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A comparison of the dynamical susceptibility of trivalent and intermediate valent TmSe studied by inelastic neutron scattering
Sqlid State Communications, Vol. 40, pp. 1011-1014. Pergamon Press Ltd. 1981. Printed in Great Britain.
0038-1098/81/47 I011-04502.00/0
A COMPARISON OF THE DYNAMICAL SUSCEPTIBILITY OF TRWALENT AND INTERMEDIATE VALENT TmSe STUDIED BY INELASTIC NEUTRON SCATTERING A. Furrer and W. BShrer Institut ftir Reaktortechnik, Eidgen6ssische Technische Hochschule Ziirich, CH-5303 WiJrenlingen, Switzerland and P. Wachter Laboratorium ftir Festk6rperphysik, ETH-H6nggerberg, CH-8093 Ztirich, Switzerland
(Received 23 August 1981 by A.R. Miederna) The inelastic neutron scattering technique has been used to measure the dynamical susceptibilities of trivalent and intermediate valent TmSe. The experiments have been performed for single-crystalline samples above and below the antiferromagnetic ordering temperatures. From the excitation spectra observed for trivalent Tmo.s~Se we have derived the crystal-field level scheme which yields a magnetic triplet ground state. For intermediate valent Tmo.~oSe there is a single dispersionless spin excitation at around l meV in the magnetically ordered state. Above the N~et temperature no crystal-field splittings were observed, but the energy spectra are characterized by a superposition of two quasielastic lines corresponding to slow and fast magnetic relaxation rates which almost differ by an order of magnitude. 1. INTRODUCTION
2. EXPERIMENTAL
AN INTERESTING CLASS among the rare earth systems are the intermediate valent compounds which are found to co-exist in two energetically equivalent electronic configurations. The most prominent example is TmSe. Recent investigations of structural, magnetic, thermal and transport properties carried out for various TmeSe single crystals established the intermediate valent character of the system, with the valence of the Tm ion varying between + 3 for Tmo.sTSe and + 2.7 for Tm~.osSe [l]. Thus, by varying the chemical composition, one can directly compare physical properties of TmSe in the "normal" trivalent state and in various intermediate valent states. In this letter we present inelastic neutron scattering measurements of the dynamical susceptibilities above and below the N4el temperature TN ~ 3 K for trivalent Tmo.sTSe and intermediate valent Tmo.~Se. The measurements have been performed for the same singlecrystalline samples used in [1]. So far the dynamical susceptibility of TmSe has only been measured for polycrystalline material [2, 3]. Because of the large homogeneity range of TmSe and the sensitive dependence of its valence upon the stoichiometric composition it is obvious that TmSe is physically better defined in the form of a small single crystal than in the form of a large polycrystalline specimen. In fact our dynamical susceptibility data obtained for Tmo.~Se are partly in contrast to the results of [2, 3].
The inelastic neutron scattering measurements were performed for single-crystalline samples of Tmo.sTSe and Tmo.99Se on a triple-axis spectrometer at Wtirenlingen. The measurements were carried out in the neutron energy-loss configuration for scattering vectors along the three symmetry directions with the analyzer energy kept fixed at 14.96 meV. A pyrolithic graphite filter was used to reduce higher-order contamination. Since the sample volumes were rather small (approximately 0.03 cm3), the experiments were performed with maximum beam focusing, i.e. a doubly bent graphite monochromator and a horizontally bent graphite analyzer [4] was used. 3. RESULTS FOR TRIVALENT Tmo.sTSe Energy spectra of neutrons scattered from Tmo.s7Se in the paramagnetic state are shown in Fig. 1. At 10 K there is a broad inelastic line at around 4 meV, which becomes less pronounced when the temperature is increased. Measurements as a function of the scattering vector Q confirmed the magnetic origin of the inelastic scattering, thus it can be interpreted in terms of crystalfield transitions. The Tm 3+ ions in Tmo.sTSe experience a cubic point symmetry. For the polar axis along the cube edge, the crystal-field Hamiltonian is given by ~ e t =- B,( o ° + 5(9~) + B6(0 ° - 21()~), (1) where the B, are the crystal-field parameters and the 0 F are operator equivalents [5]. It is customary to parametrize equation (I) in the following way [6] : 101 1
1012
TmSe STUDIED BY INELASTIC NEUTRON SCATTERING
I
!
