Neutron scattering on concentrated and diluted mixed-valent Tm-systems

Journal of Magnetism and Magnetic North-Holland Publishing Company

INVITED

Materials

38 (1983) 253-263

253

PAPER

NEUTRON SCATTERING Tm-SYSTEMS

ON CONCENTRATED

AND DILUTED

MIXED-VALENT

E. HOLLAND-MORITZ /I. Physikalisches Inslitur der Vnioersiiiit zu Kiiln, Ziilpicher SW. 77 D -5000 Cologne 41, Fed. Rep. Germany

In this paper recent measurements are presented on dilute systems Tm,,,,Y,,,,Se and Tmo,osLao,ssSe in comparison to the concentrated systems TmSe and TmSe,,,,Te,,,,. In the high temperature regime there exists a nearly temperature independent QE-linewidth and at low temperatures an inelastic line arises. As these effects are found in diluted systems as well as in the concentrated ones, they are interpreted as a single ion effect. The results are discussed with respect to some theoretical models.

1. Introduction TmSe is an intermediate valent (IV) compound. This has been proved by numerous experiments, e.g. lattice parameter [l], magnetic static susceptibility [l], XPS [2] and X-ray absorption (Lmedge) [3]. Already the early experiments [l] show that the physical properties of TmSe depend strongly on the stoichiometry of the sample. Therefore, the exact value of the valence is still controversial. Mossbauer measurements [4] on the system Tm,Se have shown that samples with a lattice parameter of about a, = 5.711 A do not show any splitting of the Mossbauer-line. In contrast, samples with a, < 5.685 A do show such a splitting effect, which was interpreted by quadrupole interaction due to a deviation from the cubic symmetry. Thus it was concluded that samples with a lattice parameter near to a, = 5.711 A are stoichiometric, which is now accepted by most of the authors in the literature. However, it should also be mentioned that samples, even with the same lattice parameter, do not show exactly the same behaviour. This can be seen, for instance, by plotting the effective moment vs. the lattice parameter [5]. If one accepts such a sample with a, = 5.71 A to be best stoichiometric, the value of the valence still depends on the experimental method used: 2.73 from lattice parameter by linear interpolation [6], 2.46 [S] or 2.52 [7] from static susceptibility, 2.58 from neutron scattering (this value was obtained be re0304-8853/83/0000-0000/$03.00

0 1983 North-Holland

analyzing the data and differs slightly from that in ref. [7]), 2.56 from XPS (a0 = 5.705) [8] and 2.58 from L,,,-edge [3]. In spite of these problems, TmSe is one of the most studied IV-compounds because it behaves in a quite different manner than the so-called “classical” IV-systems, like CePd,, CeBe,,, YbCu,Si,, etc. For instance, in TmSe the static magnetic susceptibility diverges for T + TN, which leads to the antiferromagnetic order below TN = 3.5 K [9,10]. In contrast, the static magnetic susceptibility is finite for T + 0 in the “classical” IV-systems, and these systems do not order magnetically. Neutron scattering experiments with energy analysis are a well-known method for measuring the imaginary part of the dynamic susceptibility. From their data one can extract the fluctuation energy via the width of the quasi-elastic magnetic line. To give a rough estimate a width of 4-25 meV (the width depends on the system) was found for IVsystems. These values correspond to a relaxation time of 10 X lo-i3-1.6 X lo-l3 s (tt/~ = F/2) [ll-141. In the classical IV-systems this width is nearly temperature independent, which leads to the remarkable effect that below a certain temperature the linewidth becomes larger than the thermal energy. This behaviour was not found in TmSe. Here the quasi-elastic linewidth of about 7 meV was nearly temperature independent only for T > 80 K. Below T = 80 K the linewidth decreases drastically and remains smaller than the corre-

effect. Presuming a fluctuation on a single ion the magnetic order in TmSe found by RKKY-interactions is only possible, if the valence fluctuation is a time coherent process on one Tm-ion, i.e., if there is a memory in the fluctuation process between the two magnetic valence states on one Tm-ion.

