A single line linearly polarized source of 14.4 keV radiation by means of resonant absorption

Nuclear Instruments and Methods in Physics Research B 155 (1999) 189±198

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A single line linearly polarized source of 14.4 keV radiation by means of resonant absorption J. J aschke a

a,*

, H.D. R uter a, E. Gerdau a, G.V. Smirnov b, W. Sturhahn J. Pollmann a,c

a,c

,

II. Institut f ur Experimentalphysik, Universit at Hamburg, Luruper Chaussee 149, D-22761 Hamburg, Germany b Russian Scienti®c Centre ``Kurchatov Institute'', Moscow 123182, Russian Federation c Argonne National Laboratory, Advanced Photon Source, Argonne, IL 60439, USA Received 29 December 1998; received in revised form 5 March 1999

Abstract A single line linear polarized source of 14.4 keV is realized in a conventional M ossbauer setup. In combination with the dichroism of a magnetized 57 FeBO3 or a-57 Fe absorber a single line unpolarized 57 CoCr- or 57 CoPt-source delivers P 90% linear polarized radiation and about 25% of its primary intensity. The optimal value of the internal magnetic ®eld of each absorber is selected by temperature adjustment. Calculations and measurements are in good agreement. Ó 1999 Published by Elsevier Science B.V. All rights reserved. PACS: 29.30.-h; 33.45.+x; 61.18.Fs; 76.80.+y Keywords: Polarized c-radiation; M ossbauer e€ect

1. Introduction Resonant absorption in general and therefore also any component of a nuclear transition in a M ossbauer experiment depends strongly on the orientation of the magnetic ®elds and the electric ®eld gradients in the absorber with respect to the polarization and the propagation vector of the incoming radiation [1±3]. Especially interesting in transmission geometries is the case where compo-

* Corresponding author. Tel.: +4940-8998-2156; fax: +49408998-2212; e-mail: [email protected]

nents of the spectrum of the source are almost totally absorbed when the polarization and the ®eld directions are properly chosen. Therefore polarized sources consisting of a radioactive source in combination with a polarizer may allow for a remarkable simpli®cation and an easier interpretation of absorption spectra in M ossbauer experiments [4±6]. In principle polarized radiation from a radioactive source is easily obtained. If for example a magnetic hyper®ne interaction of sucient strength is present each component of the emitted radiation is polarized. The drawback of this method is that a single line unpolarized source is

0168-583X/99/$ ± see front matter Ó 1999 Published by Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 9 ) 0 0 2 4 2 - 6

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replaced by a multiline polarized source and in a conventional transmission experiment an incoherent superposition of many absorption subspectra is generated, each containing the full information on the absorber. Thus a single line polarized source is highly desirable. At present two types of sources are used for nuclear resonance absorption experiments. This is either the traditional single line unpolarized radioactive source which emits a line of natural width C or a synchrotron insertion device (bending magnet, wiggler, undulator) which is a broadband source of nearly 100% linear polarized radiation [7,8]. The experimental demands to obtain a single line polarized source in these two cases are quite di€erent. The task in case of synchrotron radiation is to select a band of the desired width while maintaining the polarization whereas in case of a single line radioactive source the components of one polarization state have to be removed without losing too much of intensity of the components of the other polarization. Nearly natural linewidth polarized M ossbauer radiation was recently generated by di€raction of synchrotron radiation from a nuclear array of a 57 FeBO3 -single crystal [9]. The high brilliance of the synchrotron radiation is essential for this process. In principle, pure nuclear di€raction techniques may be applied also to radioactive sources. However, their brilliance is far too low to obtain sucient intensity for counting experiments (see e.g. [10]). Instead of ®ltering the desired polarization state out of an unpolarized beam by di€raction, it is possible to suppress transmission of one polarization state by selective absorption. This means that one has to combine the single line source with an absorber (i.e. the polarizer) which is split by hyper®ne interaction. The transition energy of one component of the polarizer must coincide with the energy of the source transition. This can be achieved by moving the polarizer with constant velocity with respect to the source [11,12]. In a conventional transmission experiment the M ossbauer sample has also to be moved and thus in such a setup one has to employ two synchro-

