible to experimentally obtain the Compton profiles of magnetic electrons in ferro- or ferrimagnetic materials [2]. From now on we call them the magnetic Compton profiles. Such a measurement of the magnetic Compton profile was already made on ferromagnetic iron by one of the authors [2,3] using 122 keV circularly polarized y-rays from oriented 57Co nuclei in iron metal. However, the adiabatic demagnetization method utilized to orient the nuclei at low temperatures around 50 mK was very tedious and limited in cooling power, resulting in a magnetic Compton profile of ferromagnetic iron not satisfactory enough in accuracy. Thus, a more statistically accurate measurement should be attempted to examine the momentum distribution of the magnetic electrons in detail. The present paper reports an improved and more advantageous nuclear orientation 0167-5087/84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
method which allows high statistical accuracy in the profile measurements. Besides the nuclear orientation method, the following methods seem to be applicable to obtain circularly polarized y-rays from radioactive isotopes. (1) The B-3' directional coincidence method [4]; the y-rays immediately following the B-decay are partially circularly polarized when they are emitted in the direction opposite to that of the preceding B-particles. (2) The Coulomb-excitation method; the spin of a Coulomb-excited nuclear state is polarized in the direction perpendicular to the scattering plane of the projectile. Then "r-rays, which are emitted from the coulomb-excited nuclei and counted in coincidence with the projectile scattered to a fixed direction, are partially circularly polarized. (3) The double Compton scattering method [5]; the y-rays which are Compton scattered by polarized electrons in magnetized ferromagnetic material are partially circularly polarized. The methods (1) and (2) require a time coincidence measurement, but the time resolution of the solid-state detector, which is used to analyze the energies of scattered y-rays, is at most 1 ns. Then, the counting rate of the B-particles or the scattered projectiles can not be allowed to exceed 10 9 cps, which corresponds to the effective activity of a y-ray source of 30 mCi. Although method (3) is free from this restriction, the degree of circular polarization of Compton-scattered photons is not so high, and the photons scattered in a fixed direction must further be made monochromatic, because of their broad energy spectrum represented by the Compton profile. Thus it is difficult in practice to obtain a sufficient intensity of monochromatic circularly polarized y-rays by means of the methods mentioned above.
420
Sakai el aL/ Magnetic ("ornpton profile measurement
N.
Section 2 describes the characteristic features of the spin-dependent Compton scattering experiment, and the following sections 3.1-3.3 deal with the experimental procedures for preparing a strong radioactive 7-ray source with a high degree of circular polarization, by using a 3 H e / 4 H e dilution refrigerator. The accumulation systems are described in section 3.4. In section 4, the measured magnetic Compton profile of ferromagnetic iron is presented.
Eo,Ko/
E'Kzl
/
2. Theoretical
The theoretical expression of the spin-dependent C o m p t o n scattering cross section for free electrons was developed by Lipps and Tolhoek [6] and extended by Platzman and Tzoar [7] for electrons in ferromagnetic materials, within the framework of the impulse approximation. When we observe the energy of the scattered photon, the Compton scattering cross ~section can be written as follows.
d~dE
2
Fig. 1. The spin-dependent Compton scattering of y-rays with circular polarization Pc. The energy and momentum of the incident and scattered y-rays are denoted by E 0, g o and E, K, respectively, and oo the electron spin at the initial state. ing expression is obtained,
(d~2dEJup-(d~2dEjdow, =
ff
(~° + Pl~t)
This expression indicates that the difference between the two energy spectra, one measured with the scatterer
x ff[n'(p)+n*(p)]dpxdp,
(.)]dpxdp,,}
+ po+s.,.ff [.' ( . ) - . '
(P)-.'(.))dpxdp,
Here, r0 denotes the classical electron radius, E 0 and E the energies of the incident and the scattered photons, Pj and Pc the degree of linear and circular polarization of the incident photons, and n~(p) and n*(p) the m o m e n t u m distribution of electrons having a momentum p with spin up and down, respectively. The functions ~0, ~J and ~spi. a r e the angular parts of the scattering cross section when the initial electrons are at rest, and shown by Lipps and Tolhoek to be ~0=
I + cos 2 0+
E0- E
0
(1 - c o s 0 ) ,
mc 2
- 0•
~l = sin2 0, ~spin =
Ik.l,..
i~ o
~=3~
v,0
- - ( 1 - - COS 0 )
( Eo+E
x~cos0cos~b+
E mc
sin 0 sin ~b cos 2
} ".
The function ~o is the ordinary part, whereas ~ and (~spin are the polarization dependent parts. The angle 0 is the scattering angle of photon, q~ the angle between the direction of the incident photon K 0 and that of the electron spin o 0, and ,h is the angle between the (K0, a0)-plane and the ( K 0, K)-plane as shown in fig. 1. The notation me 2 is for the electron rest mass energy. Since only the third function ~p~, changes its sign by reversing the direction of the electron spin, the follow-
I
= 60"
~=90"
Fig. 2. The variation of f as a function of the scattering angle 0 and the spin direction ~ (for the definition, see the text). For dotted loops, f < 0, and for solid loops, f > 0. The vector K o is the momentum of the incident y-rays, and o0 the electron spin of the initial state.
N. Sakai et al. / Magnetic Cornptonprofile measurement 0
421
50
150
100 i
2~.~
, , I ' , '
'
I ' '
'
191mlr in Fe
P4
~f
I--
0
I
1
0"
90'
180°
270'
.
0
I ~
360'
tV Fig. 3. The angular dependence of f on the spin direction ~, (for the definition, see the text).
magnetized in one direction and the other with the same scatterer but magnetized in the opposite direction, gives the magnetic C o m p t o n profile, Jm,s" The quality of a magnetic Compton profile measure-
f~Nl -'-0
, , , , I , L i k 1 i ~ , i 50 100 150 TEMPERATURE (ink)
Fig. 5. The temperature dependence of the degree of circular polarization Pc (lower part), and of the intensity (upper part) of 129 keV y-rays emitted in the direction of the external magnetic field. The intensity is normalized to the value at 4.2 K. Pc of 122 keV -/-rays of 57Co in iron metal is also shown in the upper figure for comparison.