.
.
.
.
.
.~4-=:
.
Vol. 40, No. 11
sufficient details to determine the crystal-field parameters directly. Therefore a least-squares fitting procedure based on the cross-section formula [7]
......
t
x I{rnt Jj_in)12~(En--E,~ - - h e ) ,
0
5
10 15 [meVl
Fig. 1. Energy spectra of neutrons scattered from Tm0.87Se at Q = 2~r/a (0.97, 0.97, 0.97) in the paramagnetic state. The lines are the results of the leastsquares fitting procedure as explained in the text. The top of the figure shows the resulting crystal-field level scheme. The allowed transitions are denoted by arrows. i
I
. ~
Tmo87 Se
/
\ \o
D O t.)
%
/
//
xx
x200
~
/
,
5
I
10 ~to [meVl
(4)
where X denotes the molecular-field parameter. We have determined X from the N~el temperature and calculated the molecular-field spectra for the three parameter sets mentioned above. The calculations based on the crystalfield parameters o f scheme I essentially predict two inelastic lines at 4 and 8 meV with an intensity ratio of 0.5, which is consistent with the experimental data. The calculations based on schemes II and tti cannot explain the observed energy spectrum. Thus we conclude that the crystal-field parameters of Tmo.svSe are
T= 15K 2
was applied, where F(Q) is the form factor, E n and t n) are the eigenvalues and eigenfunctions of the Hamiltonian (i), and J.I. iS the component of the total angular momentum operator perpendicular to the scattering vector. In the fitting procedure the parameters varied were W, x, and a linewidth parameter 7 (assuming Gaussian lineshapes). The following three parameter sets were found to be in agreement with the experimental data: W = 0.06 meV, x = -- 0. I (I); W = 0.09 meV, x = 0.4 (II); I/¢ = -- 0.06 meV, x = -- 0.2 (III). However, none of these schemes can definitely be favoured. For all schemes the linewidth turned out to be independent of temperature within the error limits (3' ~ 7 meV). A typical energy spectrum observed in the ordered state is shown in Fig. 2. There is a resolved line peaking at 4 meV with a pronounced shoulder at around 8 meV. In molecular-field theory the Hamiltonian of a rare earth system is given by = ~Ccf -- (gt.~B)2X ( j ) . j ,
i
(3)
B4 = (-- 1.0 "2--0.1) x l0 -4 meV,
J 15
B 6 --- (7.0 +- 0.2) x I0 -6 meV. This parameter set yields the triplet l~(st) as ground state, and the excited states are 1'3, 1-'4, ["b I'(52), and Y'2 in order of increasing energy with an overall crystal-field splitting o f 16 meV. This is in contrast to the crystalfield parameters known for the thulium monopnictides [8] which have the non-magnetic F1 as ground state.
Fig. 2. Energy spectrum of neutrons scattered from Tmo.sTSe at Q = 27r/a (0.95, 0.95, 0.95) and T = 1.5 K. The lines denote Gaussian fits to the experimental data. B4F4 = Wx, B6F6 = W(I - - I x ] ) , which means that by varying the parameter x in the range -- 1 ~< x ~< 1 the entire ratio o f fourth- to sixthorder crystal-field strength may be covered, The energy spectra o f Fig. i do not contain
(2) 4. RESULTS FOR INTERMEDIATE VALENT Tmo.99Se A typical energy spectrum measured for intermediate valent Tmo.99Se in the paramagnetic state is shown in Fig. 3. It differs from the analogous spectra observed
Vol. 40, No. 11
Tmog9Se
Tmo99Se 2! ~
i
T = 10K
' .....