nized velocity drives. A more simple and attractive solution is obtained if the energetic coincidence of source and absorber line is achieved by a properly designed combination of source and polarizer. Recently this technique was applied to obtain circular polarized sources [13,14]. Other work on polarized sources is described in a comprehensive review [6]. In this paper, we present our experiments performed with the aim to develop a simple linear polarized single line source for the 3/2ÿ ! 1=2ÿ 14.4 keV transition of 57 Fe by exploiting the temperature-dependent magnetic hyper®ne interaction in a polarizer. 2. General considerations 2.1. Intensity and polarization after a single line polarizer The intensity distribution dIs …E† of an unpolarized M ossbauer source is the sum of two orthogonally polarized radiation components. To describe the polarization state of the radiation we introduce a Cartesian coordinate frame x; y; z, where the z-axis indicates the propagation direction of the beam. For a base of linear polarization vectors we assume that ~ e p is directed along the x-axis and ~ e r along the y-axis. Then we write: dIs …E† ˆ dIsr …E† ‡ dIsp …E†;

…1†

with the identical Lorentzian distribution dIs…r;p† …E† ˆ

I0 C 1 dE: 2 2p …E ÿ E0 †2 ‡ C2 =4

…2†

We assume that only dIsr …E† is resonantly absorbed in a polarizer which has a transition component of relative strength w at exact resonance with the transition energy E0 of the source. The in¯uence of the other transition components in the polarizer's hyper®ne spectrum is neglected for the moment. The absorption is then described by different linear absorption coecients l: lr …E† ˆ lrres …E† ‡ lphoto and

…3†

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lp …E† ˆ lpres …E† ‡ lphoto ;

…4†

with lpres …E† ˆ 0

…5†

and lrres …E† ˆ nN0 bfA wr0

C2 =4 2

…E ÿ E0 † ‡ C2 =4

:

…6†

The resonance cross-section r0 of the resonant nuclei at E0 , the resonance width C, the isotopic abundance b and the Lamb±M ossbauer-factor fA of the polarizer have their usual meaning. The relative weight w of the resonant transition component in the hyper®ne spectrum depends on the orientation of the hyper®ne ®elds and the degeneracy of that component. The sum over the relative weights of all component lines is one. The photoabsorption coecient lphoto of the polarizer substance is calculated as: X …NX rphoto;X †: …7† lphoto ˆ n X

Here n is the number density of the elementary cells, each cell contains NX atoms of element X. X ˆ 0 denotes the element of the resonant nuclei. rphoto;X is the photoelectric cross-section of the atom X. The total e€ective resonance thickness Teff of a polarizer of geometrical thickness d is Teff ˆ nN0 dbfA r0 . We introduce the partial e€ective thickness of the polarizer for the resonantly absorbed component as Tpol ˆ w Teff . The transmission of the source radiation is immediately given as the sum of two intensity distributions: dI p …E† ˆ Isp …E† eÿlphoto d dE

…8†

and r

dI r …E† ˆ Isr …E† eÿlres …E†

d

eÿlphoto d dE:

…9†

The integral intensities I r and I p have been calculated in the early days of M ossbauer spectroscopy [15]: Ip ˆ

I0 ÿlphoto d e ; 2

…10†

Ir ˆ

  I0 ÿTpol =2 Tpol e eÿlphoto J0 i 2 2

191 d

…11†

with the Bessel-function J0 . Also the polarization P of the transmitted radiation is energy dependent because of the energy dependence of lrres …E†. For a rough estimate of the required thickness of the absorber to obtain a high degree of polarization we introduce the mean value of polarization P using the integral intensities of the di€erent polarization states: P …Tpol † ˆ