190 OS ÷ n
ment can be represented as follows by a ratio R which is essentially the signal to noise ratio of the measurement,
15./, d 191 76 OS
13-
R= 171.4 k e y
4.9 s
No ( E/Eo )2 Pc Nspin ](~spin I (No(E/Eo)ZN, otaI~O) '/2
11/2-
= ~o "~I
( -lOO'/. CE )
129.5
5/2"
E
f
82.4 .___~ ,,_ --
1//2*
+
3//2 + 191 77
[r
Fig, 4. Decay scheme of ]91Os. The metastable 1 1 / 2 - state can be oriented considerably in iron metal around 100 mK due to the large hyperfine magnetic field of 1400 kG, and the following 129 keV y-rays are circularly polarized.
~N+~. lf(O,
~P,~')1,
(/)spin
E0 ¢ 00 '
because the main " n o i s e " is due to the statistical errors of the total counts, and this total count is approximately proportional to (E/Eo)2NoNtotal~o • Here N 0, Nspin and Ntota I denote the incident photon number, the net magnetic electron number and the total electron number of a specimen, respectively. The function f in R changes its value with the geometrical arrangement of the apparatus. The dependence of f on 8 is plotted in fig. 2 for various values of ~/, with ~ = 0. The value of f is not always symmetric with respect to the direction of the electron spin. The large value of f for the backscattered geometry meets the requirement of the Compton profile
422
N. Saka~ eta/, /' Magnett ' ('mnpton profde measurement
measurement; the Doppler broadening of the energy of the scattered photon due to the motion of the electron occurs significantly on backscattering. The value of f is plotted in fig. 3 as a function of ~b for various values of 0 with ~ = 0. The angle which makes the absolute value of f maximum shifts from 180 ° to lower angles as 0 decreases from 180 °. When the angle 0 is 145 ° , as was the case of the present experiment, the maximum occurs at + = 165 °. This arrangement requires the incident y-rays impinging on one side of the specimen and the scattered y-rays emerging from the other side of the specimen. In practice, it was found to be difficult to set an electromagnet and a magnetic shield box in the space between a cryostat and a y-ray detector. Although f decreases to a value of 70% of the maximum, the arrangement with ~ = 30 ° was adopted• It is worth mentioning that an alternative arrangement with 0 = 145 ° and q~ = 120 ° gives a comparable magnitude of f to that of the present arrangement. This alternative arrangement will be useful when the size of the specimen is restricted.
3. Experimental procedures 3.1. Circularly polarized y-ray source
A useful y-ray Compton scattering experiment requires a y-ray source which emits energetically isolated high energy photons and has a relatively long lifetime. In addition to these, the following characteristics of the nucleus are also required when the nuclear orientation method [8] is applied to produce circularly polarized y-rays. Since the nuclear orientation is represented by the Boltzmann distribution among nuclear
10 7
I
I
f
I
I
magnetic hyperfine levels, the smaller the latLo of the Boltzmann factors, e x p ( - I ~ t t i n t / k T ), the higher is the expected degree of nuclear polarization, resulting in , higher degree of circular polarization of y-rays. Here t~ is the nuclear magnetic moment, and H,~ t is the hyperfine magnetic field at the site of the nucleus. Then, ( 1 ) a large nuclear magnetic moment (of the ground state of the radioactive nucleus or of the metastable excited state of the nucleus), and (2) a large hyperfine magnetic field (at the site of the radioactive nucleus) are effective for the purpose. Moreover, (3) the preferable y-ray multipolarity is E1 or M1, since the ratio R depends also on the number of the incident y-rays /V(~; if the muhipolarity is E2, for example, the intensity of photons in the direction of the magnetic field decreases as the degree of circular polarization P~, increases. After a careful survey of the characteristics of a great number of nuclei, the radioactive isotope ~ ( ) s in iron metal [9] was found to be the most suitable one for this purpose to our knowledge. The decay scheme of the nucleus is shown in fig. 4. This nucleus has a half-life of 15 d and emits 129.46 keV isolated y-rays with a multipolarity of M1 + 13% E2 [10,11]. The isomer ~91'~Ir has a large magnetic moment of 6.03 nuclear magnetons [12] and 4.9 s half-life which is sufficient to attain thermal equilibrium. The hyperfine magnetic field at iridium nuclei in iron metal is known to be - 1 4 0 3 kOe [13]. Fig. 5 shows the calculated temperature dependence of the degree of circular polarization and that of the intensity of 129 keY y-rays emitted in the direction of the external magnetic field, together with similar curves of the 57Co isotope in iron metal, which was used in the previous experiment. A degree of polarization as high as 80% can be obtained with this new isotope even at 100 n'l K .
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I
lr - KI3
"
10 6
I
1911r _y
lr-Ka
~n lO5 t-"Zt
K~.. ::
~-
• '.. 1911r_¥
J
'
' X . ~ : :'.:"
Ge
7
10 3
,< I 60
I 70
I 80
i l gO 100 ENERGY ( k e Y )
Fig. 6. The energy spectrum of V- and X-rays from
an
I 110
I 120
i 130
19lOs source measured by a pure Ge detector•
N. Sakai et al. / Magnetic Compton profile measurement
b
423
~,-ray sou •
slit
electromal]net
=+°'
+-+
x+IT+
-+++
iii
0
lOcm
Fig. 7. (a) Schematical view of the apparatus for a magnetic Compton profile measurement. The 3He/4He dilution refrigerator is suspended about 2 m above the floor. (b) Experimental arrangement of the circularly polarized y-ray source, the specimen and the y-ray detector. The scattering angle is 145_+4° .
3.2. Source preparation The radioactive isotope 191Os was prepared by neutron activation. Osmium atoms can be dissolved in iron metal to an extent of approximately 11 at.%, with the alloyed iron being kept still in the ferromagnetic state [14]. Alloys of Fe92Os 8 were prepared with an argon plasma furnace using stable isotopes of powdered 19°Os enriched to 95 at.%, and 56Fe metal prepared from 56Fe20 3 powder enriched to 99.9 at.%. Enriched isotopes were indispensable to avoid the unnecessary radioactive self-heating. An about 40 mCi y-ray source was obtained using an FeOs plate with dimensions of
~, rays
r+0++,mo0+ °°°' P H A
++I [ automatic controtter lime
read out
:
~
,
ext. stop accum.
memory
group current t o . _ _ _ ~ magnet ~-
Oo+o
l- d oi Z l I
I 1 cycle
I
l-[
F ,I
Fig. 8. Time relation between the accumulation of the PHA and the signals of the employed automatic controller.
