E xp erim en tal techniques
4.3.2 U(Pdo.995Pto.o05)
In order to characterise the transition at T = 4.6K we have looked for the existence of the superlattice reflections present in UPds at (^ + h,0,l). There are, indeed, additional reflections at these positions below T = 4.6K. We measured these, on IN20, a polarised thermal triple axis spectrometer, at the ILL, Grenoble under an applied magetic field along the a-axis. These show an enhancement over their zero field values as in pure UPdg [7] which confirms they have a magnetic character. In F ig. 4.23. we show this enhancement.
Chapter 4. U(Pdi-xPtx)3 92 (1/2,0,1 8000 7000 • n o n - s p i n - f l i p Ü s p i n - f l i p w 6000 g 5000 Ü c 4000 B / / a -a xis 5 3000 <D z 2000 1000 2 8 10 0 4 1200 1000 3 800 8 c 600 <D 400 Z 200 (1/2,0,4) • n o n - s p i n - l l i p □ s p i n - f l i p T em perature (K) 4 6 T em perature (K) 10
Figure 4.24: Spin-flip an d non-spin-flip s c atterin g from the (|,0,1) and (|,0,4) reflections a t B = 3T as a function of t e m p e r a tu r e s for U(Pdo.ggsPto.0 0 5)3-
In F ig . 4.24. we show the (|,0,1) and (|,0,4) reflections, which clearly de velop at T = 4.6K. The non-spin-flip data mean th at the moment is parallel to the neutron polarisation and the magnetic field (a-axis). The strong I = odd reflections imply th at the induced magnetic structure is the ”CD” or cubic dif ference structure in the notation of the Walker et al. [8]. If it was the ”CS” structure then we would have the I = even reflections.
The spin-flip d ata for I = odd mean th a t there is some moment in the scat tering plane. Because the susceptibility along c* is less than along a* [13], we assume th a t the moment is along a*.
The I = even data could come from a weak ”CS” component or weak hexagonal moments, either in the ”HE” or ”H 0 ” structure.
4 . 4
M agnetic excitation s in UPdg
Since the work of Murray and Buyers [5, 6, 14, 17, 34] on the magnetic excitations of UPdg, McEwen et al. [18] made a more detailed study of the low energy excitations. The motivation for this review was the finding of contradictory information on the alloy U(Pdo.9 8Pto.o2)3-
section 4.1.1. If U(Pdo.9 8Pto.o2 ) 3 does not exhibit any long range ordering, section
4.2, then we would not expect these excitations to be observed. However clear excitations are observed even at T > T i, section 4.5.1. Moreover, in the higher energy excitations we find five crystal field excitations in this compound — at energies 5meV, lOmeV, 14meV, 16meV and 20meV — instead of the two found by Murray and Buyers. We therefore decided to reexamine both the low energy and the high energy excitations in pure UPdg.
4.4.1
Low energy excitation s in UPda
We have re-measured the low energy excitations in UPdg on the IN14, cold neu tron triple axis spectrometer at ILL, Grenoble. There is a major motivation for this new experiment. Comparison with the experiments performed using the cold triple axis spectrometer IN12 at ILL, Grenoble [18] in 1991 shows a ten times in crease in intensity in the U(Pdo.9 8Pto.o2 ) 3 experiment in IN14, arising from to
the IN14/IN12 fiux ratio and the gain due to the IN14 curved analyser. Thus, there is a possibility th at the suppression of the excitations above T% observed by McEwen et al. [18] were due to low neutron intensity.
We performed the experiment on a 17gr single crystal of UPdg oriented with the a*-b* directions in the scattering plane. Two resolution configurations (con stant k f = 1.5“ ^ -f Be filter and collimation neutron guide/40 min/curved analyser) and for the details (constant k f = 1.3“ ^ -f Be filter and collimation neutron guide/40 min/curved analyser) were used. The energy resolution, deter mined from the vanadium incoherent scattering, was 0.22meV and 0.13meV for these configurations, respectively. In all cases we used a Pyrolitic Graphite (in Bragg refiection 002) vertically focusing monochromator and horizontally focus ing PG002 analyser. Extra shielding was mounted around the sample, out of the flight path to the analyser, to reduce the fast neutron background arising from fission of the residual in the sample. The magnitude of this background
Chapter 4. LYPcii-x-P^xl^ 94 o O o 4;în /) /UÜ * I ... I Ei\ rr'ieV)
Figure 4.2 5 : Inelastic scattering a t a F-point of UPdg at 1.8K, m easured on IN14
with kf = 1. 5A “ ^ fixed. M onitor 4000 corresponds to a counting time of l l m i n at O.omeV energy transfer. The curves are lorentzian fits to the d ata. T he bottom line represents the measured background.