I p ÿ I r 1 ÿ eÿTpol =2 J0 …iTpol =2† : ˆ I p ‡ I r 1 ‡ eÿTpol =2 J0 …iTpol =2†

…12†

P is a monotone function of Tpol . Thus as further on Tpol / d a large value of P is accompanied by a large value of d. Therefore one has two con¯icting demands. A high degree of polarization needs a high value of Tpol whereas low photoabsorption and high intensity of the transmitted polarized beam need a small value of d. The decrement due to photoabsorption as function of P is: P …NX rphoto;X † Tpol …P † : …13† d…P † lphoto ˆ X N 0 r0 w b fA P The ratio r ˆ X …NX rphoto;X †=…N0 r0 † which measures the total photocross-section of all constituents of an elementary cell in terms of the resonant cross-section of the resonant absorbing nuclei is of central importance for the question if photoabsorption can be kept suciently low, while polarization of the `M ossbauer line' after selective absorption can be suciently high. The ratio rphoto; Fe =r0 which takes the value 2.2410ÿ3 for the 14.4 keV radiation of 57 Fe in pure iron metal marks the minimum of r i.e. the optimal situation one can reach. Only a slight increase occurs if iron compounds containing light elements are used. Their additional contribution to the photocross-section is only a few percent of the iron photocross-section. For example for the compound FeBO3 we calculate an increase in r of 2.7% compared to pure Fe metal. As in the second factor Tpol …P †=…w b fA † of Eq. (13) each of the three numbers in the denominator is 6 1 its value is always > Tpol …P †. For a crude estimation of the conditions under which P ˆ 0:85 may be achieved

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we set in the denominator w ˆ 0.25, fA ˆ 0.75 and b ˆ 0.0217. This yields d lphoto ˆ 27.6 and excludes according to Eq. (9) the use of nonenriched iron in a polarizer for practical purposes. In case of highly enriched iron with b ˆ 0.9 and for the same P ˆ 0:85 we get d lphoto ˆ 0.66, which means that 50% of the selected polarized component passes the polarizer. 2.2. Polarizer split by hyper®ne interaction The established single line sources for the 14.4 keV transition of 57 Fe are dilute solutions of 57 Co in metallic matrices like Cr, Cu, Rh, Pd and Pt. Their transition energies di€er due to their isomer shifts. In Fig. 1 we show in the upper part the isomer shifts of the sources 57 CoCr, 57 CoRh and 57 CoPt with respect to the a-Fe reference material [16±18]. Among the Fe-polarizers acting as ®lters by absorption, the most attractive ones are those which exhibit a two line spectrum due to a quadrupole interaction because of the large value of the relative strength of the lines. Experimentally there are stringent conditions for this case. First of all

Fig. 1. Lower part: Bar diagram of the six components of the 14.4 keV transition in an a-57 Fe foil magnetized perpendicular to the c-ray axis. The length of a bar scales with its weight w. r and p indicate the eigenstates of linear polarization. Upper part: Isomer shift of 57 Fe in Cr-, Rh- and Pt-matrices with respect to a-Fe.

one of the absorber lines has to coincide in energy with the selected source transition. If this is only approximately ful®lled for a certain compound there is most probably no chance to tune the electric interaction to a sucient value by varying an experimental condition like temperature or pressure. Further a single crystal is needed, as the electric ®eld gradient cannot be aligned by an external ®eld, and, as was shown above, this single crystal has to be highly enriched in 57 Fe. We know no candidate for this case. A magnetic interaction on the other hand is tunable by varying the temperature [19,20]. For a discussion of this case a bar diagram of the absorption lines of a-57 Fe at room temperature (Bintern ˆ 33 T) is added in the lower part of Fig. 1. Linear polarization is achieved if a magnetic ®eld magnetizes the iron absorber perpendicular to the direction of the c-ray [21]. Due to the di€erent anisotropies of the six hyper®ne components of the M ossbauer spectrum the weights of the lines (numbered (1)...(6) with increasing energy) are now 0.1875, 0.25, 0.0625, 0.0625, 0.25 and 0.1875. We assign r absorption to the lines (1), (3), (4) and (6) and p-absorption to the lines (2) and (5). The total splitting of the spectrum is about 110C which means that all resonances are clearly separated from each other. Especially the resonances belonging to di€erent polarizations are separated by at least 23C. When the magnetic ®eld is reduced this separation reduces by the same fraction. The whole range of available isomer shifts of standard sources falls into the interval between lines (3) and (4) of the magnetically split iron spectrum at room temperature. Therefore, by decreasing the magnetic ®eld, gradually either line (3), (2), and then (1) or line (4), (5), and then (6) will come into resonance with the source line depending on the sign of the isomer shift between source and polarizer. One expects three extrema of the polarization in the transmitted beam as function of the magnetic ®eld. According to the discussion in the previous section the highest degree of polarization is expected by the lines with the highest weight, the lines (2) and (5). However inspection of Fig. 1 shows that a large reduction of the magnetic ®eld is necessary to achieve overlap of the polarizer's line (5) even if one selects a 57 CoPt source which