2. Experiments

I

1

200 TEMPERATURE IKI

100

Fig. 1. Temperature dependence for the Tm-IV-systems.

The polycrystalline samples of TmSe,,,,Te,,,,, Tm,,,Y,,,Se and Tm,,,La,,,,Se were prepared with the help of K. Fischer at the Institut fur Festkorperforschung der KFA Jtilich by a similar method to that used by Bucher for TmSe [l]. The samples were characterized by X-ray diffraction. The resulting lattice parameters are listed in table 1. The neutron scattering measurements were performed in the temperature range of 2-250 K on several time-of-flight (TOF) spectrometers using different incident energies. Most of the experiments were done on the D7-spectrometer at the HFR-reactor, Institut-Laue-Langevin (I.L.L.) in Grenoble with an incident energy E, = 3.5 meV. From these data the temperature dependence of the quasi-elastic linewidth could be extracted. As an inelastic line at A 2 3 meV cannot be observed on the energy gain side of the neutrons at low temperatures (Bose-factor), these studies were performed with several different incident neutron energies. A first rough experiment on the diluted systems Tm,,,,La,,,,Se and Tm,,,,Y,,,,Se was performed with E, = 20 meV on the SVZZ-spectrometer at the FRJ2 (DIDO), KFA Jtilich [16]. From this, one could estimate that more precise measurements would be achieved if for Tm,,,,Y,,,,Se a

I

300

of the quasi-elastic

lincwidths

sponding thermal energy [7] (see also fig. 1). There is an additional effect which could be observed by an experiment with thermal neutron on polycrystalline TmSe (a0 = 5.711 A). With decreasing temperature there arises an inelastic line at about 10 meV [15]. This paper gives a survey about most of the neutron scattering experiments done since 1978 on TmSe and related systems. It deals especially with recent measurements on the diluted systems Tm,,O,LaO,,,Se, Tm,,,Y,,,,Se, and in addition, on the concentrated system TmSe,,,,Te,,,. The experiment on the diluted Tm-systems was important, because one can decide from its result if the valence fluctuation in TmSe, especially if the existence of the inelastic line is really a single ion

Table 1 Obtained

fit parameters

Sample

for the inelastic

and the quasi-elastic

00

QE

(A)

r,‘2at

line. In addition

TmSe TmSeO.ssTeO.I, Tm o.osLa095Se

5.7065 5.711 5.785 6.085

is given

INE T=300K

A

CmeV)

Tmo.05’fo de

the lattice parameter

8.3+1 7.3* 1 5.6 f 0.7 4.4 * 0.5

15 10 5 5

CmeV)

r/2 CmeV)

11 10 7.8 2.6

3 il 2.5 * 0.5 1.8kO.5 1 +0.3

*1 +1 f 0.5 + 0.3

I (b) -7

9.6 k 2 +2 2.8kO.3 2 kO.7

E. Holiund- Moritr / New-on scutfering on mixed- dent

higher incident energy, and for Tm,,, La,,,Se a better absolute energy resolution, i.e. a lower incident energy, were used. Therefore, these experiments were repeated for Tm,,a,Y,,,,Se on the SV22 (KFA-Jtilich) with E, - 36 meV and for Tm,,, La,,,,Se on the IN4 (I.L.L.) with E, - 12 meV. Furthermore, measurements were performed on the IV-alloy TmSe,,,Te,,,, in the low temperature region of 5-30 K and on Tm,,,Y,,,,Se at 80 and 170 K using the IN4 with E, = 12 meV. All data were analysed with the paramagnetic scattering law given by:

S(Q,hw, T)

=+(y B )'F'(Q, xxkw

S(Q,

ho,

1_

d2a T)=k’ k, d( Ao)dS2

Tm -systems

255

ENERGY TRANSFER (meV) -10 -5

-15 015

I

I

0

I

La Se

T)

hw p(Q, e_phw

Au, T),

’

This scattering law is described in detail in refs. [14,17]. The spectral function P(Q, AU, 7’) includes both quasi-elastic and inelastic lines. Lorentzians were chosen for each line.

