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Magnetic excitations in TmH observed using inelastic neutron scattering
440
Journal of the Less-Common
Magnetic excitations in Tm-H inelastic neutron scattering S. M. Bennington Rutherford
D. K.
Appleton
Metals, 172-l 74 (1991) 440-450
observed using
and R. Osborn
Laboratory,
Chilton, Didcot, Oxon OX11 OQX (U.K.)
Ross and M. J. Benham
School of Physics and Space Research, Birmingham B15 ZTT (U.K.)
University of Birmingham,
PO Box 363,
Abstract We have performed inelastic neutron-scattering experiments to study the magnetic excitations in cr-TmH,.,, and compared these with “pure” thulium metal. Our results are similar to earlier measurements on the metal but there are additional features caused by changes in the crystal field due to hydrogen ordering, most notably a large dispersionless feature at 15 meV. We also see magnetic excitations coupled to the hydrogen vibration states.
1. Introduction Thulium is a heavy lanthanide with the h.c.p. structure characteristic of the yttrium rare earths. The free ion has a moment of gJ = 7.0 which in the metal orders antiferromagnetically at 58.5 K. Initially the ordering is sinusoidal along the c-axis, but as the temperature is lowered, higher harmonics appear as the wave “squares up”. Below 39 K the lattice gains a net magnetic moment from a seven-layer ferrimagnetic structure, with four layers spin up and three layers spin down. In the antiferromagnetic phase the moment per atom begins to exceed the free-ion moment, probaly owing to the partial polarization of the conduction electrons [l]. Tm-H has an 01phase boundary of 0.11 [H]/[M] [2]. The phase diagram is very similar to that for the other yttrium rare earths, the U-P phase boundary being independent of temperature up to about 400-500 K. Below this temperature the hydrogens begin to form pairs and occupy the two tetrahedral sites either side of the metal atom along the c-axis [3]. At temperatures below 170 K the material exhibits an anomaly in many of its properties. This has now been linked to the linear ordering of these pairs along the c-axis. The addition of hydrogen also affects the magnetic properties, suppressing both the NQel and Curie temperatures [4], presumably owing to changes in the Fermi surface caused by the presence of hydrogen, the hydrogen interfering with the RKKY (Ruderman-Kittel-KasYoshida) interaction. In the experiments of McEwen and Steigenberger [5], a triple-axis neutron spectrometer was used to study the magnetic excitations in a single
Elsevier Sequoia/Printed
in The Netherlands
441
crystal. Two almost dispersionless modes were seen at 15 and 8 meV, plus a peak at 3-4 meV, the position of which varied with Q. The lack of dispersion in the two higher energy features led the authors to ascribe these peaks to crystal field levels. However, no combination or modification of the known crystal field parameters could reproduce the observed modes. In a later paper by Fernandez-Baca et al. [6], using ultrapure thulium crystals from the Ames Laboratory, only one magnon mode was observed with limited dispersion between 8.3 and 9.6 meV. As in the earlier work [5], Q-dependent features were seen at lower energies. Fernandez-Baca et al. attributed these low energy modes to magnetovibrational scattering - the creation of a phonon via the interaction of the neutron with the magnetic moments of the ions. By comparing the data with the phonon dispersion curves measured in terbium 171, the authors were able to identify these excitations as transverse acoustic (TA) phonons. This paper presents the results of a series of measurements of the incoherent inelastic neutron scattering from thulium metal and Tm-H. The experiments were performed on powder samples using several of the spectrometers at the ISIS neutron spallation source (at the Rutherford Appleton Laboratory). The unparalleled resolutions of the spectrometers available at ISIS complement the existing triple-axis data, providing a coherent picture of both thulium and Tm-H. We discuss the origin of the observed magnetic excitations and the changes caused by the presence of hydrogen, We also look at the effect of hydrogen ordering and trace the temperature dependence of the excitations through the magnetic and hydrogen-ordering transitions. The hydrogen excitations are also studied and we are therefore able to comment on the coupling between the hydrogen vibrations and the magnetic excitations.