J. J aschke et al. / Nucl. Instr. and Meth. in Phys. Res. B 155 (1999) 189±198

shows the most convenient isomeric shift. Because of the overall shrinking of the spectrum the wings of the lines (4) and (6) at the position of (5) will seriously reduce the degree of achievable polarization as well as the intensity of the transmitted beam. The situation is more favorable in case of the inner lines. Here a moderate reduction of the magnetic ®eld is sucient for the 57 CoPt-source whereas the standard 57 CoRh-source again demands for an unacceptable reduction of the overall splitting. It is obvious that any e€ect which can shift the selected resonance of the polarizer towards the energy of the source line is highly desirable. Besides the standard terms ± the isomeric shift and the quadrupole splitting of the absorber ± one can take advantage of the second order Doppler-shift by a temperature di€erence between source and polarizer. These terms obviously work most e€ectively for the inner lines of the spectrum. The predicted behavior of the polarization for the combination of an iron absorber with the standard 57 CoRh-source is shown in Fig. 2 for three di€erent thicknesses of the polarizer as function of the magnetic ®eld. In this case we took into account the second order Doppler-shift DvDoppler …T †. In a series of measurements we obtained for Femetal: DvDoppler …T † ˆ 0:219 mm=s ÿ 7:16  10ÿ4

Fig. 2. Calculated polarization of 14.4 keV radiation from a single line 57 CoRh-source after transmission through a magnetized a-57 Fe absorber of thickness d as function of the hyper®ne ®eld Bintern . Dotted (dashed; solid) line for d ˆ 1 lm; (6 lm; 12 lm), respectively.

193

Fig. 3. Relative transmission of 14.4 keV radiation for the pand r-polarization states through a 12 lm thick a-57 Fe absorber as function of the hyper®ne ®eld Bintern .

T mm=sK. The highest degree of polarization is indeed predicted for resonance with the strongest line (5) and p-absorption. But resonance with line (4) and r-absorption will also yield a polarization of more than 90%. In case of resonance with the outermost line (6) of the spectrum the polarization is clearly reduced due to an overlap with the wing of the line (5) and its p-absorption. This e€ect in¯uences the transmitted intensity seriously as is shown in Fig. 3. Increasing the temperature, i.e. lowering the internal ®eld, the ®rst extremum is expected at about 17 T where 48% of polarized radiation is transmitted. This reduces to 21% and 2.5% at the following extrema, respectively. Therefore experiments with the inner resonances seem to be most promising. This selection also reduces the necessary temperature stability of the oven, which is used to achieve the internal magnetic ®eld via the magnetization of iron. Fig. 4 shows the curve of Fig. 2 for d ˆ 12 lm on the temperature scale. The broad minimum at the inner resonance is experimentally easy to utilize whereas in the other two cases very good temperature stability is necessary. 2.3. Experimental setup and data analysis A schematic drawing of the experimental setup for the determination of P is shown in Fig. 5. The

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saturation e€ects due to the e€ective thicknesses of all components [22]. As polarizing absorbers we used either a single crystal of 57 FeBO3 or a polycrystalline iron foil both enriched to 90% in 57 Fe. 3.

Fig. 4. Calculated polarization of 14.4 keV radiation from a single line 57 CoRh-source after transmission through a magnetized a-57 Fe absorber of thickness d as function of the temperature (compare Fig. 2). Dotted (dashed; solid) line for d ˆ 1 lm; (6 lm; 12 lm), respectively.

57

FeBO3 as polarizer

Iron borate has an antiferromagnetic rhombohedral structure [23±26]. Its Neel-temperature is 348.35(10) K which allows easy variation of the amplitude of the internal magnetic ®eld at ambient temperatures. The two magnetic sublattices have equal magnetic moments. There is a slight canting of the sublattice magnetizations so that a small ferromagnetic moment results in a direction nearly perpendicular to the sublattice magnetizations. Thus 57 FeBO3 is a planar magnet with an almost vanishing magnetic anisotropy in the plane of easy magnetization spanned by the sublattice magnetizations. Out of this (1,1,1) plane towards the crystallographic [1,1,1] direction a strong magnetic anisotropy is observed. As the internal ®elds are now perpendicular to the external ®eld the notation as r- and p- polarization is interchanged with respect to the discussion in section II. In addition, an electric ®eld gradient is present perpendicular to the magnetic plane. Fig. 6 shows the positions of the resonances with respect to available sources.