3. Results The results of the quasi-elastic spectra shall be presented first. In the case of the IV-alloys this quasi-elastic spectrum behaves TmS%.,,T%.i, quite similarly to that of TmSe [7]. Its quasi-elastic linewidth is with 5.5 meV only slightly less than that of TmSe. The temperature dependence of the width is plotted in fig. 1 (squares). Fig. 2 shows the energy spectra of Tm,,, La,,g,Se and of the reference sample LaSe at T = 220 K taken on the D7 (E, = 3.5 mev). The LaSe spectrum is formed by the nuclear incoherent elastic scattering and by the phonon scattering around 9 meV. In the spectrum of the diluted Tm-system much more intensity is visible in the energy window - 1 to - 5 meV. This means that apart from the phonon scattering and the incoherent elastic scattering (hatched areas), a broad quasi-elastic line is produced by Tm. As the Q-dependence of the scattering intensity in the energy window - 1 to - 5 agrees quite well with

ENERGY

TRANSFER

(meV)

Fig. 2. Background corrected energy spectra of Tm,,,,La,,,5Se and of the reference spectrum LaSe taken on the D7. The hatched areas in the Tmo,osLa,,,,Se spectrum are due to inelastic phonon and elastic nuclear incoherent scattering.

the magnetic formfactor, this quasi-elastic line (lower full line) is due to magnetic scattering. The other full line is a fit to the data including also the elastic and the phonon scattering. This convention is used in all the following plots of spectra to separate graphically the phonon contributions from the magnetic contribution. Fig. 3 shows spectra of Tm o,osLa,,,Se at three different temperatures. For T = 220 K and for T = 80 K the spectra of the Tm0.0,LaW Se were corrected by subtracting spectra of the reference sample LaSe. This was not done for T = 30 K because there the phonon contribution is negligible. The full lines are fits with one quasi-elastic line and an elastic peak. The quasi-elastic line was fitted by two parameters: The local static susceptibility x$ and the quasielastic width r/2. The resulting widths are plotted

015

T g

010

Tmoo5Lao&e -LaSe

T=I3OK op7Se-LaSe

,, "

-D 2 ~ @ 005:

ENERGY TRANSFER Fig. 3. The magnetic temperatures.

spectrum

of Tmo~,~sLa,,,,Se

for three

again in fig. 1 (triangles). The high temperature value is about 4.4. meV. Qualitatively the temperature dependence of Tm,,a,La,,,,Se is the same as that of the concentrated systems TmSe and From the spectrum at T = 30 K TmSea.s,Tea.i,. (fig. 3, lower part), one observes that the data points in the energy window of -2 to - 5 meV, cannot be fitted by only one quasi-elastic line. There is still some intensity left (see full line). This was already the first indication that the inelastic line will also exist at low temperatures in the diluted Tm-IV-systems [18], as observed in TmSe. This assumption will be proved clearly in the second part of this chapter. of the diluted IV-system The spectra Tm,,,Y,,,,Se taken on the IN4 at T = 80 and 170 K are shown in fig. 4 for two different scattering angles. In the high angle spectrum of T = 170 K three phonon peaks at 8.3, 15 and 24 meV are