12 x 6 × 0.2 mm 3 by neutron activation for 12 d with a neutron flux of 3 x 1013 n / s . cm 2 from the JRR-2 reactor of the Japan Atomic Energy Research Institute. Fig. 6 shows the energy spectrum of V- and X-rays from the source. The assignment of the peaks is denoted in the figure. No v-rays were observed above 129 keV except minor peaks from 192Ir impurity nuclei. 3.3. Cooling of y-ray source The isomer 191m|r can be oriented sufficiently at temperatures of about 100 m K as already shown in fig, 5. The r-particles and the internal conversion electrons are almost completely, and X-rays are partially, absorbed in the source material, causing the heating effect in the source. The estimated amount of the radioactive self-heating of a 20 mCi lmOs source is about 18 #W. A 3 H e / 4 H e dilution refrigerator (Oxford Instruments Ltd.) having a cooling power of 20/~W at 100 m K was used for the experiment. The experimental arrangement is illustrated schematically in fig. 7. The outer cryostat for the liquid He bath and the liquid N 2 bath can be lowered away from the refrigerator insert by a hand hoist, and then removed horizontally on rails for the setup of the y-ray source into the indium-sealed inner vacuum can. The y-ray source was soldered on a copper cold finger of 7 cm long under an atmosphere of argon gas. An aluminium foil was glued on the surface of the source against rust. The cold finger was screwed and soldered on the bottom of the mixing chamber of the refrigerator. A magnetic field of 7.5 kOe was supplied by a split type superconducting magnet to saturate the magnetization of the FeOs plate (see fig. 7b). The
424
N. Sakat et al. / Magnetic ('ompton profile measurement
surface of the source was approximately parallel to the direction of the magnetic field to minimize the demagnetization effect. The source temperature was determined by means of the temperature dependence of the anisotropic emission probability of 129 keV "/-rays in the direction of the magnetic field as shown in fig. 5. The source temperature thus determined was 197 mK for a 40 mCi fresh source and decreased gradually at a rate of 3 m K / d a y . During the Compton-profile measurement the source temperature was monitored by a carbon resistance thermometer on the mixing chamber•
with an energy resolution of 556 eV fwhm at 122 keV (Ortec-GLP; 25 mm active diameter and 10 mm active depth). The relatively large active diameter was effective in increasing the counting rate of the scattered y-rays, although the energy resolution was reduced slightly. A lead collimator with the hole dimensions of 20 mm wide, 40 mm high and 95 mm long was placed in front of the detector. The detector was covered with lead blocks in which a tin cylinder was inserted to absorb lead X-rays. The energy spectra of Compton scattered y-rays from the spin-up scatterer (UP) and that from the spin-down one ( D O W N ) were accumulated repeatedly in the order of UP, D O W N , D O W N , UP, D O W N , UP, UP, D O W N for 100 (live time) seconds each, to avoid systematic errors due to the decrease of the source intensity and the drift of the electronic system. Each of the two energy spectra was stored in the corresponding 1024 ch. memory group of the pulse height analyzer (PHA). The P H A accumulates the data in repeat mode and integrated counts under the Compton peak are printed out after every 100 s accumulation to monitor the condition of the equipment. As illustrated in fig. 8, an automatic controller generates two states for UP and D O W N accumulations. The controller, after receiving a print-out end signal from the PHA, makes the state to proceed to the next one and converts the PHA memory group from one to the other simultaneously with the reversal of the specimen magnetization. The PHA starts
3.4. Data accumulation
The incident circularly polarized y-rays, emerging horizontally from the refrigerator through an aluminized Mylar window, were collimated by a lead slit 8 mm in width and 24.5 mm in height. A soft iron electromagnet was used to align the direction of the electron spins in the specimen. The measured magnetization of the pure iron specimen reached a value of 93% of the saturation magnetization of pure iron. A magnetic shield box made of iron plate was prepared to cover the electromagnet, and a soft iron cylindrical magnetic shield to surround the outer cryostat of the refrigerator, The specimen included in the electromagnet is 10 cm long, 5 cm wide and 1 cm thick. The scattered ./-rays to the direction of 0 = 145 _+ 4 ° were detected by a pure germanium solid state detector
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i-., ..'. '" ...~r..". %. ~ 60
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60
70
80
90 100 110 120 130 ENERGY (keY) Fig. 9. (a) Energy spectrum of detected y- and X-rays, including 57Co "/-rays for the spectrum stabilizer. (b) Energy spectrum of Compton scattered "/-rays by magnetic electrons in a magnetized ferromagnetic iron specimen.
N. Sakai et al. / Magnetic Compton profile measurement
its accumulation after receiving an off-set of the external stop signal which is generated by the controller. The two-point digital spectrum stabilizer is coupled to the analog-to-digital converter (ADC) of the PHA to feedback the gain drift in the PHA system consisting of the ADC, amplifier, pre-amplifier and the detector. The 122 keV v-rays from 57Co and the 24 keV "t-rays from 1]9mSn were used for this purpose.
