Nuclear Bragg diffraction using synchrotron radiation A new method for hyperfine spectroscopy

Nuclear Instruments and Methods in Physics Research A303 (1991) 495-502 North-Holland

495

Nuclear Bragg diffraction using synchrotron radiation A new method for hyperfine spectroscopy R. Rilffer, E. Gerdau, M. Grote, R. Hollatz, R. Röhlsberger, H .D. Rüter and W. Sturhahn II. Institut für Experimentalphysik, Universität Hamburg, D-2000 Hamburg 50, Germany

Nuclear Bragg diffraction with synchrotron radiation as source will become a powerful new X-ray source in the A region . The brilliance of conventional Mössbauer sources is already exceeded ; giving hyperfine spectroscopy a further impulse . As examples applications to yttrium iron garnet (YIG) and iron borate will be discussed .

1 . Introduction Activity in the field of nuclear Bragg diffraction has strongly increased after the pilot experiment which used synchrotron radiation as a source [1] . Recent experiments have proved that precise determinations of hyperfine interaction parameters can be done. In the future with even higher intensities there will be applications in the field of solid state physics and y-optics. Nuclear Bragg diffraction experiments with a radioactive source were carried out soon after the discovery of the Mössbauer effect . However, the low brilliance implied very low counting rates and therefore made the experiments extremely difficult . Nevertheless many investigations were done in the last 25 years which were reviewed by Smimov [2] . The dynamical theory of nuclear Bragg diffraction was developed by two groups independently, i.e . by Trammell and Hannon [3-6] and by Kagan, Afanasev, and Kohn [7-9] . After the demonstration that synchrotron radiation can be used for nuclear Bragg diffraction experiments, it became obvious that time differential measurements are the proper technique, where the hyperfine interactions show up as quantum beats in the time spectra . In this paper a short description of nuclear Bragg diffraction is given, which is followed by a more detailed discussion about the determination of hyperfine interaction parameters for the cases of YIG and FeBO, 2 . Basic phenomena Synchrotron radiation from a bending magnet, a wiggler, or an undulator of a storage ring consists of sharp pulses of about 100-200 ps duration with a * Reprint from Hyperfine Interactions 61 (1990) 1279.

separation of about 10 ns-1 Ws between successive pulses . Massbauer nuclei with low lying excited nuclear states have lifetimes in the range of 1 ns-1 Ws . If a synchrotron radiation pulse hits a crystal containing resonant (Mössbauer) nuclei, the electronically scattered X-rays and the photoelectrons will be prompt whereas the nuclear scattering will be delayed by a time connected with the lifetime of the excited nuclear state . The pulse creates a collective nuclear excited state, the nuclear exciton, which is a superposition of all possible intermediate wavefunctions with the nuclei in the ground state except for the one which is excited . The following radiative decay exhibits the phenomenon of speed-up due to coherent enhancement and a quantum beat modulation of the decay due to the hyperfine splitting of the nuclear levels (ground and excited levels) . 2.1 . Speed-up

Coherent enhancement [3] occurs when the waves emitted from the various nuclei in the crystal interfere constructively . Then there is an increase in the radiative decay width of the nuclear exciton, as compared to that of an isolated nucleus . The partial width for the incoherent decay processes, however, remains unchanged . As the total decay width is increased, a speeded up decay of the nuclear exciton is observed . Evidently the strength of the coupling between the various nuclear oscillators in the crystal will influence the speed-up of the radiative decay. In hyperfine spectroscopy a large speed-up can be very annoying, because then the quantum beat spectrum is damped rapidly . Situations may occur where it is desirable to decrease the strength of the coupling . This is discussed in ref. [10] and can be achieved in various ways . Experimentally the expected decrease of the speed-up was observed in the case of FeB0 3 for devia-

0168-9002/91/$03 .50 © 1991 - Elsevier Science Publishers B .V. (North-Holland)