visible. This phonon scattering becomes less with decreasing scattering angle (momentum transfer). Thus, apart from the phonon scattering and from the incoherent elastic scattering (hatched areas) a broad quasi-elastic magnetic line can be clearly detected at low angles. Its width is about 8 meV at T = 170 K. However, there are still some high temperature points missing, (see fig. 1) to prove that also in this system the linewidth behaves nearly temperature independent in the high temperature region. In the following second part of this chapter the experimental results are presented with respect to the assumed inelastic line. At first the low temperature spectra of TmSe,,,,Te,,, taken on the IN4 interval 5530 K (E,= 12 meV) in the temperature are plotted in fig. 5. As expected, an inelastic line is clearly observable. The position of this line shifts from 7.6 meV at 5 K to 5.4 meV at 30 K (see fig. 9). As the magnetic cross-section of Tm is larger than the phonon cross-section, the phonon scattering contribution is negligible in the concentrated Tm-systems. However, because of the low Tm-concentration the phonon scattering becomes very important in analysing the dilute IVTm-systems as already shown in fig. 2. In fig. 6 two spectra of Tm,,,,La,,,,Se are shown taken on the IN4 (E, = 12 meV) at the common temperature T = 5 K, but for different scattering angles. As the phonon scattering contribution increases quadratically and the magnetic scattering contribution decreases (form factor) with increasing momentum transfer, one can separate the magnetic from the phonon scattering. From this and from fig. 6 one can conclude that the inelastic line around 2.8 meV is magnetic, while the other line around 9 meV is due to phonon scattering. Furthermore, there is magnetic scattering intensity around 5 meV. One cannot decide from the fits if this intensity is due to a quasi-elastic line with r/2 = 4 meV or due to an inelastic line at A = 5 meV. The detection of the inelastic line in the dilute IV-system TmO,OSYO,gSSewas much more difficult. Fig. 7 shows the background corrected spectra of this system taken on the IN4 at T = 15 and 135 K. The hatched areas around 9 and 15 meV are due to phonon scattering in agreement with fig. 4.

E. Hollund

- Moritr / Neutron scattering on mixed -vulent Tm -systems

251

phonor1

ENERGY TRANSFER ImeVl Fig. 4. Background corrected spectra of Tm o,osY,,,,Se taken on the IN4 are shown for two different temperatures. The hatched areas are due to inelastic phonon and elastic nuclear incoherent scattering.

Comparing the spectra of Tm,,,Y,,,,Se at T = 15 K with that of 135 K, one observes that the intensity at Ao = 11 meV is larger for T = 15 K than for 135 K. As the phonon scattering intensity increases with increasing temperature, this intensity can only be due to a magnetic excitation, i.e. at low temperatures, an inelastic magnetic line exists at about 11 meV, which vanishes with increasing temperature. At T = 135 K the magnetic contribution is formed only by a broad quasi-elastic line with I’/2 = 8 meV. Nevertheless, the value of the excitation energy corresponding to the inelastic line cannot be given exactly because the phonon contributions around 9 and 15 meV are too narrow for the magnetic excitation line. With the new knowledge about the phonon contributions the old data with E, = 20 meV [16] were reanalysed. From that the inelastic line was found at about 12 meV (see fig. 8), which is slightly less than that published in ref. [16]. Nevertheless there

angles

and at two different

are some differences between the two measurements (compare fig. 8 with fig. 7. Note that in fig.. 8 the scattering law S(0, ttw) is plotted instead of the double differential cross section k,/k, * S(d, tie) as done in the corresponding figure of ref. [16]). The intensity around 17 meV is larger for E, = 20 meV than for E, = 36 meV. This is due to the fact that in time of flight spectra the signal-background ratio becomes very bad for hw > 10 meV on the energy loss side of neutrons using E, = 20 meV. Therefore, little uncertainties existing in the background are amplified when transforming the TOF data to the scattering law (eq. (l), energy scale). On the other hand the measurement with E, = 36 meV has the disadvantage that because of the larger incoming energy the momentum transfer is larger. Moreover, the probability for double scattering at low angles (Bragg-phonon) becomes larger with increasing incident energy (see fig. 16 in ref. [14]). Therefore

258

E. Hoikmd-

Moritz

/

Neutron

stuttering

on mixed-cdent

ENERGY TRANSFER [meVl -2

0

2

4

6

-4

8

-2

Tm -.ystenu

ENERGY TRANSFER [meVl 0 2 4 6

8

10

020

015

0.10 z +I >, 005 E Z b = 000 .K %i

r

2 0.20 * 015

010

005

0°%

0.0 -4

-2

0

2

4

6

-2

0 2 6 EN,ERGY TRANSFER [m&l

0

Fig. 6. Background corrected spectra of Tm, osLa09sSe taken on the IN4 are shown for two different angles at T = 5 K. The hatched areas are due to inelastic phonon and elastic nuclear incoherent scattering.