Fig. 5. Schematic setup for the determination of the polarization. The unpolarized source and the polarizer (heated in an oven) are tightly coupled. The analyzer is mounted on a M ossbauer drive. External magnetic ®elds are applied by permanent magnets or by an electromagnet. The detector is a standard proportional counter.

source consists of the single line radioactive source tightly coupled to the polarizer. For the analysis of the degree of polarization a nonenriched iron foil of e€ective thickness Teff ˆ 5 was mounted on a conventional M ossbauer drive. It was polarized in an external ®eld of 0.08 T. The measured spectra were analyzed with the program packet CONUSS which takes into account the complete setup including source, polarizer and analyzer and also

Fig. 6. As Fig. 1, but with

57

FeBO3 as polarizer.

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195

perature while at the same time protecting it against oxidation. Magnetization of the iron foil at higher temperatures is achieved in very low external magnetic ®elds according to the tenth-power law of the anisotropy constant K1 [27]  10 Ms …T † : …14† K1 …T † ˆ K1 …0† Ms …0†

Fig. 7. Polarization of 14.4 keV radiation after transmission through a magnetized 57 FeBO3 single crystal (d ˆ 61 lm, Teff ˆ 290) as function of the hyper®ne ®eld with a 57 CoRh- and a 57 CoCr-source.

The isomeric shift of the spectrum is 0.385 mm=s. The quadrupole interaction  ˆ ÿ0:38 mm=s shifts the resonance (3) by an additional 0.1 mm=s. There is no noteworthy second order Doppler-shift. 57 CoCr is the best single line source for this case. A ¯at oven was built with the source only 3 cm upstream of the exit window. Magnetization was achieved by two permanent magnets with a special yoke built to obtain a unidirectional polarizing ®eld of 0.06 T. The 57 FeBO3 crystal consisted of a plate of 6  4 mm2 area and 61 lm thickness. This corresponds to an e€ective thickness of Teff ˆ 290 at room temperature. The beam was limited to a circular aperture of 3 mm diameter. P was measured as function of the internal magnetic ®eld with a 57 CoRh- and a 57 CoCr-source. The results are shown in Fig. 7. They are in good agreement with the theoretical predictions. A beam with jP j > 0.9 is obtained. The low weight of the polarizing setup allows to move this unit by a standard M ossbauer drive as a polarized source. 4.

57

Ms is the saturation magnetization of iron. Because of the extreme magnetic weakness of the foil at temperatures near the Curie point it was carefully shielded against disturbing external ®elds which could easily cause unwanted reorientation of the direction of magnetization in the foil. We used an electromagnet in the form of a closed magnetic circuit, which provides a polarizing ®eld of 0.03 T. A current resistive driven heating system allowed to reach temperatures up to 1000 K which was necessary to observe the polarization at all nuclear resonances. In all experiments with an iron polarizer we used a foil of 36 lm thickness with 90% enrichment in 57 Fe. Fig. 8 displays the results for P with the 57 CoRh-source as function of the internal magnetic ®eld in Fe. The maximal measured degree of the polarization of 80% was unexpectedly low compared to the theoretical prediction. But the shape of the theoretical curve is reproduced and a

Fe as polarizer

A polarizer consisting of pure iron has the advantage that it is easily available in any laboratory. The disadvantage is that an oven is needed which allows to heat the iron foil to relatively high tem-

Fig. 8. Polarization of 14.4 keV radiation after transmission through a magnetized a-57 Fe absorber (d ˆ 36 lm) as function of the hyper®ne ®eld with a 57 CoRh-source. The magnetic alignment of the absorber foil is disturbed by the heater current.