.~
T= 15K
I°3i ii !
O
L
[ ..........
L
o
I L
t
0
1013
TmSe STUDIED BY INELASTIC NEUTRON SCATTERING
•
__
t
5 10 "ha) [meVl
[
5 "h~ [meV]
-g
Fig. 4. Ener~' spectrum of neutrons scattered from Tmo.99Se at Q = 27r/a (0, 0.95, 0.95) at T = 1.5 K. The line is drawn as a guide to the eye.
t
15
Fig. 3. Energy spectrum o f neutrons scattered from Tmo.99Se at Q = 27r/a (0.97, 0.97, 0.97) and T = 10K. The lines are the results of the least-squares fitting procedure as explained in the text.
to the observed energy spectrum are shown in Fig. 3; the corresponding linewidths (half width at half maximum) corrected for instrumental resolution are F~ = 0.6 ± 0.3meV, P~ = 4 + - t m e V ,
for trivalent Tmo.sTSe (see Fig. 1) in the sense that there is almost no structure in the inelastic part of the spectrum, but the major part of the magnetic scattering contribution is condensed into the elastic region giving rise to a quasielastic line. Its width is a direct measure of the magnetic relaxation rates, i.e. the lifetimes of the 4flevels, and is generally obtained by fitting a Lorentzian to the experimental data. However, we did not succeed in fitting a single Lorentzian to the data of Fig. 3. Inspection of the data rather suggests that the quasietastic scattering consists of a superposition of two lines with very different linewidths. In fact the presence of two quasielastic lines has been predicted for intermediate valent Tm compounds [9] and is due to the fact that the Hund's rule ground states of both Tm 3÷ and Tm z÷ are magnetic. Thus we have interpreted the observed energy spectrum in terms of a general crosssection formula
d'fzdca"" t - e x p [ - ~ ) j
x(Q,c~),
(51
where the first term is the detailed balance factor and the second term is the dynamical susceptibility which for the actual problem may be described by
x(O,
= F(Q) Izrr (h~) = + L
+ ;" ~o)z + (r;)~j.
and for the intensity ratio we obtained I+/[ - = 0.2 -+ 0.1, in reasonable agreement with tile values predicted in the high temperature limit [9]: F~/FT = 15, I+/I- = 0.09. There is also agreement between the observed PT and the value given in [2, 3]. The linewidths are related to the magnetic relaxation rates by +
2h
r~ = ~ ,
(7)
Vi
thus we obtain a slow relaxation rate z~" = 2.2 -+ 1.1 psec and a fast relaxation rate r~ = 0.33 ± 0.08 psec. Figure 4 shows an energy spectrum for Tmo.99Se in the ordered state. Again the spectrum does not exhibit much inelastic structure. There is a pronounced shoulder o f the elastic line at around 1 meV corresponding to an excitation of a spin wave which could not be completely resolved in the present experiments. This line was also observed in experiments on polycrystaltine material [2, 3]; however, our measurements give no evidence for another inelastic line at around 10 meV as described in [2, 31. Instead we observe an appreciable amount o f quasielastic scattering reminiscent of the fast relaxation rate as clearly demonstrated by FN. 4. 5. CONCLUSION
(FD ~
(6)
The results of least-squares fitting equations (5) and (6)
We have presented an inelastic neutron scattering study of TmeSe single crystals with the aim to compare the dynamical susceptibilities for trivalent Tmo.svSe and intermediate valent Tmo.~Se. The most important result is that we have not observed crystal-field excitations in
1014
TmSe STUDIED BY INELASTIC NEUTRON SCATTERING
intermediate valent TmSe. At present there is considerable controversy about the applicability of the crystalfield concept in intermediate valent systems. In two recent publications [3, 10] it is claimed that crystal-field splittings have been observed. The observations for TmSe [3] are not supported by our measurements. For the system Ceo.9.cLacTho.l [t0] the rather large uncertainty about the actual valence imposes caution with respect to the interpretation of the observed spectra. It is Likely that, e.g. the polycrystatline sample of Ceo: Lao.2Tho. t used in [ I01 (among other compositions) still contains trivalent cerium ions giving rise to the observed crystal-field transition, since its valence range is reported to be 3.t -+ 0.I. Thus in our opinion the existence of crystal-field excitations in intermediate valent systems has not been reliably demonstrated. What is needed are experiments on small single-crystalline samples with homogeneous stoichiometric composition and consequently well defined valence. Acknowledgement - The authors are grateful to E. Kaldis for the growth and chemical analysis of the singIe crystals.