8

ENERGY TRANSFER [meVl Fig. 5. Background corrected spectra on the IN4 for three temperatures.

of TmSe,,,,Te,,,,

taken

the observable phonon contributions also increase with increasing incident energy. All results regarding the quasi-elastic linewidth and the magnetic excitation energy are summarized in fig. 9 for T < 150 K. Notice that the results for TmSe obtained by reanalysing the data (circles) differ slightly from those published earlier [14,17,19,20]. Especially the excitation energy of TmSe is temperature independent between 2.5 and 30 K in agreement with Shapiro [21], and decreases then to 8 meV at 60 K.

4. Discussion All Tm-systems examined in this work show qualitatively the same behaviour: at high temperatures (T > 120 K) the quasi-elastic linewidth is nearly temperature iindependent, and it decreases uniformly with r/2 5: 0.7 X k,T (fig. 9) for T --) 0. Furthermore, an inelastic line appears at low temperatures in all these systems with concentrated and diluted Tm-ions. In table 1 the lattice parameter and some characteristic parameters obtained from fitting the neutron spectra are listed. There is a surprising systematic: if the lattice parameter increases, then the excitation energy, the width of the corresponding inelastic line, the intensity of

E. Hollund

- Moritz

/ Neutron

stuttering

ENERGY TRANSFER [meVl

-4

-2

0

2

4

6

8

10

12

14

16

18

ENERGY TRANSFER [meVl Fig. 7. Background corrected spectra of Tm,,,sYc .&Se taken on the SV22 with E, = 36 meV are shown at two temperatures. The hatched areas are due to inelastic phonon and elastic nuclear incoherent scattering.

4

8

12

16

20

ENERGY TRANSFER ImeVl

Fig. 8. Background corrected spectrum of Tmo,,,sY,,s.,Se taken on the SV22 with E, = 20 meV. The full lines are fits obtained by a reanalysis of the data. Therefore they differ from those in fig. 1 of ref. [16]. Note that here s(19, trw) is plotted while in ref. [16] k,/k, * S(6’, hw) is shown.

on mixed - valerzt Tm - svstetws

259

that line and the width of the magnetic quasi-elastic line at room temperature decrease. From that, one also obtains a direct correlation between the excitation energy and the high temperature linewidth, which is in agreement with the model calculation of Schlottmann [22] because both the linewidth and the excitation energy are proportional to the hybridization integral IT~~V’. First the behaviour of the quasi-elastic scattering shall be discussed. The temperature dependence of this scattering (fig. 1) agrees qualitatively with that extracted by Schlottmann from his model [22]. Another theoretical work by Kuramoto and Miiller-Hartmann calculates the magnetic relaxation rate r, [23] and the paramagnetic CurieWeiss-temperature 8 [24] in dependence on the valence of the IV-system. This theory is only valid in the high temperature limit. Therefore the relaxation rate r, should correspond to the experimental linewidth r/2 at high temperatures. As already mentioned in the introduction the exact value of the valence is controversial. However, a variation of the valence does not much influence the value of r, in the valence range of 2.4-2.6. For the following discussion the valences are taken from the magnetic cross-section obtained in the neutron scattering experiment. Thus the valence Y and the linewidth r/2 are taken from the same measurement. The significant values are listed in table 2. rM(y) is taken from fig. 2 in ref. [23]. Comparing the measured r/2 with this r, one can calculate the hybridization energy W, and hence the paramagnetic Curie-Weiss-temperature 6 from a similar figure [24] as for I’,. The paramagnetic Curie-Weiss-temperatures extracted from the measured linewidths by this model are a little larger than the experimental values [25] for the diluted Tm-IV-systems, whereas this is inverted for the concentrated Tm-systems. The latter may be due to the fact that the experimental values also contain the RKKY-interactions, which is important in the concentrated systems, but is negligible in diluted Tm-systems. The resulting values of W, depends on the system: the hybridization energy decreases with increasing lattice parameter. This means that most of the magnetic properties in Tm-IV-systems depends on the volume, which is available for a Tm-ion in the lattice.