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R . Riiffer et al. / Nuclear Bragg diffraction using SR

tions of the incident angle with respect to the Bragg angle [111 (fig. 1) . The same effect occurs if one compares different orders of reflections, e.g. the (111)- and (333)-reflection of FeB03 (figs . 1 and 5, respectively) . 2 .2 . Quantum beats If there are hyperfine splittings of the nuclear levels or line shifts between different sites, then quantum beats will appear in the time spectra of the coherently scattered radiation. These beats occur at the difference of frequencies S2,( n, m, p ; n', m', p)=wn.(p)-wn'm'(p of all allowed nuclear hyperfine transitions w,_(p) from all different nuclear sites p, giving a direct measure of the energy splittings of both the excited and ground states, as well as of different sites . As the dynamical

effects strongly modify the response from isolated resonances, giving broadened widths and resonance shifts in the radiative decay, one might expect a strong modification of the quantum beat spectrum too . However, in most cases the modifications are rather minor and most aspects of the quantum beat spectrum can be explained in the limit of first order Born approximation . To demonstrate the origin of quantum beats we consider a simple case, where only two nuclear resonances of energies El and E2 (Et .2 = It wo ± '-z AE) and of equal oscillator strength are involved. Considering spatial phases Tt = 0 and T2 = m, the frequency response is given by R(w) a (

E l -hw-

2 Fo)

_

10

AE t 2 r't

)

.

3 . Experimental setup

1000

100

10 1000

á 0 U

(

Fig . 2 shows theoretical spectra for different splittings DE . The figures on the left show the energy spectra and on the right the corresponding time spectra . The quantum beats show up as the pronounced modulation with frequency AE/(2h) .

0 U

G ::) 0 U

E2-Aw- -f F.)

and the corresponding time response by I(t) aI R(t) 12cce-ro`'hsin2

1000

(

100

10 00

1000

t [ns]

Fig . 1 . Time spectra of the decay of the collective nuclear state for the (111)-reflection of FeBO3 measured at different angular positions : (a) exact, (b) below, and (c) above the Bragg angle . The solid lines are the calculated theoretical spectra . The dotted lines show the natural exponential decay e - ""0 (To =140 ns), and the dashed lines show the initial enhanced decay with lifetime r [111 .

The high resolution spectrometer built at HASYLAB (Hamburger Synchrotronstrahlungslabor) uses synchrotron radiation from a bending magnet of DORIS (DESY, Hamburg) [12] . Fig . 3 shows the scheme of the setup . The synchrotron radiation is linearly polarized and consists of pulses with a duration of about 150 ps and a separation of 240 ns between successive pulses . A conventional Si monochromator filtered the synchrotron radiation at 14 .4 keV ("Fe transition) to an energy band of about 10 eV width and an angular width of about 20 grad. After this monochromator a slit system defines a 20 mm X 2 mm beam with an intensity of about 5 X 10 1° photons/s (75 mA electron current and 3 .7 GeV electron energy of DORIS) . The nuclear monochromator consists of two identical goniometers and thereby allows flexible response to various experimental demands . In the experiments described below the first goniometer carried a totally reflecting mirror to suppress higher harmonics in the beam, whereas the crystal under investigation was mounted on the second goniometer . For the time differential measurements a fast detector with a good signal-to-noise ratio was installed [13] . Typical counting rates of resonant -y-quanta diffracted from 57 Fe containing crystals were in the range

49 7

R. Riiffer et al. / Nuclear Bragg diffraction using SR

01 L 01 -0 1 01

-0 .1 L 25

001

AE/f

125

0

t /ns

\1 001 500

Fig . 2. Contour plot (left) of the frequency response I(co) for two resonances with a splitting DE of 50F (above) and 5r (below), and the corresponding time response I(t) (right) integrated over the angle 00 = 0.1 mrad [211 .

of 1-20 Hz . This is sufficient to determine hyperfine interaction parameters within hours .

4. Experiments The experiments carried out so far made use of pure nuclear reflections to overcome the large nonresonant background . These reflections are forbidden for electronic diffraction due to the crystal symmetry, but allowed for nuclear diffraction due to the lower symmetry of the nuclei . This is possible because the nuclei, in contrast to the electrons, are sensitive to the internal fields in the crystal which give rise to another symmetry class . Many crystals which contain the Mbssbauer iso-

tope 57 Fe show pure nuclear reflections ; examples are YIG, FeBO3 , and Fe203 . According to experiments and calculations it seems in fact to be quite common that a crystal exhibits pure nuclear reflections [14,151 . In the following two crystals with different structures will be discussed : the simple "antiferromagnet" FeB0 3 and the very exciting but complicated YIG . 4.1 . FeBOj FeBO3 represents a model antiferromagnet scatterer (the weak ferromagnetism which is introduced by the small canting angle between the magnetic fields [16] can be neglected in this context) . In an antiferromagnet the pure nuclear reflections arise entirely from the changing detector