Vol. 40, No. I t
REFERENCES 1.
B. Batlo~. H.R. Ott. E. Kaldis, W. Th6ni & P. Wachter, Phys. Rev. BI9, 247 (1979). 2. M. Loewenhaupt & E. Holland-Moritz, J. Magn. Magn. Mater. 9, 50 (t 978), 3. E. Hotland-Moritz & M. Loewenhaupt, J. de PfLvs. 40, C5-359 (1979). 4. W. Biihrer, R. BiJh.rer,A. tsacson, M. Koch & R. Thut, Nuct. Instr. and Meth. 179,259 (1981). 5. K.W.H. Stevens, Proc. Phys. Soc. A65,209 (1952). 6. K.R. Lea, M.J.M. Leask&W.P. Wolf, J. Chem. Phys. Solids 23, 1381 (1962). 7. P.G. de Gennes, Magnetism, Vol. 3, p. I t 5. Academic Press, New York and London (1969). 8. H.L. Davis & H.A. Mook, Magnetism and Magnetic Materials - 1973, p. 1068. AIP Conf. Proc. No. 18, Part 2. 9. E. MtiUer-Hartmann, Electron Correlation and Magnetism in Narrow Band Systems, Vol. 29, p. 178, Springer Series in Solid State Sciences (1981). 10. B.H. Grier, S.M. Shapiro, C.F. Majkrzak & R.D. Parks, Phys. Rev. Lett. 45, 666 (1980).
0038-1098/81/47 I011-04502.00/0
A COMPARISON OF THE DYNAMICAL SUSCEPTIBILITY OF TRWALENT AND INTERMEDIATE VALENT TmSe STUDIED BY INELASTIC NEUTRON SCATTERING A. Furrer and W. BShrer Institut ftir Reaktortechnik, Eidgen6ssische Technische Hochschule Ziirich, CH-5303 WiJrenlingen, Switzerland and P. Wachter Laboratorium ftir Festk6rperphysik, ETH-H6nggerberg, CH-8093 Ztirich, Switzerland
(Received 23 August 1981 by A.R. Miederna) The inelastic neutron scattering technique has been used to measure the dynamical susceptibilities of trivalent and intermediate valent TmSe. The experiments have been performed for single-crystalline samples above and below the antiferromagnetic ordering temperatures. From the excitation spectra observed for trivalent Tmo.s~Se we have derived the crystal-field level scheme which yields a magnetic triplet ground state. For intermediate valent Tmo.~oSe there is a single dispersionless spin excitation at around l meV in the magnetically ordered state. Above the N~et temperature no crystal-field splittings were observed, but the energy spectra are characterized by a superposition of two quasielastic lines corresponding to slow and fast magnetic relaxation rates which almost differ by an order of magnitude. 1. INTRODUCTION
2. EXPERIMENTAL
AN INTERESTING CLASS among the rare earth systems are the intermediate valent compounds which are found to co-exist in two energetically equivalent electronic configurations. The most prominent example is TmSe. Recent investigations of structural, magnetic, thermal and transport properties carried out for various TmeSe single crystals established the intermediate valent character of the system, with the valence of the Tm ion varying between + 3 for Tmo.sTSe and + 2.7 for Tm~.osSe [l]. Thus, by varying the chemical composition, one can directly compare physical properties of TmSe in the "normal" trivalent state and in various intermediate valent states. In this letter we present inelastic neutron scattering measurements of the dynamical susceptibilities above and below the N4el temperature TN ~ 3 K for trivalent Tmo.sTSe and intermediate valent Tmo.~Se. The measurements have been performed for the same singlecrystalline samples used in [1]. So far the dynamical susceptibility of TmSe has only been measured for polycrystalline material [2, 3]. Because of the large homogeneity range of TmSe and the sensitive dependence of its valence upon the stoichiometric composition it is obvious that TmSe is physically better defined in the form of a small single crystal than in the form of a large polycrystalline specimen. In fact our dynamical susceptibility data obtained for Tmo.~Se are partly in contrast to the results of [2, 3].