2. Experimental
details
Two samples were used in these experiments, one “pure” metal and one containing hydrogen. Both were made from 99.99% pure thulium metal. The sample containing hydrogen was first annealed in a vacuum of 10m6mbar or better at a temperature of 600 “C for several hours. Hydrogenation was effected volumetrically at 600 “C to give a concentration of 0.06 [HI/[ M]. The sample was then cooled slowly to room temperature in stages over a period of 556 h. The deuterium sample was prepared by first removing the hydrogen by annealing at lo-? mbar at 600 ~‘C for several hours and then deuterating in the same way as for the hydrogen loading. As has been mentioned, all the experiments were performed at the ISIS neutron spallation source. Three different spectrometers were used. TFXA: the time-focused crystal analyser spectrometer. This has an inverted geometry (the final energy is fixed) and used graphite analysers to reflect 4 meV neutrons to two groups of 16 “He detectors. The energy resolution is better than 2%, producing excellent resolution at energies below
442
100 meV. In this geometry the momentum transfer is proportional to the square root of the energy transfer. Thus at high energies the intensity of the observed features is small owing to their Debye-Waller factor or their magnetic form factor. HET: the high energy transfer spectrometer. This is a direct geometry time-of-flight spectrometer which uses a Fermi chopper to select an incident energy between 40 and 2000 meV. There are three detector banks: (i) a low angle bank between 3” and 12” situated 4 m from the sample; (ii) a medium angle bank between 12” and 30” at 2.5 m; (iii) a high bank at 136” and 4 m. The energy resolution at energy transfers just below the incident energy is about 1%. MARI: the multiangle rotor instrument. This is very similar in design to HET. It has almost the same energy range but has full angular coverage from 3” to 136”, all at a constant 4 m from the sample. Its resolution is not greatly different from that of HET.
3. Results The incoherent spectrum of thulium metal was taken on TFXA at a temperature of 4 K using a helium cryostat. The results (Fig. 1) are essen-
15
Energy)k~nsfer
El-E2
26
(meV)
Fig. 1. Spectrum of “pure” thulium metal taken at 4 K. On TFXA, scattering windows of .the helium cryostat makes the data unreliable below 2 meV.
from the aluminium
443
tially the same as seen by Fernandez-Baca et al. There is an intense structured peak between 8 and 10 meV, a peak at 3 meV, plus a smaller feature at 15 meV similar to that seen by McEwen and Steigenberger, only weaker. All these features are broader than the instrument resolution, although the structure within the peak at 8-10 meV has widths limited by the instrument. The 8-10 meV peak is generally agreed to be a crystal field level. Although it has observable width, this is significantly less than the energy gap. The crystal field parameters, found by Touborg [S) from paramagnetic susceptibility measurements, predict a value for this level of 7.7 meV. The addition of hydrogen changes this spectrum (Fig. 2). The features at 15 and 3 meV are dramatically enhanced and the crystal field peak at 8 10 meV loses a large part of its intensity. By using BET, it is possible to track these peaks through momentum space. The features all die away rapidly with Q owing to their magnetic form factor. The features at 8-10 and 15 meV show no observable energy change, whereas the features at lower energies change their position and structure with Q. This is also consistent with the observations of the previous researchers. At a hydrogen concentration of 0.06 at.% the NQel and Curie temperatures can be estimated to be 48 and 32 K respectively 141. Experiments were performed on TFXA at temperatures of 25, 40, 55 and 150 K to investigate the scattering in each magnetic phase (Fig. 3). There are several points to note.
10
t5
Energytransfer El-E2 (meV) Fig.
Spectrum
of
at 4
taken
on
Fig. 3. Temperature on TFXA.
dependence
of low energy part of n-TmK spectrum. AH the runs were done
(1) The elastic line broadens with increasing temperature. (2) The intensit;y of the scattering between the elastic line and the crystal field peak becomes progressively smaJIer as the temperature rises. (3) The 8-10 meV crystal field peak is weakened in the antiferromagn&c phase and disappears completely in the paramagne~~c phase. (4) The 15 meV peak is unaffected by the magnetic phase and only begins to lose intensit,y at 150 K. (5) A small peak begins to appear at 18 meV in the 150 K run.