(around 80 counts/iuoiiitor=4000) was measured by rotating the analyser off 15° away from the Bragg refiection position.
The results show four modes at a general wave vector. In addition we see another mode around 5meV, F ig. 4.25. which overlaps the results seen in the higher energy excitations measured at a thermal triple axis spectrometer, see section 4.4.2.
Little dispersion is observed when measuring the inelastic spectra at different wave vectors, in agreement with [18]. The motivation for this experiment was the tem perature dependence, so a careful study of the /v-point ( |, f ,0 ) temperature dependence was done, see F ig. 4.26.
At 1.7K, we have modes at 1.30meV, 1.67meV, 2.20meV and 2.62meV. At 3.5K, the situation is very similar. The peaks have not moved, but the one centred at 1.67meV has decrease considerably in intensity while the others remain unchanged. At 5.OK, above T2, we see th a t all the modes have moved in energy
800 600 400 i- 200 800 T=3.49K T=7.10K 6 G ( ' c 400 M+4,+ii+u, ffT7m-n-rrr-,,,,7T c 200 0 L- 8 0 0 p- T=5.04K 600 400 200 E N ( m e V )
Figure 4.26: T em p eratu re dependence of the inelastic scatterin g at Q = (§,§,0) in UPdg, measured with fixed k j = 1.3A~h Remind transition te m p e ra tu res for U P d3, see section 4.1.1. T y = 7.8K, T i = 6.8K, T2 = 4.4K.
Chapter 4. U(Pdi-xPtx)3 96
and they come closer together. Now the excitations are seen much more damped. Now we have peaks at 1.41meV, 1.77meV, 2.15meV and 2.56meV. At 6.20K all the excitations are very damped , and it is no longer possible to observe directly the four modes, although they might be there as the tails of the spectrum have gone up, indicating damped excitations which add up to the background. At 7.10K, above T i, it is not possible to distinguish any excitations, although the scattering is well above background, indicating the presence of at least one very damped excitation. At 9.9K, above Ti>, the spectrum is very similar to the one below T%. In the paramagnetic region it is not possible to distinguish different excitations. This is a very im po rtan t difference with respect to the doped compound U(Pdo.9 8Pto.o2 ) 3 where different excitations are observed.
There is an im portant difference with the previous work of McEwen et al.
[18]. In this work, they observed a change from four excitations below T2 to two
excitations above this temperature, probably by the lack of instrumental resolu tion in the previous experiment. However the disappearance of the excitations above T i has been confirmed.
4.4.2
H igh energy excitation s in UPdg
To study a higher energy range we used a therm al triple axis spectrometer. The thermal distribution of such kind of neutrons allows a higher range of energy transfer to be studied, from 2meV to 60meV, at the cost of instrumental resolu tion. The experiments were performed at the INS thermal triple axis spectrom eter at ILL, Grenoble using the same single crystal th a t we used for the lower energy excitations. The experiments were done with the orientations (1,1,0)- c* and a*-b* in the scattering plane. Two resolution configurations were used (constant k f = 2.662Â~^ 4- P C filter with PG002 monochromator and colli mation 50min/40 m in/curved analyser) and for higher energy transfers (constant
1 0 0 0 M ovu c o A I I I %...t .4 : " \w / A % ..-.... ;rreV
Figure 4.27: Inelastic scan of UPds at the wave vector Q — (2.5,0,0) a t lOK fitted with five lorentzians. T h e energy resolution w idth for this configuration (k/ = 2.662A“ ^) is l.OOrneV a t zero energy transfer. M onitor 5000 corresponds to a counting time of 4inin at 5rneV energy transfer. T h e b o tto m line represents the m easured background.
niiii/ciirved analyser) were used. The energy resolution, deteriiiiued from the vanadium incoherent scattering, was l.OGmeV and 3.18meV at zero energy trans fer for these configurations, respectively. In all cases we used a Pyrolitic Graphite (in Bragg reflection 002) horizontally focusing analyser.