Fig . 3 . Scheme of the high resolution spectrometer at HASYLAB . IV . MATERIALS SCIENCE

49 8

R . Rüffer et al. / Nuclear Bragg diffraction using SR

(6)

(4)

(3)

(1)

+B

(1)

(3)

(4)

(6)

-B

bQ(i .s) Fig . 4. Hyperfine shifts of the four "OJ " _ ± 1 transitions m iron borate . Here the transitions are (1) _ [ + i H + 2 ], (3) _ [ + 2 H- z], (4) = [ - 2H+2 ], and (6)=[-2H-z] . In the drawing the c shifts of the full Hamiltonian are added. The room temperature values are hS2(1, 6) = UM (1, 6) =110 .5F, hV(3, 4)=hQ ti,(3, 4) =17 .5F, d=-3 .9F, c'=+0 .06T, c"-0.06T with T= 4 .665 x 10 -9 eV [10] . directions of the internal magnetic field . The magnetic unit cell is twice as large as the crystallographic unit cell. In the case of FeB0 3 the (nnn)-reflections for odd n (referred to the rhombohedral unit cell) are pure nuclear reflections. The main axis of the electric field gradient (EFG) is perpendicular to the corresponding planes . All measurements of FeB03 were done with a crystal with a size of about 1 cm2 in Bragg geometry . The crystal was placed in a weak external magnetic field perpendicular to the scattering plane (k  kou,) in order to align the internal fields parallel to k,, + k,,, . The relative position of the four transition energies are shown in fig . 4 . Because of the crossed geometry of B and the EFG, Jz is not a good quantum number. Fig . 5 shows the time spectrum of the radiative coherent decay of the nuclear exciton for the (333)-reflection . Over the entire time range a well resolved

1000

too

Fig. 5 . Time spectrum of the decay of the collective nuclear state for the (333) pure nuclear reflection of 57 FeB0 3 . The solid line is the result of the fitting by the dynamical theory. The dotted line shows the natural exponential decay c-`/To (7o =140 ns), and the dashed line shows the initial enhanced decay with lifetime r.

quantum beat pattern is observed which can be fitted very well by the dynamical theory of nuclear Bragg diffraction (solid line) . Due to the large number of periods in the quantum beat spectrum the magnetic interaction and consequently the magnetic field can be determined very precisely . The XZ value is 1 .8 and the uncertainty of the internal magnetic field is 0 .02 T . To understand the origin of the quantum beat pattern it is much easier to use the first order Born approximation than the full dynamical theory . The relative phases and strengths of the transitions (fig . 4) are +1, - ;, + ;, and -1 respectively . The four contributing waves then sum up to give the simple quantum beat spectrum (the symbols are explained in fig . 4) I(t) a e-rrlhlsin[,Egm(1, 6 ) t] -

;e

-c~ /2h1a

r sin [ _2Q M (3, 4) t]

12 .

This result gives the characteristic quantum beat pattern for any simple 57Fe antiferromagnet. The frequency S2 m (1, 6), which is the magnetic splitting of the outer two transitions, dominates the spectrum . The contribution of the inner two lines Q M (3, 4) is a very perceptible modulation, which gives the "high-low" pattern of successive beats . The electric interaction = z eQV,, induces a slow overall modulation . An independent direct measure of the electric interaction (the value and the sign) is achievable . by comparing the quantum beat amplitudes above and below the Bragg angle (fig . 1) [111 . Quadrupole interaction causes an asymmetry since the difference between the intensities above and below the Bragg angle is equal to

R (t,

80)12-

R(t, -â0)

2a

- sin(f k d t)

x sin[ W nt (3, 4) t] sm[ 2S2~,,(1, 6) t]~ , which gives a direct value of 4 . Because of the proportionality to sin(z S2 ,, (1, 6) t) this appears as a Reissverschluss asymmetry in the amplitudes of the fast beats above and below the Bragg angle. Another striking application is the determination of the temperature dependence of the magnetisation in a single crystal. For demonstration FeB03 is quite suitable because of the low Mel temperature (75 .2'C). After mounting a small furnace on top of the second goniometer, measurements were performed from room temperature up to the Mel temperature [17] . Fig . 6 shows the spectra which were measured within about 35 hours . The solid lines are the result of the fitting with the dynamical theory . All X2 values were below 1 .8 . The measurements allowed the determination of the magnetic fields with an error of less than 0 .02 T. They show the characteristic magnetisation curve of iron borate [16] .