The inelastic neutron scattering measurements were performed for single-crystalline samples of Tmo.sTSe and Tmo.99Se on a triple-axis spectrometer at Wtirenlingen. The measurements were carried out in the neutron energy-loss configuration for scattering vectors along the three symmetry directions with the analyzer energy kept fixed at 14.96 meV. A pyrolithic graphite filter was used to reduce higher-order contamination. Since the sample volumes were rather small (approximately 0.03 cm3), the experiments were performed with maximum beam focusing, i.e. a doubly bent graphite monochromator and a horizontally bent graphite analyzer [4] was used. 3. RESULTS FOR TRIVALENT Tmo.sTSe Energy spectra of neutrons scattered from Tmo.s7Se in the paramagnetic state are shown in Fig. 1. At 10 K there is a broad inelastic line at around 4 meV, which becomes less pronounced when the temperature is increased. Measurements as a function of the scattering vector Q confirmed the magnetic origin of the inelastic scattering, thus it can be interpreted in terms of crystalfield transitions. The Tm 3+ ions in Tmo.sTSe experience a cubic point symmetry. For the polar axis along the cube edge, the crystal-field Hamiltonian is given by ~ e t =- B,( o ° + 5(9~) + B6(0 ° - 21()~), (1) where the B, are the crystal-field parameters and the 0 F are operator equivalents [5]. It is customary to parametrize equation (I) in the following way [6] : 101 1
1012
TmSe STUDIED BY INELASTIC NEUTRON SCATTERING
I
!
.
.
.
.
.
.~4-=:
.
Vol. 40, No. 11
sufficient details to determine the crystal-field parameters directly. Therefore a least-squares fitting procedure based on the cross-section formula [7]
......
t
x I{rnt Jj_in)12~(En--E,~ - - h e ) ,
0
5
10 15 [meVl
Fig. 1. Energy spectra of neutrons scattered from Tm0.87Se at Q = 2~r/a (0.97, 0.97, 0.97) in the paramagnetic state. The lines are the results of the leastsquares fitting procedure as explained in the text. The top of the figure shows the resulting crystal-field level scheme. The allowed transitions are denoted by arrows. i
I
. ~
Tmo87 Se
/
\ \o
D O t.)