4. Results and discussion The energy spectrum of the scattered ),-rays from the specimen of magnetized polycrystalline ferromagnetic iron is shown in fig. 9a. The broad peak around 89 keV is the Compton peak of the circularly polarized 129 keV "t-rays of 191Os, and peaks in the lower energy region around 58 keV and 53 keV are the Compton peaks of Ir Kp X-rays and Ir K~ X-rays, respectively. The sharp peak at 122 keV is the photo-peak of 57Co v-rays used as one of the standard peaks for the digital spectrum stabilizer. The difference between the UP energy spectrum and the DOWN one is shown in fig. 9b. The residual peak around 89 keV is the magnetic Compton profile of ferromagnetic iron. The complete disappearance of other peaks in fig. 9a indicates the absence of systematic errors in this subtracted spectrum; the unpolarized X-rays do not distinguish the direction of the electron spins. The overall accumulation time was 165.1 h for both the UP and DOWN spectra and the total counts under the magnetic Compton profile was 6.4 x 105 counts. It should be noted that the total amount of the magnetic Compton profile is 2.59% of that of the UP Compton profile. This percentage agrees
425
well with that evaluated with the present experimental parameters and 2.2 magnetic electrons per iron atom. After the converting procedure on the spectrum from the energy scale to the momentum scale of the electron (here 1 keV Doppler broadening corresponds to 0.956 a.u. in momentum scale), the magnetic Compton profile in momentum scale is obtained as shown in fig. 10. The counts are summed up every 5 channels to increase the statistical accuracy. The correction was made for "long tail" and also for self-absorption in the specimen, but was not made for multiple scattering, which is estimated to cause at most 10% change in the shape of the magnetic Compton profile. The momentum resolution of the system including energy and geometrical resolution was 1.05 a.u. The gain drift of the PHA system, estimated by the differences of the standard peaks, was found to be less than 10 -2 channels or 1.07 x 10 -3 a.u. A detailed discussion on the magnetic Compton profile of ferromagnetic iron including the comparison with theoretical profiles will be published shortly. One of the excellent features of the nuclear orientation method is the utilization of high energy photons, because the ratio R is roughly proportional to the ratio I~spinl/~0 -- EO/mc2"Circularly polarized photons are obtained from the synchrotron radiation when photons are emitted at a small angle to the orbital plane of the circulating electrons or from a helical wiggler installed at a synchrotron [15]. Although the intensity of the synchrotron radiation is significantly high, it does not seem easy to obtain sufficient intensity of circularly polarized monochromatic photons having energies above 100 keV.
5. Conclusion
13 %
x 104 6
Fe
u 5
to
2
g~ c3
2 1
0-8
-6
-4
i
i
I
i
-2
0
2
4
0
6
8
Pz (a.u.)
Fig. 10. Measured magnetic Compton profile of the ferromagnetic iron.
The utilization of the nuclear orientation method using the radioactive isotope 191Os in iron metal, the 3H e / 4 He dilution refrigerator and the solid state detector having a larger active diameter, remarkably improved the accuracy of the magnetic Compton profile measurement in comparison with the previous measurement, and verified its usefulness in measuring the magnetic Compton profile. If a larger dilution refrigerator with a cooling power higher than the present one is used, it will permit measurements with much better statistical accuracy by allowing a stronger radioactive ),-ray source of several Ci. The authors wish to express their gratitude to Prof. K. t3no of the Institute for Solid State Physics (ISSP), the University of Tokyo for his valuable comments and to Dr. M. Shinohara of ISSP for his helpful advice on the dilution refrigerator. They are also grateful to Dr. N. Shiotani of our Institute for stimulating discussion on our experiment.
426
N. Sakat et al,
Magnetic ('ornpton profile measurement
References [1] K.-F. Berggren, S. Manninen, T. Paakkari, O. Aikala and K. Mansikka, Compton scattering, ed., B. Williams (McGraw-Hill, New York, 1977) ch. 6, p. 139. [2] N. Sakai and K. Ono, Phys. Rev. Lett. 37 (1976) 357. [3] N. Sakai and K. Ono, J. Phys. Soc. Jpn 42 (1977) 770. [4] R.M. Steffen and H. Frauenfelder, Alpha- beta- and gamma-ray spectroscopy, ed., K. Siegbahn (North-Holland, Amsterdam, 1965) vol. 2, p. 1453. [5] J. Felsteiner and R. Ophel, Phys. Rev. B16 (1977) 4400. [6] F.W. Lipps and H.A. Tolhoek, Physica 20 (1954) 395. [7] P.M. Platzman and N. Tzoar, Phys. Rev. B2 (1970) 3557.
[8] S,R. de Groot, H.A. Tolhoek and W.J. Huiskamp, Alpha-, beta- and gamma-ray spectroscopy, ed., K, Siegbahn (North-Holland, Amsterdam, 1965) vol. 2, p. 1199. [9] T, Simon and H. Daniel, Phys. Rev. A 15 (1977) 1015. [10] S.G. Malmskog and A. Bgcklin, Ark. Fysik 39 {1969) 411, [11] F.E. Wagner, B.D. Dunlap, G.M. Kalvius, tt. Schaller, R. Felscher and H. Spieler, Phys. Rev. Lett, 28 ~1~72) 530. [12] G. Eska, |:-. Hagn, T. Butz and P. Kienle, Phys. Lett. 36B (1971) 328. [13] T.A. Koster and D.A. Shirley, Hyperfine interactions in excited nuclei, eds,, G. Goldring and R, Kalish (Gordon and Breach, New York, 1971) vol. 4, p. 1239. [14] M. Fallot, Ann. Phys. 10 (1938) 291. [15] R.S. Holt and M.J. Cooper. private communication.
419
MAGNETIC COMPTON PROFILE MEASUREMENT USING CIRCULARLY POLARIZED G A M M A - R A Y S F R O M O R I E N T E D 191mIr N U C L E I N. S A K A I , O. T E R A S H I M A a n d H. S E K I Z A W A
The Institute of Physical and Chemical Research, Wako, Saitama, 351, Japan Received 28 June 1983 Circularly polarized 129 keV y-rays from oriented 191mlrnuclei are used to measure the Compton profile of magnetic electrons in ferromagnetic iron. A high degree of circular polarization is obtained even at temperatures about 200 mK owing to the large hyperfine magnetic field at the Ir site in Fe metal. Utilization of a 40 mCi v-ray source, together with a 3He/4He dilution refrigerator and a solid state detector, is found to be effective in obtaining high statistical accuracy. Efficient geometrical arrangement of the apparatus is discussed based on the cross section of the spin-dependent Compton scattering. Experimental procedures, source preparation and data accumulation are described in detail.