R Miffer et al / Nuclear Bragg diffraction using SR

1000 100 1000 100 1000 100 1000 100 1000 100 1000 100 1000 100 0 t/ns 200 Fig. 6 . Time spectra of the decay of the collective nuclear state for the (333) pure nuclear reflection of 57 Fe1303 between room temperature and the Néel temperature . The solid lines are the resulting fits by the dynamical theory . Due to the collapse of the pure nuclear reflection at the Néel point, the diffracted intensity becomes very low in the vicinity of the Néel temperature [18] . This can be overcome by the use of "allowed reflections" which show high diffracted intensity in the whole temperature range. Then, precise determinations of critical exponents are possible .

49 9

electric interaction . Whilst the electric interaction strength is equal for all d-sites, the main axes of the EFGs (Vzz) lie along the coordinate axes of the cubic crystal system and vary periodically within the unit cell . One obtains the d l , d z , and d 3 subgroups with the Vz axes along the [100]-, [010]-, and [001]-directions, respectively . Only the d t - and d 2 -sites contribute to the (n00) pure nuclear reflections with n = 4m + 2 (m = 0, 1, 2, - - - ) . Their V, axes lie within the (001)-surface . The d 3-site has a vanishing structure factor for these reflections . In the following some new aspects will be discussed which could not be demonstrated in the case of FeB03 , e .g . pure nuclear reflections due to changing directions of the main axis of the EFG and the influence of the angle between the hyperfine field and the main axis of an EFG . But of course the parameters of the magnetic and electric interactions for YIG can be determined in the same way as for FeB03 . All measurements were done with YIG films (enriched in 57 Fe) of about 15 ~Lm thickness epitaxially grown on the {100)-surface of a gadolinium gallium garnet single crystal, 30 mm in diameter [1] . A weak external magnetic field aligned the internal fields in the desired direction. In a classical Massbauer experiment all iron sites are always affected and very complicated spectra are obtained . In nuclear Bragg diffraction it is possible to select the a- or d-sites by choosing an appropriate reflection . This leads to a simplified diffraction spectrum . As an example the diffraction spectrum of the (0 0 10) pure nuclear reflection of the d-sites is shown in fig . 7 . The magnetic field B is chosen perpendicular to the scattering plane (k  ko ,) . The origin of the quantum beat spectra is again easily understood in the first order Born approximation . For B perpendicular to the scattering plane (k, kou,) the splitting of the excited nuclear level is given in fig. 8. For incident 45-polarization the transitions 1 and 6 have

4.2. YIG The unit cell of YIG contains 160 atoms including 40 iron atoms [19] . They belong to two different crystallographic sites : 16 of them to the a-site and 24 to the d-site . The iron ions are exposed to a combined magnetic and electric interaction . For both sites independent pure nuclear reflections are predicted. So far only reflections of the d-site have been investigated . All ions of the d-site are ferromagnetically coupled and the nuclei experience an identical magnetic interaction strength. They become distinguishable by their

Fig. 7 . Time spectrum of the decay of the collective nuclear state for the (0 0 10) pure nuclear reflection of YIG with y? = 90 ° (for an explanation of qp see fig . 9) . The solid line is the result of a fit using the dynamical theory . IV . MATERIALS SCIENCE

R. Riiffer et at. / Nuclear Bragg diffraction using SR

500

[001]

h~l si

Fig. 8. Hyperfine shifts of the eight "AJ" = f1 transitions (filled symbols) and between the four "A J" = 0 transitions (open symbols) at the d,- and d 2-sites when B is perpendicular to the scattering plane (k, k"t ). Here the transitions are (1)

= [ +

2

H

+

2 ], ( 2 ) = [ + 2

H

+ 2 ],

(3)

