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Temperature dependence of the spectral width in the intermediate valence compound CeAl3
523—526. ~~Solid Coasnunications, Vol.36,inpp. ~~/PergamonState Press Ltd. 1980. Printed Great Britain.
TEMPERATURE DEPENDENCE OF THE SPECTRAL WIDTH IN THE INTERMEDIATE VALENCE COMPOUND CeA1 3 1~, K.H.J. Buschow~,A. Benoit~, and 3. Flouquet~ A.P. Murani~, K. Knorr a) Institut Laue—Langevin, BP 156 X, b) Institut für Physik, Univ. Mainz, c) Philips Research Lab., Eindhoven, d) Centre de Recherches sur lea Très Grenoble—Cedex, France.
38042 Grenoble—Cedex, France 6500 Mainz, RFA The Netherlands Basses Temperatures, CNRS, BP 166 X, 38042
Rece~ued4 Aaga~s.t 1980 by E.F.
‘t.tauI~
We report measurements of the quasi—elastic spectral component of the compound CeAl 3 in the temperature range 60 mK < T < 125 K. At low temperatures, below 1 K, the quasi—elastic spectral width is effectively constant but increases as Tl/2 at higher tetnperatures.One possible interpretation of this behaviour is that it reflects the transformation of the f electrons from a Fermi liquid at low temperatures to a classical liquid at higher temperatures.
2 at low resistivity temperatures.(6) y( 1620 mJ/mole K) very and the increasing Neutron as scattering T measurements have recently been reported on several interme— diate valence systems. In CePd 3 a broad quasi— elastic spectrum of half width 20 meV is observed which remains essentially tempeç~— alloys also show ture independent below 9) room temperature.’ broad quasi—elastic spectra (half width Measurements on Ce—Th~ ~ 20 meV), but upon cooling the alloys under—
Some of the rare earth metals and inter— metallic also Sm, Eu compounds and Tm often involving showCeanomalous and Yb and thermal and magnetic properties which in recent years have been classified as the intermediate valence or mixed valence beha— viour.(U In some systems the effects of intermediate valency are fairly strong, and are accompanied by anhigh unmistakably large noticeable at relatively temperatures anomaly in the lattice parameters of the systems. For example CePd 3, a well acclaimed intermediate valence system, shows an appro— ximately temperature independent suscepti— bility (a broad shallow maximum at ISO K) and has lattice parameters çg~respondingto an average valency of 3~45•~’) In other systems such as CeAI2 and CeAl~, for example, the lattice parameter anomaly is very much smaller and the physical properties of the compounds at higher temperatures are accoun— table simply in t9rms of the Kondo effect of the Ce~~+ ~ At low temperatures the compound CeAl2 orders magnetically 4) CeAI with a complex magnetic structure.( 3, on the other hand, shows a magnetic behaviour which is a scaled down 2), YbAlCu~5), and compounds many others. version of th~tobserved in the suchlow At as temperatures CePd3¼ the magnetic suscepti— biliry, for example, deviates strongly from a Curie—Weiss behaviour observed at high temperatures, goes through a broad maximum around 0.7 K~6) (as compared with 27 K for YbAlCu(5) and 150 K for CePd 2) and becomes essentially temperature inaependent 3)( as T * 0 K. Thermal expansion measurements of the compound CeAI 3 show a negative coef— ficient around the temperature of the maximum in the susceptibility ; below 300 mK the thermal expansion is negative and linear in of ‘He~ ). Other remarkable tem~er~ure as observed for low the temperature liquid phase properties of this compound include a very large linear specific heat coefficient
go a second—order structural phase transi— tion to the ct-phase. The magnetic scattering is found to persist even in this phase but the quasi—elastic spectrum is very much broader (half width ~, 70 meV). In the following we report what we believe are the first systematic measure— ments of the spectral width of the quasi— elastic scattering in an intermediate valence system over a wide—enough reduced temperature range (relative to some characteristic tem— perature Te associated with valence fluctua— tions) which permit a meaningful determina— tion of the temperature dependence of the spectral width. This is possible because the characteristic temperature T0 is low for systems investigated far thisof temperature CeA13 (~ I K) whereas sofor most the other is quite high (> 100 K) so that measurements up to several hundred degrees or more need to be made to cover the same reduced tempera— ture range. The measurements were made on the cold source time—of—flight spectrometer 1N5 at the Institute Laue—Langevin, usi~gneutrons of incident energy 3.5 meV (4.8 A), with an overall elastic energy resolution of 230 ~jeV. The temperature range covered in the measu— rements is between 60 mK and 125 K, the low 3He” dilution refrigerator temperatur~sbeing obtained by the and use the of higher the He temperatures by the use of a normal He4 cryostat. The time—of—flight spectra normalised
523
524
THE INTERMEDIATE VALENCE COMPOUND CeAI
3
relative to vanadit~standard and corrected for background (cryostat) scattering and self—shielding were converted into S(q,w) and are shown in Fig. I for one detector angle and for several representative tempe— for CeAl At low temperatures the spectra ratures. 3 show the central elastic peak as well as a quasi—elastic scattering contribu— tion which is seen only in neutron energy loss (+ ye w). As the temperature increases more to 10 symmetric K the quasi—elastic and at higher scattering temperatures becomes we
Vol. 36, No. 6
see additional, progressively increasing inelastic structure which becomes visible through up scattering of neutrons (i.e. neutron energy gain) from the higher lying 10,II). crystal field states as these become populated( We express the neutron scattering cross—section for a polycrystalline para— magnetic sample with crystal field split N(X!.~) ~— S(q,w) (I) magnetic 2c states as —d — d~dw mc 0 with
12
$=24.6°
S(q,w)a[
2(q)(a
1...eXp~_(0,kT)][x(~)1J av F 8
0f0(q,W)
n
4~ -
+ ~
~
a~f~(q,w±w~~)}
where the symbols have their usual meanings. The first term inside the curly brackets, 8
i.e. f,(q,w), represents the quasi—elastic spectral function centered about zero energy transfer and the second term is the summation over the inelastic excitations between crystal field states of the system. The constants a0, aa (ci—I,n) are the normalized temperature dependent probability factors. The solid lines in figure I are the result of fits to the data in the energy range —2.5 .~ u~2.5 meV, using Lorentzian form for the central mode spectral function f~(q,w). Over this energy range the q— variation for a given detector angle e is such that the variation of intensity through the 4f form factor F(q) is a maximum of 3 1 at
—
b)
______
7
C)
74. ‘I
10K
________________________
8
6
______
d)
C. 20K
~‘.