The aim of the experiment was to determine whether the five excitations found in U(Pdo.9 8Pto.o2).3 exist in pure UPdg and make a definitive study of these excitations. In F ig. 4.27, we see an inelastic scan at the zone boundary. A/-point (2.5,0,0), in which we clearly observe five modes. At higher energies, 25-35me\’, at least two other extra modes are observed. F ig. 4.28.
When the spectrometer is operated with k f fixed and the filter in the scattered beam, the presence of higher order reflections from the monochromator affects the inelastic spectra collected. The higher order neutrons may interact with the sample, giving additional background or spurious signals. Furthermore, they are
8
:
.
\
^ A: 6 /üüü i N ; \ f il ..VV“ “? ; U : \
;. /.' / V % /"'■ r\ l. M.i 0 (.) '.N (meV)Figure 4 .2 8 : Inelastic scan of UPda at the wave vector Q = (2.5,0,0) at lOK. At least two e x tra modes are observed at higher energies. T h e energy resolution width for this configuration (k/ = 4.1.4“ *) is 3.18meV a t zero energy transfer. Monitor 5000 corresponds to a counting time of 9min a t 27nie\' energy transfer. The bottom line represents the measured background.
detected by the incident beam monitor, which determines the connting time for each da ta point. For a correct normalisation of d a ta taken with variable k, and without filter in the incident beam, it is necessary to correct the monitor counts for this latter effect. Let Cri ki ) be the total monitor count rate and Cj{ki) the count rate due to the j t h order neutrons. We can then write:
CtA.) = C i(r,) + y ] c , ( r , ) (4.6)
J- 2 and define a correction factor:
p , , , c y y _ Cl (A) , , .
by which the monitor count rate should be multiplied. Empirical expressions exist for all the spectrometers used in this work. This effect is specially im portant for the low energy transfers, where Cj(ki) for j > 1 is bigger, and it can be as big as 40%. As a result, after correction for this effect, the real counting for the low energy transfer measured points increases.
Another im portant correction when comparing inelastic spectra taken at dif ferent reciprocal lattice positions, is the form factor, see section 3.2.2. For re ciprocal lattice points far away from the origin it tends to reduce the response. In order to compare intensities at different Q positions we divide the intensity count rate by P { Q ) of from [35]. It is not always possible to compare inten sities from different experiments when changing the crystal orientation. However in the two orientations th a t we have investigated, (l,l,0)-c* and a*-b*, we have compared the intensities of the common reciprocal point (1,1,0) and we obtain similar spectra when normalising to 1500 and 5000 monitor counts respectively, so this is the normalisation we have used in all the presented plots.
To eliminate the instrumental resolution function, we deconvoluted the fitted peaks with the gaussian vanadium width at every energy transfer.
In F ig . 4.29, 4.30, 4.31, 4.32, 4.33, and 4.34, we show the deconvoluted fitted lorentzians to the data, after all the necessary corrections have been made. We have used a 3D representation to show how the energies of the modes and their intensity varies at the same time. We plot the fitted response for the several measured reciprocal lattice points and we interpolate between them. The result are the coloured surfaces shown in the figures and the plots which show the dispersion in energy of the modes as well as their intensity through symmetry lines in reciprocal space.
The intensity of the modes decreases at higher temperatures, as the ground state is being depopulated. This shows th a t they are indeed crystal field excita tions.
Chapter 4. U(Pdi-xh^C)3 100 T-2K 10 15 20 E(meV) T-2K I xIO 3.5 S 4000-' 2 0 0 0- E(meV) X10 10,, 3 . 5 4 . 5 Q(O.O.I) 5 . 5 6 3 . 5 5 . 5
Figure 4.29: Crystal field modes of UPda along Q = (0,0,1) at 2K. We clearly observe four modes in this energy range. The top figure shows the strong dispersion of the m ost intense mode. The middle figure shows a section in order to observe the weaker modes. The two bottom figures show the fitted centre of the lorentzians and their area in the same colour.
T-2K X 10