1. Introduction
When monochromatic photons are Comptonscattered to a fixed direction, the observed energy spectrum of the scattered photons is Doppler-broadened because of the quantum mechanical motion of electrons in matter. This spectrum, the so-called Compton profile, provides information about the momentum distribution of electrons. Hitherto many Compton-profile measurements have revealed the momentum distribution of conduction electrons in various solids [1]. However, no direct information on the spin states of electrons in magnetic solids can be obtained by these ordinary unpolarized-photon Compton-profile measurements. When the incident photons are circularly polarized, the Compton-scattering cross section becomes dependent on the direction of the electron spins. Then, using circularly polarized photons, it is possible to experimentally obtain the Compton profiles of magnetic electrons in ferro- or ferrimagnetic materials [2]. From now on we call them the magnetic Compton profiles. Such a measurement of the magnetic Compton profile was already made on ferromagnetic iron by one of the authors [2,3] using 122 keV circularly polarized y-rays from oriented 57Co nuclei in iron metal. However, the adiabatic demagnetization method utilized to orient the nuclei at low temperatures around 50 mK was very tedious and limited in cooling power, resulting in a magnetic Compton profile of ferromagnetic iron not satisfactory enough in accuracy. Thus, a more statistically accurate measurement should be attempted to examine the momentum distribution of the magnetic electrons in detail. The present paper reports an improved and more advantageous nuclear orientation 0167-5087/84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
method which allows high statistical accuracy in the profile measurements. Besides the nuclear orientation method, the following methods seem to be applicable to obtain circularly polarized y-rays from radioactive isotopes. (1) The B-3' directional coincidence method [4]; the y-rays immediately following the B-decay are partially circularly polarized when they are emitted in the direction opposite to that of the preceding B-particles. (2) The Coulomb-excitation method; the spin of a Coulomb-excited nuclear state is polarized in the direction perpendicular to the scattering plane of the projectile. Then "r-rays, which are emitted from the coulomb-excited nuclei and counted in coincidence with the projectile scattered to a fixed direction, are partially circularly polarized. (3) The double Compton scattering method [5]; the y-rays which are Compton scattered by polarized electrons in magnetized ferromagnetic material are partially circularly polarized. The methods (1) and (2) require a time coincidence measurement, but the time resolution of the solid-state detector, which is used to analyze the energies of scattered y-rays, is at most 1 ns. Then, the counting rate of the B-particles or the scattered projectiles can not be allowed to exceed 10 9 cps, which corresponds to the effective activity of a y-ray source of 30 mCi. Although method (3) is free from this restriction, the degree of circular polarization of Compton-scattered photons is not so high, and the photons scattered in a fixed direction must further be made monochromatic, because of their broad energy spectrum represented by the Compton profile. Thus it is difficult in practice to obtain a sufficient intensity of monochromatic circularly polarized y-rays by means of the methods mentioned above.
420
Sakai el aL/ Magnetic ("ornpton profile measurement
N.
Section 2 describes the characteristic features of the spin-dependent Compton scattering experiment, and the following sections 3.1-3.3 deal with the experimental procedures for preparing a strong radioactive 7-ray source with a high degree of circular polarization, by using a 3 H e / 4 H e dilution refrigerator. The accumulation systems are described in section 3.4. In section 4, the measured magnetic Compton profile of ferromagnetic iron is presented.
Eo,Ko/
E'Kzl
/
2. Theoretical
The theoretical expression of the spin-dependent C o m p t o n scattering cross section for free electrons was developed by Lipps and Tolhoek [6] and extended by Platzman and Tzoar [7] for electrons in ferromagnetic materials, within the framework of the impulse approximation. When we observe the energy of the scattered photon, the Compton scattering cross ~section can be written as follows.
d~dE
2
Fig. 1. The spin-dependent Compton scattering of y-rays with circular polarization Pc. The energy and momentum of the incident and scattered y-rays are denoted by E 0, g o and E, K, respectively, and oo the electron spin at the initial state. ing expression is obtained,
(d~2dEJup-(d~2dEjdow, =
ff
(~° + Pl~t)
This expression indicates that the difference between the two energy spectra, one measured with the scatterer
x ff[n'(p)+n*(p)]dpxdp,
(.)]dpxdp,,}
+ po+s.,.ff [.' ( . ) - . '
(P)-.'(.))dpxdp,
Here, r0 denotes the classical electron radius, E 0 and E the energies of the incident and the scattered photons, Pj and Pc the degree of linear and circular polarization of the incident photons, and n~(p) and n*(p) the m o m e n t u m distribution of electrons having a momentum p with spin up and down, respectively. The functions ~0, ~J and ~spi. a r e the angular parts of the scattering cross section when the initial electrons are at rest, and shown by Lipps and Tolhoek to be ~0=
I + cos 2 0+
E0- E
0
(1 - c o s 0 ) ,
mc 2
- 0•
~l = sin2 0, ~spin =
Ik.l,..
i~ o
~=3~
v,0
- - ( 1 - - COS 0 )
( Eo+E
x~cos0cos~b+
E mc
sin 0 sin ~b cos 2
} ".
The function ~o is the ordinary part, whereas ~ and (~spin are the polarization dependent parts. The angle 0 is the scattering angle of photon, q~ the angle between the direction of the incident photon K 0 and that of the electron spin o 0, and ,h is the angle between the (K0, a0)-plane and the ( K 0, K)-plane as shown in fig. 1. The notation me 2 is for the electron rest mass energy. Since only the third function ~p~, changes its sign by reversing the direction of the electron spin, the follow-
I
= 60"
~=90"
Fig. 2. The variation of f as a function of the scattering angle 0 and the spin direction ~ (for the definition, see the text). For dotted loops, f < 0, and for solid loops, f > 0. The vector K o is the momentum of the incident y-rays, and o0 the electron spin of the initial state.
N. Sakai et al. / Magnetic Cornptonprofile measurement 0
421
50
150
100 i
2~.~
, , I ' , '
'
I ' '
'
191mlr in Fe
P4
~f
I--
0
I
1
0"
90'
180°
270'
.