445
The loss of intensity of the scattering between 2 and 8 meV is consistent with the magnetovibrational interpretation of Fernandez-Baca et al. Such scattering is proportional to the magnetization and so is at its most intense in the ferrimagnetic phase; it decreases in the antiferromagnetic phase and goes to zero in the paramagnetic. If the 8-10 meV peak were a pure crystal field level, its intenstiy would be largely independent of temperature. However, the peak has observable width, indicative of exchange coupling. Thus we would expect the intensity of this peak to also be dependent on the magnetization. At low temperatures the magnetovibrational scattering in a material with a periodic structure of characteristic wavevector Q has the form
where Y(K) describes the magnetic and geometric form factors for momentum transfer K, q and E, are the wavevector and energy of the phonon respectively, 5, is the polarization of the phonon, n(E,) is the Bose thermal population factor, k, and hi are the final and initial neutron wavevectors respectively and P is a unit vector along the direction of K. In our particular case, where the scattering is from a polycrystalline sample, an average over all directions of K must be taken. The scattering is almost identical to that for phonon scattering except that the Debye-Waller factor is replaced by a magnetic form factor. The only unexplained feature is the sharp peak at 15 meV. This is almost certainly a crystal field level caused by the presence of hydrogen. If the two hydrogens form a pair on the tetrahedral sites either side of the thulium atom, as is suggested by the structural work on these systems [3], then the metal atom should be subject to a strong tetragonal crystal field. From simple point charge models such a field is likely to be as strong as if not stronger than the crystal field due to the metal lattice. The dilute nature of the hydrogen in the metal means that exchange coupling should be small. This explains the lack of observable structure or dispersion in the peak. The feature begins to lose its intensity at 150 K. This is well into the paramagnetic phase and so it is unlikely that it is linked to the magnetic structure of the metal. In electron irradiation experiments [9] the damage to the hydrogen sublattice begins to anneal at 150 K. Thus the loss in intensity is probably caused by the onset of hydrogen mobility. The small mode at 18 meV may well be caused by a different local hydrogen configuration. The integrated intensities of the 15 and 8810 meV peaks as a function of Q are almost identical. Since we know that the lower energy peak is magnetic, we must also assume that the higher energy peak has the same origin (Fig. 4). If some of the magnetic scattering that we observe is caused by the crystal field due to the hydrogen order, then by quenching our sample to alter this order, we should be able to identify the structures caused by the hydrogen. We attempted this by quenching the sample in liquid nitrogen
446
48
10 meV peak
15 meV peak t
0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
QfA 'I
Fig. 4. Q dependence of intensity for S-10 and 15 meV peaks. The data were taken on MAR1 at The two features have essentially the same form factors. 15 K on a sample of TmD,,.
prior to transferring it to a cryostat and cooling to 15 K. For comparison, in a second experiment the sample was cooled slowly to 15 K over period of a few hours. The results are shown in Fig. 5. The only observable change is the small growth in intensity around the 15 meV peak and the growth of additional structures between 2 and 8 meV. The intensity around the 15 meV peak is reminiscent of the spectra taken at 150 K and reinforces the hypothesis that this scattering is due to different local hydrogen configurations. We have already done a considerable amount of work on the hydrogen excitations in the tl phase of Y-H [lo]. This system is the non-magnetic analogue of Tm-H with an almost identical crystal and electronic structure. Because of this we expected the excitation spectra in the two metals to be very similar. However, the spectra look at first sight to be completely dissimilar (Fig. 6). On closer inspection the same hydrogen excitations do exist. There are the singly degenerate level at 100 meV due to an excitation oriented along the c direction and the doubly degenerate level at 134 meV due to excitations oriented in the basal plane [ll], just as in yttrium. The difference is caused by the presence of two extra peaks at 122 and 141 meV. These are likely to be magnetic in origin, because it is difficult to see how they could be due to hydrogen since there is no evidence for occupation of
+
Quenched
+ Slowly Cooled
V 7
e
6
4
IO
12
Energy transfer El-E2 Fig. 5. Comparison
between quenched
10
I.
?O
18
(meV)
and slowly cooled TmH,,,,, taken at 15 K on TFXA J-
8000
7000
i
0
6000
5000 > +J 4000 3i $ 2 P In
3000
0
2000
eo
90
IO0
110
120
130
140
150
160
Energy Transfer (meV) Fig. 6. First hydrogen excitations in r-TmH, “s taken at 20 K on HET with an incident energy of 200 meV. All the low angle 4 m banks were summed together. The insert is an identical spectrum at the same temperature and with the same instrumental configuration. taken on wYH,,,
448
150 K
0.25
f
25 K i
B 0.20 7, z b 5, f F 5 i
0.15
0.10
0.05
t 80
90
100
110
120
130
Energy transfer El-E2
Fig. 7. Temperature dependence of first excited hydrogen both done on TFXA, one at 25 K and one at 150 K.
140
150
160
170
180
(m&4)
level in a-TmH,,,,.
There
are two runs,
the octahedral site and X-ray diffraction indicates that the sample is entirely tl phase. The exact origin of these peaks is still uncertain, but they may be magnetovibrational two-phonon sidebands to the hydrogen peaks. At these low temperatures, only the lowest energy phonons can exist and so all the scattering is neutron energy loss, which is consistent with what is observed. The peaks show no discernible change on quenching and there is no growth of small auxiliary features as is seen at low energies. However, they do show a strong temperature dependence (Fig. 7): at 150 K the peaks decrease in intensity and there is the growth of extra features at about 115 and 130 meV. Moreover, runs done on HET seem to show some change in the peak position with Q. Both these results are consistent with the hypothesis that the large features at 122 and 141 meV are powerful magnetovibrational sidebands.