=[+ 2

H

'1,

(4) =

3 . and (6)=[-21 [- Z"+'], (5)=[-'--'-a], 21 In the 2 2 drawings the E shifts of the full Hamiltonian are added. This causes corrections of the order of 10 -3 to the magnetic interactions and a few percent to the electric interactions . The room temperature values are hS?(1, 6)=hd2,(1, 6)=126 .9x, hQ(3, 4) = h2 m (3, 4) = 20.0x, hQ(2, 5) = h9,(2, 5) = 73 .5F, hd2(i) +E(t)=hS2 E , A=9 .17x, E(l)=-E(3)=-E(5)=0.32x, and c(2) = e(4) = -e(6) = 0.2717 with F = 4 .665 x 10 -9 eV .

relative strength 1 and the transitions 3 and 4 relative strength -'3 . The transitions 2 and 5 have relative strength for incident i-polarization. The contributions from the dl- and d 2 -sites are 180 ° out of phase. With these amplitudes and phases the 6 contribution of the waves sums up to

nhf

Fig. 9. Diffraction geometry for the YIG crystal with azimuthal angle (p, scattering plane (k  k"u,), and Bragg angle ©. The direction of the hyperfine field Bhf and the orientation of the main axis of the EFG within the (001)-surface are shown for the dl- and d2site . angle (p . This rotation changes the relative angle between the hyperfine field which is aligned by the external field, and the main axes of the EFGs at the dt- and d2-sites which are fixed to the crystallographic axes .

1000

k

900 1

lu

100

f

ki

Is (t) ac e -r°` l h sin2(ZÜE t)Icos[2d,(1, 6) t] - ' e -(i/4h)á t cos [ z12,(3, 4) t1 I2.

1000

The fast beating is determined by the magnetic interaction with frequencies 12,(1, 6) and Q,(3, 4) of the outer and inner lines, respectively (fig. 8). From the over 30 beats the magnetic field can be derived very precisely . The term sin2 (z2Et) with the electric field gradient splitting hO E = áa between two distinguishable dl- and d 2 -sites gives the pronounced overall modulation of the YIG diffraction spectrum (fig . 7) and is responsible for the pure nuclear reflection. This is a typical feature of diffraction spectra if there are two adjacent excited nuclear levels at different nuclear sites. Furthermore this slow modulation gives a measure of the quadrupole interaction [20] . Due to the small value and the restricted time range only two periods are detectable . Another interesting feature is the influence of the and the relative angle between the hyperfine field main axis of an EFG. For demonstration the expertments described in ref. [14] were utilized . The experimental situation is shown in fig. 9. A YIG crystal, placed in a weak external magnetic field fixed perpendicular to the scattering plane, is rotated by the

100

f

;

I

s 100

67 5°

", A

t

f ~

56 .3°

4e

A

~

1f

t

ç

ir

45 0° 100

Bhf

Fig. 10 . Time spectra of the decay of the collective nuclear state for the (002) pure nuclear reflection of YIG. The angle between B and the [100]-axis is 90 ° , 67 .5 ° , 56.25 ° , and 45 ° , respectively. The solid lines are the result of a fit using the dynamical theory of nuclear Bragg diffraction.

R. Rüffer et al. / Nuclear Bragg diffraction using SR

,~ E/peV 0 15 0 10

00 -005 -0 10 -0 15

Fig. 11 . Splitting of the excited nuclear state for the d l-site (solid line) and the d2-site (dashed line) as function of the angle op between B and the [100]-axis . Fig. 10 shows the corresponding diffraction spectra for four different angles 4p . The frequencies of the fast beat pattern are the same for all angles (p which means that the magnetic interaction stays constant. However, the frequency of the slow overall modulation sin2(Zd2 E t) changes drastically. This can be easily understood from the level splitting of the dl- and d 2-sites (fig . 11). For q) = 90' the splitting of the two sites h12E is maximal which leads to a relatively "high" frequency of the modulation . With decreasing angle q) the splitting becomes smaller and consequently the frequency decreases too. The theoretical calculations additionally show a sensitive dependence of the beat amplitudes on the angle 4p . 5. Conclusion The discussed examples of YIG and FeB0 3 demonstrate that even with counting rates available at bending magnets hyperfine spectroscopy is not only possible, but can be carried out already fast and with precise results. For special applications which need high brilliance (e .g . scattering experiments), synchrotron radiation is already better than radioactive sources. The use of wiggler and especially of undulator beam lines will increase the counting rates further. Experiments carried out on Fe203 [221 at a wiggler beam line of CHESS (Cornell) reached slightly higher resonant counting rates. Corresponding experiments with YIG carried out at the 14 .4 keV undulator of PEP (Stanford) were done with resonant counting rates of up to 500 Hz [23] . At the proposed Mössbauer beamline of ESRF (Grenoble) [24] undulators will be available for the whole energy range of low lying Mössbauer transitions (6-30 keV). The -y-ray beam size will be about 0.1-1