0
I ~
360'
tV Fig. 3. The angular dependence of f on the spin direction ~, (for the definition, see the text).
magnetized in one direction and the other with the same scatterer but magnetized in the opposite direction, gives the magnetic C o m p t o n profile, Jm,s" The quality of a magnetic Compton profile measure-
f~Nl -'-0
, , , , I , L i k 1 i ~ , i 50 100 150 TEMPERATURE (ink)
Fig. 5. The temperature dependence of the degree of circular polarization Pc (lower part), and of the intensity (upper part) of 129 keV y-rays emitted in the direction of the external magnetic field. The intensity is normalized to the value at 4.2 K. Pc of 122 keV -/-rays of 57Co in iron metal is also shown in the upper figure for comparison.
190 OS ÷ n
ment can be represented as follows by a ratio R which is essentially the signal to noise ratio of the measurement,
15./, d 191 76 OS
13-
R= 171.4 k e y
4.9 s
No ( E/Eo )2 Pc Nspin ](~spin I (No(E/Eo)ZN, otaI~O) '/2
11/2-
= ~o "~I
( -lOO'/. CE )
129.5
5/2"
E
f
82.4 .___~ ,,_ --
1//2*
+
3//2 + 191 77
[r
Fig, 4. Decay scheme of ]91Os. The metastable 1 1 / 2 - state can be oriented considerably in iron metal around 100 mK due to the large hyperfine magnetic field of 1400 kG, and the following 129 keV y-rays are circularly polarized.
~N+~. lf(O,
~P,~')1,
(/)spin
E0 ¢ 00 '
because the main " n o i s e " is due to the statistical errors of the total counts, and this total count is approximately proportional to (E/Eo)2NoNtotal~o • Here N 0, Nspin and Ntota I denote the incident photon number, the net magnetic electron number and the total electron number of a specimen, respectively. The function f in R changes its value with the geometrical arrangement of the apparatus. The dependence of f on 8 is plotted in fig. 2 for various values of ~/, with ~ = 0. The value of f is not always symmetric with respect to the direction of the electron spin. The large value of f for the backscattered geometry meets the requirement of the Compton profile
422
N. Saka~ eta/, /' Magnett ' ('mnpton profde measurement
measurement; the Doppler broadening of the energy of the scattered photon due to the motion of the electron occurs significantly on backscattering. The value of f is plotted in fig. 3 as a function of ~b for various values of 0 with ~ = 0. The angle which makes the absolute value of f maximum shifts from 180 ° to lower angles as 0 decreases from 180 °. When the angle 0 is 145 ° , as was the case of the present experiment, the maximum occurs at + = 165 °. This arrangement requires the incident y-rays impinging on one side of the specimen and the scattered y-rays emerging from the other side of the specimen. In practice, it was found to be difficult to set an electromagnet and a magnetic shield box in the space between a cryostat and a y-ray detector. Although f decreases to a value of 70% of the maximum, the arrangement with ~ = 30 ° was adopted• It is worth mentioning that an alternative arrangement with 0 = 145 ° and q~ = 120 ° gives a comparable magnitude of f to that of the present arrangement. This alternative arrangement will be useful when the size of the specimen is restricted.
3. Experimental procedures 3.1. Circularly polarized y-ray source
A useful y-ray Compton scattering experiment requires a y-ray source which emits energetically isolated high energy photons and has a relatively long lifetime. In addition to these, the following characteristics of the nucleus are also required when the nuclear orientation method [8] is applied to produce circularly polarized y-rays. Since the nuclear orientation is represented by the Boltzmann distribution among nuclear
10 7
I
I
f
I
I
magnetic hyperfine levels, the smaller the latLo of the Boltzmann factors, e x p ( - I ~ t t i n t / k T ), the higher is the expected degree of nuclear polarization, resulting in , higher degree of circular polarization of y-rays. Here t~ is the nuclear magnetic moment, and H,~ t is the hyperfine magnetic field at the site of the nucleus. Then, ( 1 ) a large nuclear magnetic moment (of the ground state of the radioactive nucleus or of the metastable excited state of the nucleus), and (2) a large hyperfine magnetic field (at the site of the radioactive nucleus) are effective for the purpose. Moreover, (3) the preferable y-ray multipolarity is E1 or M1, since the ratio R depends also on the number of the incident y-rays /V(~; if the muhipolarity is E2, for example, the intensity of photons in the direction of the magnetic field decreases as the degree of circular polarization P~, increases. After a careful survey of the characteristics of a great number of nuclei, the radioactive isotope ~ ( ) s in iron metal [9] was found to be the most suitable one for this purpose to our knowledge. The decay scheme of the nucleus is shown in fig. 4. This nucleus has a half-life of 15 d and emits 129.46 keV isolated y-rays with a multipolarity of M1 + 13% E2 [10,11]. The isomer ~91'~Ir has a large magnetic moment of 6.03 nuclear magnetons [12] and 4.9 s half-life which is sufficient to attain thermal equilibrium. The hyperfine magnetic field at iridium nuclei in iron metal is known to be - 1 4 0 3 kOe [13]. Fig. 5 shows the calculated temperature dependence of the degree of circular polarization and that of the intensity of 129 keY y-rays emitted in the direction of the external magnetic field, together with similar curves of the 57Co isotope in iron metal, which was used in the previous experiment. A degree of polarization as high as 80% can be obtained with this new isotope even at 100 n'l K .
I
I
lr - KI3
"
10 6
I
1911r _y
lr-Ka
~n lO5 t-"Zt
K~.. ::
~-
• '.. 1911r_¥
J
'
' X . ~ : :'.:"
Ge
7
10 3
,< I 60
I 70
I 80
i l gO 100 ENERGY ( k e Y )
Fig. 6. The energy spectrum of V- and X-rays from
an
I 110
I 120
i 130
19lOs source measured by a pure Ge detector•
N. Sakai et al. / Magnetic Compton profile measurement
b
423
~,-ray sou •
slit
electromal]net
=+°'
+-+
x+IT+
-+++
iii
0
lOcm
Fig. 7. (a) Schematical view of the apparatus for a magnetic Compton profile measurement. The 3He/4He dilution refrigerator is suspended about 2 m above the floor. (b) Experimental arrangement of the circularly polarized y-ray source, the specimen and the y-ray detector. The scattering angle is 145_+4° .