%
/
//
xx
x200
~
/
,
5
I
10 ~to [meVl
(4)
where X denotes the molecular-field parameter. We have determined X from the N~el temperature and calculated the molecular-field spectra for the three parameter sets mentioned above. The calculations based on the crystalfield parameters o f scheme I essentially predict two inelastic lines at 4 and 8 meV with an intensity ratio of 0.5, which is consistent with the experimental data. The calculations based on schemes II and tti cannot explain the observed energy spectrum. Thus we conclude that the crystal-field parameters of Tmo.svSe are
T= 15K 2
was applied, where F(Q) is the form factor, E n and t n) are the eigenvalues and eigenfunctions of the Hamiltonian (i), and J.I. iS the component of the total angular momentum operator perpendicular to the scattering vector. In the fitting procedure the parameters varied were W, x, and a linewidth parameter 7 (assuming Gaussian lineshapes). The following three parameter sets were found to be in agreement with the experimental data: W = 0.06 meV, x = -- 0. I (I); W = 0.09 meV, x = 0.4 (II); I/¢ = -- 0.06 meV, x = -- 0.2 (III). However, none of these schemes can definitely be favoured. For all schemes the linewidth turned out to be independent of temperature within the error limits (3' ~ 7 meV). A typical energy spectrum observed in the ordered state is shown in Fig. 2. There is a resolved line peaking at 4 meV with a pronounced shoulder at around 8 meV. In molecular-field theory the Hamiltonian of a rare earth system is given by = ~Ccf -- (gt.~B)2X ( j ) . j ,
i
(3)
B4 = (-- 1.0 "2--0.1) x l0 -4 meV,
J 15
B 6 --- (7.0 +- 0.2) x I0 -6 meV. This parameter set yields the triplet l~(st) as ground state, and the excited states are 1'3, 1-'4, ["b I'(52), and Y'2 in order of increasing energy with an overall crystal-field splitting o f 16 meV. This is in contrast to the crystalfield parameters known for the thulium monopnictides [8] which have the non-magnetic F1 as ground state.
Fig. 2. Energy spectrum of neutrons scattered from Tmo.sTSe at Q = 27r/a (0.95, 0.95, 0.95) and T = 1.5 K. The lines denote Gaussian fits to the experimental data. B4F4 = Wx, B6F6 = W(I - - I x ] ) , which means that by varying the parameter x in the range -- 1 ~< x ~< 1 the entire ratio o f fourth- to sixthorder crystal-field strength may be covered, The energy spectra o f Fig. i do not contain
(2) 4. RESULTS FOR INTERMEDIATE VALENT Tmo.99Se A typical energy spectrum measured for intermediate valent Tmo.99Se in the paramagnetic state is shown in Fig. 3. It differs from the analogous spectra observed
Vol. 40, No. 11
Tmog9Se
Tmo99Se 2! ~
i
T = 10K
' .....
.~
T= 15K
I°3i ii !
O
L
[ ..........
L
o
I L
t
0
1013
TmSe STUDIED BY INELASTIC NEUTRON SCATTERING
•
__
t
5 10 "ha) [meVl
[
5 "h~ [meV]
-g
Fig. 4. Ener~' spectrum of neutrons scattered from Tmo.99Se at Q = 27r/a (0, 0.95, 0.95) at T = 1.5 K. The line is drawn as a guide to the eye.
t
15
Fig. 3. Energy spectrum o f neutrons scattered from Tmo.99Se at Q = 27r/a (0.97, 0.97, 0.97) and T = 10K. The lines are the results of the least-squares fitting procedure as explained in the text.
to the observed energy spectrum are shown in Fig. 3; the corresponding linewidths (half width at half maximum) corrected for instrumental resolution are F~ = 0.6 ± 0.3meV, P~ = 4 + - t m e V ,
for trivalent Tmo.sTSe (see Fig. 1) in the sense that there is almost no structure in the inelastic part of the spectrum, but the major part of the magnetic scattering contribution is condensed into the elastic region giving rise to a quasielastic line. Its width is a direct measure of the magnetic relaxation rates, i.e. the lifetimes of the 4flevels, and is generally obtained by fitting a Lorentzian to the experimental data. However, we did not succeed in fitting a single Lorentzian to the data of Fig. 3. Inspection of the data rather suggests that the quasietastic scattering consists of a superposition of two lines with very different linewidths. In fact the presence of two quasielastic lines has been predicted for intermediate valent Tm compounds [9] and is due to the fact that the Hund's rule ground states of both Tm 3÷ and Tm z÷ are magnetic. Thus we have interpreted the observed energy spectrum in terms of a general crosssection formula
d'fzdca"" t - e x p [ - ~ ) j
x(Q,c~),
(51
where the first term is the detailed balance factor and the second term is the dynamical susceptibility which for the actual problem may be described by
x(O,
= F(Q) Izrr (h~) = + L
+ ;" ~o)z + (r;)~j.