50 1

mm2 , the divergence about 10 Wrad (vertical and horizontal), and the flux of Mössbauer quanta up to 50 kHz per ra (for 57 Fe). Though a larger resonant counting rate is important, another important aspect is the development of a convenient -y-ray beam as a general source for hyperfine spectroscopy . With such a source not only crystals but also polycrystalline and amorphous samples could be investigated . Some attempts in this direction using single line [18] and absorber filtering [25] have already been made. Another new method is the use of grazing incidence antireflecting films (GIAR films) [26,271. The application of these films should produce -y-ray beams with band widths up to 200ro around the selected Mössbauer transition energy [28] . Such a band width is sufficient to investigate the hyperfine interaction of any compound which contains the appropriate resonant nuclei by means of time differential experiments .

Acknowledgement This work has been funded by the Bundesministerium für Forschung und Technologie under Contract No . 05270 GUI9 .

References

[21 [31 [4] [51 [6] [71 [81 [9] [10] [111 [121 [13]

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[14] R. Rüffer, E. Gerdau, H.D . Rilter, W. Sturhahn, R. Hollatz and A. Schneider, Phys . Rev. Lett . 63 (1989) 2677 . [151 R. Hollatz, W. Sturhahn, H.D . Röter and E. Gerdau, Hyperfine Interactions 58 (1990) 2457 . [16] M. Eibschütz and M.E . Lines, Phys . Rev. B7 (1973) 4907 . [17] H.D . Röter, R. Rüffer, E. Gerdau, R. Hollatz, A.I . Chumakov, M.V . Zelepukhin, G.V . Smimov and U. van Bürck, Hyperfine Interactions 58 (1990) 2473 . [18] A.I . Chumakov, M.V . Zelepukhin, G.V . Smirnov, U. van Bürck, R. Rüffer, R. Hollatz, H.D. Rilter and E. Gerdau, Phys . Rev. B41 (1990) 9545 . [19] H. Winkler, R. Eisberg, E. Alp, R. Rüffer, E. Gerdau, S. Lauer, A.X . Trautwein, M. Grodzicki and A. Vera, Z. Phys . B49 (1983) 331 . [201 R. Rüffer, E. Gerdau, R. Hollatz and J.P. Hannon, Phys. Rev. Lett . 58 (1987) 2359; 57 (1986) 1141 . [21] R. Rüffer, R. Hollatz, E. Gerdau, U. van Bürck and J.P. Hannon, Hyperfine Interactions 42 (1988) 1161 .

[22] D.P. Siddons, J.B . Hastings, G. Faigel, L.E . Berman, P.E. Haustein and J.R. Grover, Phys. Rev. Lett. 62 (1989) 1384 . [23] J. Arthur, G.S . Brown, D.E . Brown and S.L . Ruby, Phys . Rev. Lett 63 (1989) 1626 . [24] ESRF, Foundation Phase Report, Grenoble (1987) . [25] U. van Bürck, R.L . M6ssbauer, E. Gerdau, W. Sturhahn, H.D. Riiter, R. Rüffer, A.I . Chumakov, M.V. Zelepukhin and G.V. Smirnov, Europhys. Lett. 13 (1990) 371. [26] J.P . Hannon, G.T . Trammell, M. Mueller, E. Gerdau, H. Winkler and R. Rüffer, Phys . Rev. Lett . 43 (1979) 636. [27] J.P . Hannon, G.T . Trammell, M. Mueller, E. Gerdau, R. Rüffer and H. Winkler, Phys . Rev. B32 (1985) 6374 . [28] E. Gerdau, M. Grote and R. Röhlsberger, Hyperfine Interactions 58 (1990) 2433 .