4. Discussion The ground state of thulium is J= 6. The quadrupolar potential that would be created by the proximity of hydrogens on the two neighbouring tetrahedral sites would, using a simple point charge model, give a
449
perturbation of the form 35, - J(J + 1). This splits the ground state into a series of levels with J, = 0, + 1, + 2, . . , + 6. Depending on the sign of the quadrupolar field, the ground state will be either J, = 0 or J, = k6. The matrix elements for dipole transitions are such that AJ, = ) 1; thus we would expect only one crystal field peak due to the pairing of the hydrogens either side of the yttrium atom, since at the low temperatures at which these experiments are performed only the ground state is occupied. The weaker fields from more distant hydrogen atoms would cause crystal field levels at lower energies, but since there are a large number of possible configurations of these more distant hydrogens it is unlikely that there is a single identifiable peak. In the comparison between the quenched and unquenched spectra there would be considerable change in the low energy region between 2 and 8 meV. This may be due to the change in the crystal field resulting from differences in the ordering of the pairs. In both the quenched and the high temperature spectra scattering was seen in the wings of the 15 meV peak. This scattering may be caused by a small number of thulium ions with a single hydrogen atom as a neighbour. One of the more puzzling features in the work is the nature of the scattering around the hydrogen excitations. If the features at 100 and 134 meV are hydrogen excitations, which seems likely from the Y-H data [lo], then the peaks at 121 and 142 meV must be magnetic. They could simply be crystal field levels that happen to be coincident with hydrogen vibration states. Another explanation is that it is the coupling of hydrogen and magnetic excitations. If this is the case, the 121 meV feature must be associated with the 100 meV c direction excitation and the 141 meV peak with the 134 meV basal plane excitation, because at these low temperatures all the scattering must be on the neutron energy loss side. The problem with this interpretation is the sharpness and intensity of the magnetic peaks compared to the hydrogen modes with which they are supposed to be coupling. This could be a coherency effect. For a neutron to excite a hydrogen state, its Q vector must be aligned in some particular direction within the crystallite (the scattering has the form (e * Q)“, where e is the polarization of the hydrogen). Magnetic sidebands are governed by a form factor which confines the scattering to low values of Q and hence to a direction in the crystallite close to the Q defined by the hydrogen scattering. Thus a particular section of the magnetovibrational dispersion curve will be picked out, a different one in each sideband. Further work is necessary before we can come to any definitive conclusion on this matter.
5. Conclusions The addition of hydrogen to thulium obviously has a profound influence on the magnetic structure of the metal. If it were possible to determine the nature of the ground state, then the crystal field level would give information on the HPTm interaction and it would be possible to determine the valency
450
of the hydrogen. Magnetism could thus be an excellent probe of the changes in the electronic structure caused by the presence of hydrogen. It may also be a useful measure of the hydrogen concentration and the short-range order of the hydrogen ions. Thus magnetic neutron scattering should prove to be a powerful probe in these systems.
References 1 B. Coqblin, Electronic Structure of Rare Earth Metals and Alloys, Academic, London, 1977. 2 J. P. Burger, J. N. Daou, A. Lucasson, P. Lucasson and P. Vajda, Z. Phys. Chem. N.F. 143 (1985) 111. 3 M. W. McKergow, D. K. Ross, J. E. Bonnet, I. S. Anderson and 0. Schaerpf, J. Phys. C: Solid State Phys., 20 (1987) 1909. 4 J. N. Daou, P. Vajda, A. Lucasson and P. Lucasson. J. Phys. C: Solid State Phys., 14 (1981) 129. 5 K. A. McEwen and U. Steigenberger, J. Phys. (Paris), Colloq. CS, 49 (1988) 335. 6 J. A. Fernandez-Baca, R. M. Nicklow Z. Tun and I. J. Rhyne, Phys. Rev. I?., 43 (1991) 3188. 7 J. C. G. Houmann and R. M. Nicklow, Phys. Reu. B, I (1970) 3943. 8 P. Touborg, Phys. Rev. B, 16 (1977) 1201. 9 J. N. Daou, P. Radhakrishna, R. Tur and P. Vajda, J. Phys. F: Met. Phys. 11 (1981) L263. 10 S. M. Bennington, M. J. Benham, D. K. Ross, A. D. Taylor and Z. A. Bowden, Z. Phys. Chem. N.F., 163 (1989) 1071. 11 I. S. Anderson, J. J. Rush, T. Udovic and J. M. Rowe, Phys. Reu. Lett., 57 (1986) 2822.