and for the intensity ratio we obtained I+/[ - = 0.2 -+ 0.1, in reasonable agreement with tile values predicted in the high temperature limit [9]: F~/FT = 15, I+/I- = 0.09. There is also agreement between the observed PT and the value given in [2, 3]. The linewidths are related to the magnetic relaxation rates by +
2h
r~ = ~ ,
(7)
Vi
thus we obtain a slow relaxation rate z~" = 2.2 -+ 1.1 psec and a fast relaxation rate r~ = 0.33 ± 0.08 psec. Figure 4 shows an energy spectrum for Tmo.99Se in the ordered state. Again the spectrum does not exhibit much inelastic structure. There is a pronounced shoulder o f the elastic line at around 1 meV corresponding to an excitation of a spin wave which could not be completely resolved in the present experiments. This line was also observed in experiments on polycrystaltine material [2, 3]; however, our measurements give no evidence for another inelastic line at around 10 meV as described in [2, 31. Instead we observe an appreciable amount o f quasielastic scattering reminiscent of the fast relaxation rate as clearly demonstrated by FN. 4. 5. CONCLUSION
(FD ~
(6)
The results of least-squares fitting equations (5) and (6)
We have presented an inelastic neutron scattering study of TmeSe single crystals with the aim to compare the dynamical susceptibilities for trivalent Tmo.svSe and intermediate valent Tmo.~Se. The most important result is that we have not observed crystal-field excitations in
1014
TmSe STUDIED BY INELASTIC NEUTRON SCATTERING
intermediate valent TmSe. At present there is considerable controversy about the applicability of the crystalfield concept in intermediate valent systems. In two recent publications [3, 10] it is claimed that crystal-field splittings have been observed. The observations for TmSe [3] are not supported by our measurements. For the system Ceo.9.cLacTho.l [t0] the rather large uncertainty about the actual valence imposes caution with respect to the interpretation of the observed spectra. It is Likely that, e.g. the polycrystatline sample of Ceo: Lao.2Tho. t used in [ I01 (among other compositions) still contains trivalent cerium ions giving rise to the observed crystal-field transition, since its valence range is reported to be 3.t -+ 0.I. Thus in our opinion the existence of crystal-field excitations in intermediate valent systems has not been reliably demonstrated. What is needed are experiments on small single-crystalline samples with homogeneous stoichiometric composition and consequently well defined valence. Acknowledgement - The authors are grateful to E. Kaldis for the growth and chemical analysis of the singIe crystals.
Vol. 40, No. I t
REFERENCES 1.
B. Batlo~. H.R. Ott. E. Kaldis, W. Th6ni & P. Wachter, Phys. Rev. BI9, 247 (1979). 2. M. Loewenhaupt & E. Holland-Moritz, J. Magn. Magn. Mater. 9, 50 (t 978), 3. E. Hotland-Moritz & M. Loewenhaupt, J. de PfLvs. 40, C5-359 (1979). 4. W. Biihrer, R. BiJh.rer,A. tsacson, M. Koch & R. Thut, Nuct. Instr. and Meth. 179,259 (1981). 5. K.W.H. Stevens, Proc. Phys. Soc. A65,209 (1952). 6. K.R. Lea, M.J.M. Leask&W.P. Wolf, J. Chem. Phys. Solids 23, 1381 (1962). 7. P.G. de Gennes, Magnetism, Vol. 3, p. I t 5. Academic Press, New York and London (1969). 8. H.L. Davis & H.A. Mook, Magnetism and Magnetic Materials - 1973, p. 1068. AIP Conf. Proc. No. 18, Part 2. 9. E. MtiUer-Hartmann, Electron Correlation and Magnetism in Narrow Band Systems, Vol. 29, p. 178, Springer Series in Solid State Sciences (1981). 10. B.H. Grier, S.M. Shapiro, C.F. Majkrzak & R.D. Parks, Phys. Rev. Lett. 45, 666 (1980).