E. Holhd-

260

t

Morirz / Neutron scurtermg O~Imxed

vulew Tm -sysrem

I

R’

_A+-

TmSe

Tm%85Te0.15

-r-- Tmo.dao,&

OB=‘L* 0

’

’

’ 50

’

’

6

’

0

150

100

TEMPERATURE IK1 Fig. 9. Temperature

dependence

of the quasi-elastic

linewidth

(lower right part) and of the excitation

Now the results of the inelastic line shall be discussed. Firstly one observes from fig. 9 that the excitation energy decreases with increasing temperature for TmSe,,,,Te,,,,. A similar result is obtained on TmSe for T > 30 K. In the case of Tm o.osLa,,,,Se such a temperature effect could not be detected because the excitation energy is very low and the inelastic line has already merged with the quasi-elastic line at T = 30 K. The excitation energy in Tm,,,Y,,,,Se seems to be temperature independent up to 80 K; exact values of A cannot be extracted because of the difficulties with the phonons in this system as mentioned above. This observed temperature behaviour can be

Table 2 Comparison

between

theory [24] and experiment Valence

Tm 0.05Y0.95Se TmSe TmSeo.s,Teo.I, Tm o.osLao.g$e

2.47 2.58 2.49 2.38

energy (upper

left part)

qualitatively explained by a two energy-level system with a damping due to conduction electronhole excitations as described by Becker et al. [26]. There are two controversial theoretical concepts explaining the inelastic line in TmSe. As the fluctuating valence states in TmSe are both magnetic (J = 6 and 7/2), one concept explains the magnetic order in TmSe below TN < 3.5 K, the decrease of the quasielastic magnetic line for T 3.5 K and the existence of the inelastic line by assuming a spatially coherent valence fluctuation in TmSe. For instance, the theory of Fedro and Sinha [27] is based on this idea. They describe the inelastic line as an excitation over a hybridization

(see text)

r/2

rM 1231

w,

0 (241

8 (experiment)

(meV)

(2rW,)

(meV)

(K)

(K)

8.3 1.3 5.6 4.4

0.192 0.2 0.196 0.172

6.88 5.809 4.541 4.071

29.1 22 19.2 17

22 [25] 40-50 [32,17] 27 [32] 10 [25]

E. Hollund

- Moritz

/ Neutron

stuttering

gap formed by the hybridization of the 4f-band and the conduction band. This theory was able to explain the intensity dispersion of the inelastic line, which was found by Grier and Shapiro by experiments on single crystals (a,, = 5.714 A) [28]. However, Fedro and Sinha predict from their theory that the inelastic line should not appear in dilute Tm-IV-systems, which is in disagreement with the experimental results described above. On the ofher hand, Mazzaferro, Alascio and Balseiro explain the existence of this inelastic line by a single ion effect [29], i.e. they assume a time coherent valence fluctuation on a single Tm-ion. Therefore they have predicted that the inelastic line should also exist in dilute Tm-IV-systems. However, this simple single ion model cannot explain the intensity dispersion of the inelastic line in TmSe because 4f-impurities cannot form bands. Thus it seems that up to now, the primary effect the existence of the inelastic line - is best explained by a single ion effect, i.e. by a time coherent valence fluctuation. As this kind of coherent fluctuation does not work against the RKKY-interaction, TmSe orders magnetically at low temperatures. The intensity dispersion, however, is a secondary effect, and can be described by adding the lattice model of B. Alascio, A.A. Aligia, J. Mazzaferro and C. Balseiro [30] to their single ion model [31]. In addition to the inelastic line at about 2.8 meV, a strong magnetic intensity around 5 meV This cannot be exwas found in Tm,,O, La,,,Se. plained by the theories mentioned above. When looking at the valence of the examined systems, Tm0,0,La,.,, Se is the system where the valence is nearest to the divalent state (Tm*+). Therefore one can presume that in this system the features of a time coherent fluctuating Tm-ion are still mixed with the residual features of crystal-field splittings due to Tm*+. It should be mentioned here that a weak additional intensity is visible, also in the spectrum of TmSe at T = 2 K [15]. TmSe and YSe have nearly the same lattice constant. Therefore, the physical properties of Tm in the concentrated compound TmSe and in the diluted system Tm,,,Y,,,,Se should be similar. Indeed the experimental results (see table 1) are even quantitatively quite similar, especially the