Journal of the Less-Common
Magnetic excitations in Tm-H inelastic neutron scattering S. M. Bennington Rutherford
D. K.
Appleton
Metals, 172-l 74 (1991) 440-450
observed using
and R. Osborn
Laboratory,
Chilton, Didcot, Oxon OX11 OQX (U.K.)
Ross and M. J. Benham
School of Physics and Space Research, Birmingham B15 ZTT (U.K.)
University of Birmingham,
PO Box 363,
Abstract We have performed inelastic neutron-scattering experiments to study the magnetic excitations in cr-TmH,.,, and compared these with “pure” thulium metal. Our results are similar to earlier measurements on the metal but there are additional features caused by changes in the crystal field due to hydrogen ordering, most notably a large dispersionless feature at 15 meV. We also see magnetic excitations coupled to the hydrogen vibration states.
1. Introduction Thulium is a heavy lanthanide with the h.c.p. structure characteristic of the yttrium rare earths. The free ion has a moment of gJ = 7.0 which in the metal orders antiferromagnetically at 58.5 K. Initially the ordering is sinusoidal along the c-axis, but as the temperature is lowered, higher harmonics appear as the wave “squares up”. Below 39 K the lattice gains a net magnetic moment from a seven-layer ferrimagnetic structure, with four layers spin up and three layers spin down. In the antiferromagnetic phase the moment per atom begins to exceed the free-ion moment, probaly owing to the partial polarization of the conduction electrons [l]. Tm-H has an 01phase boundary of 0.11 [H]/[M] [2]. The phase diagram is very similar to that for the other yttrium rare earths, the U-P phase boundary being independent of temperature up to about 400-500 K. Below this temperature the hydrogens begin to form pairs and occupy the two tetrahedral sites either side of the metal atom along the c-axis [3]. At temperatures below 170 K the material exhibits an anomaly in many of its properties. This has now been linked to the linear ordering of these pairs along the c-axis. The addition of hydrogen also affects the magnetic properties, suppressing both the NQel and Curie temperatures [4], presumably owing to changes in the Fermi surface caused by the presence of hydrogen, the hydrogen interfering with the RKKY (Ruderman-Kittel-KasYoshida) interaction. In the experiments of McEwen and Steigenberger [5], a triple-axis neutron spectrometer was used to study the magnetic excitations in a single
Elsevier Sequoia/Printed
in The Netherlands
441
crystal. Two almost dispersionless modes were seen at 15 and 8 meV, plus a peak at 3-4 meV, the position of which varied with Q. The lack of dispersion in the two higher energy features led the authors to ascribe these peaks to crystal field levels. However, no combination or modification of the known crystal field parameters could reproduce the observed modes. In a later paper by Fernandez-Baca et al. [6], using ultrapure thulium crystals from the Ames Laboratory, only one magnon mode was observed with limited dispersion between 8.3 and 9.6 meV. As in the earlier work [5], Q-dependent features were seen at lower energies. Fernandez-Baca et al. attributed these low energy modes to magnetovibrational scattering - the creation of a phonon via the interaction of the neutron with the magnetic moments of the ions. By comparing the data with the phonon dispersion curves measured in terbium 171, the authors were able to identify these excitations as transverse acoustic (TA) phonons. This paper presents the results of a series of measurements of the incoherent inelastic neutron scattering from thulium metal and Tm-H. The experiments were performed on powder samples using several of the spectrometers at the ISIS neutron spallation source (at the Rutherford Appleton Laboratory). The unparalleled resolutions of the spectrometers available at ISIS complement the existing triple-axis data, providing a coherent picture of both thulium and Tm-H. We discuss the origin of the observed magnetic excitations and the changes caused by the presence of hydrogen, We also look at the effect of hydrogen ordering and trace the temperature dependence of the excitations through the magnetic and hydrogen-ordering transitions. The hydrogen excitations are also studied and we are therefore able to comment on the coupling between the hydrogen vibrations and the magnetic excitations.