3.2. Source preparation The radioactive isotope 191Os was prepared by neutron activation. Osmium atoms can be dissolved in iron metal to an extent of approximately 11 at.%, with the alloyed iron being kept still in the ferromagnetic state [14]. Alloys of Fe92Os 8 were prepared with an argon plasma furnace using stable isotopes of powdered 19°Os enriched to 95 at.%, and 56Fe metal prepared from 56Fe20 3 powder enriched to 99.9 at.%. Enriched isotopes were indispensable to avoid the unnecessary radioactive self-heating. An about 40 mCi y-ray source was obtained using an FeOs plate with dimensions of
~, rays
r+0++,mo0+ °°°' P H A
++I [ automatic controtter lime
read out
:
~
,
ext. stop accum.
memory
group current t o . _ _ _ ~ magnet ~-
Oo+o
l- d oi Z l I
I 1 cycle
I
l-[
F ,I
Fig. 8. Time relation between the accumulation of the PHA and the signals of the employed automatic controller.
12 x 6 × 0.2 mm 3 by neutron activation for 12 d with a neutron flux of 3 x 1013 n / s . cm 2 from the JRR-2 reactor of the Japan Atomic Energy Research Institute. Fig. 6 shows the energy spectrum of V- and X-rays from the source. The assignment of the peaks is denoted in the figure. No v-rays were observed above 129 keV except minor peaks from 192Ir impurity nuclei. 3.3. Cooling of y-ray source The isomer 191m|r can be oriented sufficiently at temperatures of about 100 m K as already shown in fig, 5. The r-particles and the internal conversion electrons are almost completely, and X-rays are partially, absorbed in the source material, causing the heating effect in the source. The estimated amount of the radioactive self-heating of a 20 mCi lmOs source is about 18 #W. A 3 H e / 4 H e dilution refrigerator (Oxford Instruments Ltd.) having a cooling power of 20/~W at 100 m K was used for the experiment. The experimental arrangement is illustrated schematically in fig. 7. The outer cryostat for the liquid He bath and the liquid N 2 bath can be lowered away from the refrigerator insert by a hand hoist, and then removed horizontally on rails for the setup of the y-ray source into the indium-sealed inner vacuum can. The y-ray source was soldered on a copper cold finger of 7 cm long under an atmosphere of argon gas. An aluminium foil was glued on the surface of the source against rust. The cold finger was screwed and soldered on the bottom of the mixing chamber of the refrigerator. A magnetic field of 7.5 kOe was supplied by a split type superconducting magnet to saturate the magnetization of the FeOs plate (see fig. 7b). The
424
N. Sakat et al. / Magnetic ('ompton profile measurement
surface of the source was approximately parallel to the direction of the magnetic field to minimize the demagnetization effect. The source temperature was determined by means of the temperature dependence of the anisotropic emission probability of 129 keV "/-rays in the direction of the magnetic field as shown in fig. 5. The source temperature thus determined was 197 mK for a 40 mCi fresh source and decreased gradually at a rate of 3 m K / d a y . During the Compton-profile measurement the source temperature was monitored by a carbon resistance thermometer on the mixing chamber•
with an energy resolution of 556 eV fwhm at 122 keV (Ortec-GLP; 25 mm active diameter and 10 mm active depth). The relatively large active diameter was effective in increasing the counting rate of the scattered y-rays, although the energy resolution was reduced slightly. A lead collimator with the hole dimensions of 20 mm wide, 40 mm high and 95 mm long was placed in front of the detector. The detector was covered with lead blocks in which a tin cylinder was inserted to absorb lead X-rays. The energy spectra of Compton scattered y-rays from the spin-up scatterer (UP) and that from the spin-down one ( D O W N ) were accumulated repeatedly in the order of UP, D O W N , D O W N , UP, D O W N , UP, UP, D O W N for 100 (live time) seconds each, to avoid systematic errors due to the decrease of the source intensity and the drift of the electronic system. Each of the two energy spectra was stored in the corresponding 1024 ch. memory group of the pulse height analyzer (PHA). The P H A accumulates the data in repeat mode and integrated counts under the Compton peak are printed out after every 100 s accumulation to monitor the condition of the equipment. As illustrated in fig. 8, an automatic controller generates two states for UP and D O W N accumulations. The controller, after receiving a print-out end signal from the PHA, makes the state to proceed to the next one and converts the PHA memory group from one to the other simultaneously with the reversal of the specimen magnetization. The PHA starts
3.4. Data accumulation
The incident circularly polarized y-rays, emerging horizontally from the refrigerator through an aluminized Mylar window, were collimated by a lead slit 8 mm in width and 24.5 mm in height. A soft iron electromagnet was used to align the direction of the electron spins in the specimen. The measured magnetization of the pure iron specimen reached a value of 93% of the saturation magnetization of pure iron. A magnetic shield box made of iron plate was prepared to cover the electromagnet, and a soft iron cylindrical magnetic shield to surround the outer cryostat of the refrigerator, The specimen included in the electromagnet is 10 cm long, 5 cm wide and 1 cm thick. The scattered ./-rays to the direction of 0 = 145 _+ 4 ° were detected by a pure germanium solid state detector
xlO4
I
'
I
I
I
50
I
I
I
(a)
f'
c o
0
Z
..-"
~.......'...
~ 50 xlO 4 ' '
~.
/
i-., ..'. '" ...~r..". %. ~ 60
70
--
BO
100
90
,
.
cl
-.
I
I
;
| ,;.,
110
120
i
I
.1
130
(b)
.,
Z i
,!.' Z
•5'
05
~, :#,.;.:'. ".".,..~-:.~',,.'C:.:,.::,:'.,:~.,,,.:...,:A,~,'.:..~,..:',,,:.~',~'~;"':.'..' 50 " ......
60
70
80
90 100 110 120 130 ENERGY (keY) Fig. 9. (a) Energy spectrum of detected y- and X-rays, including 57Co "/-rays for the spectrum stabilizer. (b) Energy spectrum of Compton scattered "/-rays by magnetic electrons in a magnetized ferromagnetic iron specimen.