on mixed

- vulent

Tm

-systems

261

0

c

E

02

60-

Iz

Et=147

z 0

40-

F + ?I 5 c 2

20-

OO

5

mev

I

1

I

IO

15

20

AE (me’4 Fig. ref. low and

10. Energy spectra of Tm,,,Se and Tm,,,,Se taken from [21]. Note that the lattice parameters given on the figure are temperature values. The room temperature values are 5.714 5.691 A, respectively.

intensity given per Tm-ion and the linewidth of the inelastic line have nearly the same values. From this it becomes clear that the inelastic line in TmSe cannot be due to a nonstoichiometric effect, i.e. the used TmSe-sample has not the composition Tm, +,Se, as assumed by Furrer, Biihrer and Wachter [32]. Here again, a comment on the quality of samples should be given with respect to the existence of the inelastic line for different TmSesamples. Shapiro and Grier reported neutron scattering experiments on several single crystals with different lattice parameters [21]. They found that the sample with a, = 5.69 A show only a shoulder and no clear peak (fig. 10). Therefore it is not surprising that Furrer, Btihrer and Wachter do

262

E. Hoilund Moritz / Neutron scurrering on mixed-dent

not detect the inelastic line on their single crystal with a, < 5.7 A [32]. Moreover the elastic incoherent cross-section is a good measure for the number of defects in a crystal. In fact the polycrystalline A used in refs. sample with a,, = 5.711 [7,14,15,17,19,20], has a very low elastic cross-section (0.7 b), whereas the single crystal with a, < 5.7 A used in ref. [32] shows a much larger incoherent scattering [33]. This observation agrees quite well with the Mossbauer study [4] mentioned in the introduction. Using a sample with a lot of defects each Tm-ion may have its individual environment, i.e. the local lattice parameter varies over the sample due to lattice defects. That may cause an individual excitation energy for each Tm-ion and therefore the inelastic line (which is a single ion effect) is smeared out in the average of all Tm-ions. This is analogous to the fact that the excitation energy depends on the lattice parameter (table 1). From this it may become more clear why the inelastic line vanishes if the number of defects increases. Another observation by Kobler and Fischer [34] may be interesting with respect to the quality of the TmSe-sample. They found that that part of the single crystal which has the largest paramagnetic Curie-Weiss-temperature (39 K) had the best stoichiometry. The polycrystalline sample used in the neutron scattering experiments [7,14,15,17,19, 201 has a paramagnetic Curie-Weiss-temperature of about 50 K [17]. Thus it seems that the preparation of a good stoichiometric polycrystal is easier than that of a good stoichiometric single crystal ]351.

5. Conclusion The neutron scattering experiments on dilute Tm-systems show that the valence fluctuation is mainly a single ion effect, i.e. a time coherent fluctuation process. This process is possible because both mixing valence states of the Tm-ion are magnetic, which allows finally the magnetic order. Thus the single ion concept used by Mazzaferro, Balseiro and Alascio [29], by Schlottmann [22] and by Kuramoto and Mtiller-Hartmann [23] is confirmed by these experiments.

Tm - s_rstenrs

Acknowledgements I would like to thank K. Fischer for help in preparing the samples at the IFF/KFA Jtilich, H. Scheuer and A.P. Murani for their help during the performance of the experiments at the I.L.L. in Grenoble, M. Prager and J. Raebiger for performing the experiments on the SV22 at the KFA-Jtilich, E. Mtiller-Hartmann, P. Schlottmann, D. Wohlleben and U. Walter for many helpful discussions. This work was supported by the Deutsche Forschungsgemeinschaft through Sonderforschungsbereich SFB 125.

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