2. Experimental
details
Two samples were used in these experiments, one “pure” metal and one containing hydrogen. Both were made from 99.99% pure thulium metal. The sample containing hydrogen was first annealed in a vacuum of 10m6mbar or better at a temperature of 600 “C for several hours. Hydrogenation was effected volumetrically at 600 “C to give a concentration of 0.06 [HI/[ M]. The sample was then cooled slowly to room temperature in stages over a period of 556 h. The deuterium sample was prepared by first removing the hydrogen by annealing at lo-? mbar at 600 ~‘C for several hours and then deuterating in the same way as for the hydrogen loading. As has been mentioned, all the experiments were performed at the ISIS neutron spallation source. Three different spectrometers were used. TFXA: the time-focused crystal analyser spectrometer. This has an inverted geometry (the final energy is fixed) and used graphite analysers to reflect 4 meV neutrons to two groups of 16 “He detectors. The energy resolution is better than 2%, producing excellent resolution at energies below
442
100 meV. In this geometry the momentum transfer is proportional to the square root of the energy transfer. Thus at high energies the intensity of the observed features is small owing to their Debye-Waller factor or their magnetic form factor. HET: the high energy transfer spectrometer. This is a direct geometry time-of-flight spectrometer which uses a Fermi chopper to select an incident energy between 40 and 2000 meV. There are three detector banks: (i) a low angle bank between 3” and 12” situated 4 m from the sample; (ii) a medium angle bank between 12” and 30” at 2.5 m; (iii) a high bank at 136” and 4 m. The energy resolution at energy transfers just below the incident energy is about 1%. MARI: the multiangle rotor instrument. This is very similar in design to HET. It has almost the same energy range but has full angular coverage from 3” to 136”, all at a constant 4 m from the sample. Its resolution is not greatly different from that of HET.
3. Results The incoherent spectrum of thulium metal was taken on TFXA at a temperature of 4 K using a helium cryostat. The results (Fig. 1) are essen-
15
Energy)k~nsfer
El-E2
26
(meV)
Fig. 1. Spectrum of “pure” thulium metal taken at 4 K. On TFXA, scattering windows of .the helium cryostat makes the data unreliable below 2 meV.
from the aluminium
443
tially the same as seen by Fernandez-Baca et al. There is an intense structured peak between 8 and 10 meV, a peak at 3 meV, plus a smaller feature at 15 meV similar to that seen by McEwen and Steigenberger, only weaker. All these features are broader than the instrument resolution, although the structure within the peak at 8-10 meV has widths limited by the instrument. The 8-10 meV peak is generally agreed to be a crystal field level. Although it has observable width, this is significantly less than the energy gap. The crystal field parameters, found by Touborg [S) from paramagnetic susceptibility measurements, predict a value for this level of 7.7 meV. The addition of hydrogen changes this spectrum (Fig. 2). The features at 15 and 3 meV are dramatically enhanced and the crystal field peak at 8 10 meV loses a large part of its intensity. By using BET, it is possible to track these peaks through momentum space. The features all die away rapidly with Q owing to their magnetic form factor. The features at 8-10 and 15 meV show no observable energy change, whereas the features at lower energies change their position and structure with Q. This is also consistent with the observations of the previous researchers. At a hydrogen concentration of 0.06 at.% the NQel and Curie temperatures can be estimated to be 48 and 32 K respectively 141. Experiments were performed on TFXA at temperatures of 25, 40, 55 and 150 K to investigate the scattering in each magnetic phase (Fig. 3). There are several points to note.
10
t5
Energytransfer El-E2 (meV) Fig.
Spectrum
of
at 4
taken
on
Fig. 3. Temperature on TFXA.
dependence
of low energy part of n-TmK spectrum. AH the runs were done
(1) The elastic line broadens with increasing temperature. (2) The intensit;y of the scattering between the elastic line and the crystal field peak becomes progressively smaJIer as the temperature rises. (3) The 8-10 meV crystal field peak is weakened in the antiferromagn&c phase and disappears completely in the paramagne~~c phase. (4) The 15 meV peak is unaffected by the magnetic phase and only begins to lose intensit,y at 150 K. (5) A small peak begins to appear at 18 meV in the 150 K run.