N. Sakai et al. / Magnetic Compton profile measurement
its accumulation after receiving an off-set of the external stop signal which is generated by the controller. The two-point digital spectrum stabilizer is coupled to the analog-to-digital converter (ADC) of the PHA to feedback the gain drift in the PHA system consisting of the ADC, amplifier, pre-amplifier and the detector. The 122 keV v-rays from 57Co and the 24 keV "t-rays from 1]9mSn were used for this purpose.
4. Results and discussion The energy spectrum of the scattered ),-rays from the specimen of magnetized polycrystalline ferromagnetic iron is shown in fig. 9a. The broad peak around 89 keV is the Compton peak of the circularly polarized 129 keV "t-rays of 191Os, and peaks in the lower energy region around 58 keV and 53 keV are the Compton peaks of Ir Kp X-rays and Ir K~ X-rays, respectively. The sharp peak at 122 keV is the photo-peak of 57Co v-rays used as one of the standard peaks for the digital spectrum stabilizer. The difference between the UP energy spectrum and the DOWN one is shown in fig. 9b. The residual peak around 89 keV is the magnetic Compton profile of ferromagnetic iron. The complete disappearance of other peaks in fig. 9a indicates the absence of systematic errors in this subtracted spectrum; the unpolarized X-rays do not distinguish the direction of the electron spins. The overall accumulation time was 165.1 h for both the UP and DOWN spectra and the total counts under the magnetic Compton profile was 6.4 x 105 counts. It should be noted that the total amount of the magnetic Compton profile is 2.59% of that of the UP Compton profile. This percentage agrees
425
well with that evaluated with the present experimental parameters and 2.2 magnetic electrons per iron atom. After the converting procedure on the spectrum from the energy scale to the momentum scale of the electron (here 1 keV Doppler broadening corresponds to 0.956 a.u. in momentum scale), the magnetic Compton profile in momentum scale is obtained as shown in fig. 10. The counts are summed up every 5 channels to increase the statistical accuracy. The correction was made for "long tail" and also for self-absorption in the specimen, but was not made for multiple scattering, which is estimated to cause at most 10% change in the shape of the magnetic Compton profile. The momentum resolution of the system including energy and geometrical resolution was 1.05 a.u. The gain drift of the PHA system, estimated by the differences of the standard peaks, was found to be less than 10 -2 channels or 1.07 x 10 -3 a.u. A detailed discussion on the magnetic Compton profile of ferromagnetic iron including the comparison with theoretical profiles will be published shortly. One of the excellent features of the nuclear orientation method is the utilization of high energy photons, because the ratio R is roughly proportional to the ratio I~spinl/~0 -- EO/mc2"Circularly polarized photons are obtained from the synchrotron radiation when photons are emitted at a small angle to the orbital plane of the circulating electrons or from a helical wiggler installed at a synchrotron [15]. Although the intensity of the synchrotron radiation is significantly high, it does not seem easy to obtain sufficient intensity of circularly polarized monochromatic photons having energies above 100 keV.
5. Conclusion
13 %
x 104 6
Fe
u 5
to
2
g~ c3
2 1
0-8
-6
-4
i
i
I
i
-2
0
2
4
0
6
8
Pz (a.u.)
Fig. 10. Measured magnetic Compton profile of the ferromagnetic iron.
The utilization of the nuclear orientation method using the radioactive isotope 191Os in iron metal, the 3H e / 4 He dilution refrigerator and the solid state detector having a larger active diameter, remarkably improved the accuracy of the magnetic Compton profile measurement in comparison with the previous measurement, and verified its usefulness in measuring the magnetic Compton profile. If a larger dilution refrigerator with a cooling power higher than the present one is used, it will permit measurements with much better statistical accuracy by allowing a stronger radioactive ),-ray source of several Ci. The authors wish to express their gratitude to Prof. K. t3no of the Institute for Solid State Physics (ISSP), the University of Tokyo for his valuable comments and to Dr. M. Shinohara of ISSP for his helpful advice on the dilution refrigerator. They are also grateful to Dr. N. Shiotani of our Institute for stimulating discussion on our experiment.
426
N. Sakat et al,
Magnetic ('ornpton profile measurement
References [1] K.-F. Berggren, S. Manninen, T. Paakkari, O. Aikala and K. Mansikka, Compton scattering, ed., B. Williams (McGraw-Hill, New York, 1977) ch. 6, p. 139. [2] N. Sakai and K. Ono, Phys. Rev. Lett. 37 (1976) 357. [3] N. Sakai and K. Ono, J. Phys. Soc. Jpn 42 (1977) 770. [4] R.M. Steffen and H. Frauenfelder, Alpha- beta- and gamma-ray spectroscopy, ed., K. Siegbahn (North-Holland, Amsterdam, 1965) vol. 2, p. 1453. [5] J. Felsteiner and R. Ophel, Phys. Rev. B16 (1977) 4400. [6] F.W. Lipps and H.A. Tolhoek, Physica 20 (1954) 395. [7] P.M. Platzman and N. Tzoar, Phys. Rev. B2 (1970) 3557.
[8] S,R. de Groot, H.A. Tolhoek and W.J. Huiskamp, Alpha-, beta- and gamma-ray spectroscopy, ed., K, Siegbahn (North-Holland, Amsterdam, 1965) vol. 2, p. 1199. [9] T, Simon and H. Daniel, Phys. Rev. A 15 (1977) 1015. [10] S.G. Malmskog and A. Bgcklin, Ark. Fysik 39 {1969) 411, [11] F.E. Wagner, B.D. Dunlap, G.M. Kalvius, tt. Schaller, R. Felscher and H. Spieler, Phys. Rev. Lett, 28 ~1~72) 530. [12] G. Eska, |:-. Hagn, T. Butz and P. Kienle, Phys. Lett. 36B (1971) 328. [13] T.A. Koster and D.A. Shirley, Hyperfine interactions in excited nuclei, eds,, G. Goldring and R, Kalish (Gordon and Breach, New York, 1971) vol. 4, p. 1239. [14] M. Fallot, Ann. Phys. 10 (1938) 291. [15] R.S. Holt and M.J. Cooper. private communication.