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Fig. 9. Polarization of 14.4 keV radiation after transmission through a magnetized a-57 Fe absorber (d ˆ 36 lm) as function of the hyper®ne ®eld with a 57 CoPt-source without perturbation by the heater current.

netization vectors of two sets of sublattices [28,29]. Below the spin ¯ip transition at 415 K the direction of spontaneous magnetization is perpendicular to the [0, 0, 1]-direction of the crystal and within the plane of the crystal slab. Therefore no external magnetic ®eld is necessary to orient the internal magnetic ®eld of the crystal. There are at least two nonequivalent crystal sites for iron both of which show a pronounced electric interaction. We performed transmission experiments with a rpolarized beam propagating along the [0, 0, 1]-axis of the 57 Fe3 BO6 crystal which was rotated in the (0,0,1)-plane before each spectrum. The two spectra where the line intensities take their extreme value as function of the rotation angle are shown in Fig. 10. Clearly either the lines (1), (3), (4) and (6) or the lines (2) and (5) are seen. The lacking lines seem perfectly suppressed. The positions of

scaling factor of 0.8 yields good agreement with the data. Additional experiments proved that this reduction was due to a distortion of the unidirectional magnetization over the polarizer area by the spurious magnetic ®eld of the heater current. Fig. 9 shows the results of measurements where the heater current was switched o€. The electromagnet providing the orienting ®eld produces part of the heating as a byproduct as well. We used a 57 CoPt source in this case. Its favorable isomeric shift allows to reach the optimal condition for high polarization at 770 K which is 150 K below the temperature needed with a 57 CoRh source. Higher temperatures that would have been needed to observe the other extrema were not possible in this arrangement. In contrast to the case of 57 Fe3 BO3 this oven is too heavy to be moved easily. Thus in experiments with this polarized source the absorber has to be moved. 5.

57

Fe3 BO6 as absorber in a linear polarized beam

In a ®rst application of the 57 FeBO3 polarized source we measured M ossbauer spectra from a single crystal of 57 Fe3 BO6 . 57 Fe3 BO6 is a complex antiferromagnet with a slight canting of the mag-

Fig. 10. M ossbauer spectra of a single crystal of 57 Fe3 BO6 measured with linear polarized radiation (57 FeBO3 -polarizer) at room temperature. The upper and the lower curve belong to two perpendicular orientations of the magnetization in the (0,0,1)-plane.

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the lines as well as their intensities are not in accordance with the assumption that the axes of the ®eld gradients are directed along crystallographic axes. The analysis which will be published in a separate paper revealed that in all sites a ®eld gradient of strong axial anisotropy exists.

its plane. Complete alignment of the magnetization parallel to the beam and thus circular polarized radiation should also be achievable in a future development.

6. Conclusions

This work was supported by the Deutsche Forschungsgemeinschaft under project GE 384/132. WS and JP are supported by the U.S. Department of Energy, Basic Energy Sciences, Oce of Science, under Contract No. W-31-109-ENG-38.

A single line linearly polarized source for the 14.4 keV-c-radiation of 57 Fe was developed. It combines standard single line sources with polarizers which absorb one polarization component nearly completely and simultaneously weaken the other component by photoabsorption by a factor of about two. This is only possible if highly enriched polarizers are employed. A major goal of this development was to avoid the necessity of two drives for standard M ossbauer experiments with this polarized source. Therefore the polarizer line had to be shifted exactly to the position of the source line. This was achieved by varying the internal magnetic hyper®ne ®eld of the polarizer via the temperature. Further on favorable line shifts by second order Doppler-shift and quadrupole interaction were exploited. Two solutions for this concept were realized. In both cases a degree of polarization of P 90% is obtained. In the ®rst setup a standard 57 CoCr-source and a 57 FeBO3 -single crystal kept at a temperature of 340 K are combined. The low weight of this setup including the heating of the polarizer allows to mount it on a M ossbauer driving unit. Because of the low photoabsorption in the polarizer and the small distance of less than 4 cm between the source and the exit window of the oven experiments with high counting rates are possible. The second setup combines a 57 CoPt-source with a 57 Fe metal polarizer. Contrary to 57 FeBO3 single crystals an enriched iron foil is easily available. The necessary reduction of the internal ®eld is achieved at a temperature of  770 K which is far below the Curie point of iron, but nevertheless the oven which is needed is too heavy to be moved. The remarkable magnetic weakness of iron metal near its Curie point allowed magnetic alignment of the polarizer foil by a weak magnetic ®eld within

Acknowledgements

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