445
The loss of intensity of the scattering between 2 and 8 meV is consistent with the magnetovibrational interpretation of Fernandez-Baca et al. Such scattering is proportional to the magnetization and so is at its most intense in the ferrimagnetic phase; it decreases in the antiferromagnetic phase and goes to zero in the paramagnetic. If the 8-10 meV peak were a pure crystal field level, its intenstiy would be largely independent of temperature. However, the peak has observable width, indicative of exchange coupling. Thus we would expect the intensity of this peak to also be dependent on the magnetization. At low temperatures the magnetovibrational scattering in a material with a periodic structure of characteristic wavevector Q has the form
where Y(K) describes the magnetic and geometric form factors for momentum transfer K, q and E, are the wavevector and energy of the phonon respectively, 5, is the polarization of the phonon, n(E,) is the Bose thermal population factor, k, and hi are the final and initial neutron wavevectors respectively and P is a unit vector along the direction of K. In our particular case, where the scattering is from a polycrystalline sample, an average over all directions of K must be taken. The scattering is almost identical to that for phonon scattering except that the Debye-Waller factor is replaced by a magnetic form factor. The only unexplained feature is the sharp peak at 15 meV. This is almost certainly a crystal field level caused by the presence of hydrogen. If the two hydrogens form a pair on the tetrahedral sites either side of the thulium atom, as is suggested by the structural work on these systems [3], then the metal atom should be subject to a strong tetragonal crystal field. From simple point charge models such a field is likely to be as strong as if not stronger than the crystal field due to the metal lattice. The dilute nature of the hydrogen in the metal means that exchange coupling should be small. This explains the lack of observable structure or dispersion in the peak. The feature begins to lose its intensity at 150 K. This is well into the paramagnetic phase and so it is unlikely that it is linked to the magnetic structure of the metal. In electron irradiation experiments [9] the damage to the hydrogen sublattice begins to anneal at 150 K. Thus the loss in intensity is probably caused by the onset of hydrogen mobility. The small mode at 18 meV may well be caused by a different local hydrogen configuration. The integrated intensities of the 15 and 8810 meV peaks as a function of Q are almost identical. Since we know that the lower energy peak is magnetic, we must also assume that the higher energy peak has the same origin (Fig. 4). If some of the magnetic scattering that we observe is caused by the crystal field due to the hydrogen order, then by quenching our sample to alter this order, we should be able to identify the structures caused by the hydrogen. We attempted this by quenching the sample in liquid nitrogen
446
48
10 meV peak
15 meV peak t
0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
QfA 'I
Fig. 4. Q dependence of intensity for S-10 and 15 meV peaks. The data were taken on MAR1 at The two features have essentially the same form factors. 15 K on a sample of TmD,,.
prior to transferring it to a cryostat and cooling to 15 K. For comparison, in a second experiment the sample was cooled slowly to 15 K over period of a few hours. The results are shown in Fig. 5. The only observable change is the small growth in intensity around the 15 meV peak and the growth of additional structures between 2 and 8 meV. The intensity around the 15 meV peak is reminiscent of the spectra taken at 150 K and reinforces the hypothesis that this scattering is due to different local hydrogen configurations. We have already done a considerable amount of work on the hydrogen excitations in the tl phase of Y-H [lo]. This system is the non-magnetic analogue of Tm-H with an almost identical crystal and electronic structure. Because of this we expected the excitation spectra in the two metals to be very similar. However, the spectra look at first sight to be completely dissimilar (Fig. 6). On closer inspection the same hydrogen excitations do exist. There are the singly degenerate level at 100 meV due to an excitation oriented along the c direction and the doubly degenerate level at 134 meV due to excitations oriented in the basal plane [ll], just as in yttrium. The difference is caused by the presence of two extra peaks at 122 and 141 meV. These are likely to be magnetic in origin, because it is difficult to see how they could be due to hydrogen since there is no evidence for occupation of
+
Quenched
+ Slowly Cooled
V 7
e
6
4
IO
12
Energy transfer El-E2 Fig. 5. Comparison
between quenched
10
I.
?O
18
(meV)
and slowly cooled TmH,,,,, taken at 15 K on TFXA J-
8000
7000
i
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5000 > +J 4000 3i $ 2 P In
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eo
90
IO0
110
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Energy Transfer (meV) Fig. 6. First hydrogen excitations in r-TmH, “s taken at 20 K on HET with an incident energy of 200 meV. All the low angle 4 m banks were summed together. The insert is an identical spectrum at the same temperature and with the same instrumental configuration. taken on wYH,,,
448
150 K
0.25
f
25 K i
B 0.20 7, z b 5, f F 5 i
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Energy transfer El-E2
Fig. 7. Temperature dependence of first excited hydrogen both done on TFXA, one at 25 K and one at 150 K.
140
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(m&4)
level in a-TmH,,,,.
There
are two runs,
the octahedral site and X-ray diffraction indicates that the sample is entirely tl phase. The exact origin of these peaks is still uncertain, but they may be magnetovibrational two-phonon sidebands to the hydrogen peaks. At these low temperatures, only the lowest energy phonons can exist and so all the scattering is neutron energy loss, which is consistent with what is observed. The peaks show no discernible change on quenching and there is no growth of small auxiliary features as is seen at low energies. However, they do show a strong temperature dependence (Fig. 7): at 150 K the peaks decrease in intensity and there is the growth of extra features at about 115 and 130 meV. Moreover, runs done on HET seem to show some change in the peak position with Q. Both these results are consistent with the hypothesis that the large features at 122 and 141 meV are powerful magnetovibrational sidebands.
4. Discussion The ground state of thulium is J= 6. The quadrupolar potential that would be created by the proximity of hydrogens on the two neighbouring tetrahedral sites would, using a simple point charge model, give a
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perturbation of the form 35, - J(J + 1). This splits the ground state into a series of levels with J, = 0, + 1, + 2, . . , + 6. Depending on the sign of the quadrupolar field, the ground state will be either J, = 0 or J, = k6. The matrix elements for dipole transitions are such that AJ, = ) 1; thus we would expect only one crystal field peak due to the pairing of the hydrogens either side of the yttrium atom, since at the low temperatures at which these experiments are performed only the ground state is occupied. The weaker fields from more distant hydrogen atoms would cause crystal field levels at lower energies, but since there are a large number of possible configurations of these more distant hydrogens it is unlikely that there is a single identifiable peak. In the comparison between the quenched and unquenched spectra there would be considerable change in the low energy region between 2 and 8 meV. This may be due to the change in the crystal field resulting from differences in the ordering of the pairs. In both the quenched and the high temperature spectra scattering was seen in the wings of the 15 meV peak. This scattering may be caused by a small number of thulium ions with a single hydrogen atom as a neighbour. One of the more puzzling features in the work is the nature of the scattering around the hydrogen excitations. If the features at 100 and 134 meV are hydrogen excitations, which seems likely from the Y-H data [lo], then the peaks at 121 and 142 meV must be magnetic. They could simply be crystal field levels that happen to be coincident with hydrogen vibration states. Another explanation is that it is the coupling of hydrogen and magnetic excitations. If this is the case, the 121 meV feature must be associated with the 100 meV c direction excitation and the 141 meV peak with the 134 meV basal plane excitation, because at these low temperatures all the scattering must be on the neutron energy loss side. The problem with this interpretation is the sharpness and intensity of the magnetic peaks compared to the hydrogen modes with which they are supposed to be coupling. This could be a coherency effect. For a neutron to excite a hydrogen state, its Q vector must be aligned in some particular direction within the crystallite (the scattering has the form (e * Q)“, where e is the polarization of the hydrogen). Magnetic sidebands are governed by a form factor which confines the scattering to low values of Q and hence to a direction in the crystallite close to the Q defined by the hydrogen scattering. Thus a particular section of the magnetovibrational dispersion curve will be picked out, a different one in each sideband. Further work is necessary before we can come to any definitive conclusion on this matter.
5. Conclusions The addition of hydrogen to thulium obviously has a profound influence on the magnetic structure of the metal. If it were possible to determine the nature of the ground state, then the crystal field level would give information on the HPTm interaction and it would be possible to determine the valency
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of the hydrogen. Magnetism could thus be an excellent probe of the changes in the electronic structure caused by the presence of hydrogen. It may also be a useful measure of the hydrogen concentration and the short-range order of the hydrogen ions. Thus magnetic neutron scattering should prove to be a powerful probe in these systems.
References 1 B. Coqblin, Electronic Structure of Rare Earth Metals and Alloys, Academic, London, 1977. 2 J. P. Burger, J. N. Daou, A. Lucasson, P. Lucasson and P. Vajda, Z. Phys. Chem. N.F. 143 (1985) 111. 3 M. W. McKergow, D. K. Ross, J. E. Bonnet, I. S. Anderson and 0. Schaerpf, J. Phys. C: Solid State Phys., 20 (1987) 1909. 4 J. N. Daou, P. Vajda, A. Lucasson and P. Lucasson. J. Phys. C: Solid State Phys., 14 (1981) 129. 5 K. A. McEwen and U. Steigenberger, J. Phys. (Paris), Colloq. CS, 49 (1988) 335. 6 J. A. Fernandez-Baca, R. M. Nicklow Z. Tun and I. J. Rhyne, Phys. Rev. I?., 43 (1991) 3188. 7 J. C. G. Houmann and R. M. Nicklow, Phys. Reu. B, I (1970) 3943. 8 P. Touborg, Phys. Rev. B, 16 (1977) 1201. 9 J. N. Daou, P. Radhakrishna, R. Tur and P. Vajda, J. Phys. F: Met. Phys. 11 (1981) L263. 10 S. M. Bennington, M. J. Benham, D. K. Ross, A. D. Taylor and Z. A. Bowden, Z. Phys. Chem. N.F., 163 (1989) 1071. 11 I. S. Anderson, J. J. Rush, T. Udovic and J. M. Rowe, Phys. Reu. Lett., 57 (1986) 2822.