to aims—2.5
—~
8
e)
99~g...1~.74 .,<<~
1.24125K O.
<
2.5 meV we have achieved two
mentary TOF spectro— meter neutrons ofanother higher incident energyusing ofexperiment 12.5 meV on where crystal field exci—
.
~.
~
0 ________________________________________..
—7.5
—50
—2.5
0
2.5
c.~(meV) Fig. I
w
contribution due to crystal field states. We have verified this by carrying out a supple—
0.552
-10.0
<
a) excluded any phonon contribution which lies mainly above 10 meV and is negligible below, as seen from our measurements on a LaA13 sample and b) excluded almost completely, any inelastic
__________
8
the ends of the range, which we have ignored. A similar fitting procedure using a Gaussian form for f,(q,w) was found to give distinctly poorer fits. In limiting the range of the fit
S(q,u) vs w (with q varying) obtai— ned from the TOF spectra for the CeAl 3 sample at a series of tempe— ratures. The continuous curves represent fits to the data over the energy range — 2.5 < w < 2.5 meV using the Lorentzian form for the quasi—elastic spectral function f0(q,w). The assymmetry of the spectra is due to the detailed balance factor.
in tations energy are gain. observed both energy loss andq In Fig. 2 we show the inhalf-width r vs obtained from the least—square fits to the central quasi—elastic spectral component for the whole range of temperatures studied where the circled points for q — 0.8 are the results of fits to the constant—q data obtained using the cubic spline interpolation technique. The large scatter at low q’s is due to poorer statistics resulting from the smaller number of detectors which could be positioned at some of these low angles within a given q—resolution width. In Fig. 3 we plot the temperature ~epen— dence of the half—width for q — 0.55 A on a linear temperature scale. In the figure we also plot the same data points on a tempera—
Vol. 36, No. 6
THE INTERMEDIATE VALENCE COMPOUND CeAI
3
525
0
0
3.0
-
20
-
1.0
-
0
I
I
0.2
0.4
0.6
I
I
0.8
1.0
1)
1.2
q(~’-
The half—width r (half—width at half— height) vs q at a series of temperatures for the CeAl 3 sample obtained from the Lorentzian fits to the central mode of the spectra. The scatter among the data points give an indication of the error bars. The circled point for q — 0.8 A~ are obtained from fits to the interpolated constant—q data. The continuous curves are drawn to guide the eye.
Fig. 2
4.0 a,
3.0
= 0.55
-
Th/2 (K1t2)
2
II
0
25
4 I
I
6 I
50 T (K) half—yidth r vs
8
II
75
10
100
Fig. 3 : The T and T for q — 0.55 A~. The continuous curve through12the scale datarepresents points plotted the best on straight line through the 4 K and the T~ higher temperature points.
12
II
125
526
THE INTERMEDIATE VALENCE COMPOUND CeAI
3
ture scale proportional to Thl’2. On this plot the data points at higher temperatures (4 K upwards) lie on a reasonable straight line but the lower temperature points below ~ I K show saturation to a constant temperature— independent width. We estimate the values of a — 1/2 for the Tm power law to be accurate to within a maximum possible error of ±0.1. The existence of quasi—elastic scatte— ring and the temperature dependence of its line width in CeAl1 is puzzling. At low temperatures (T < ~O K) and for the usual exchange Hamiltonian, the quasi—elastic scattering is predominantly due to nag— netic dipole transitions within the crystaL field ground state. In a perfect 1±3/2> ground state dipole transitions are forbidden. For this reason the theoretical treatment of Becker et al. (12) on the linewidth problem can not be quantitatively applied to the present system and the strong k—f interaction may oeed to be treated using the Coqblin— Schrieffer Hamiltonian (13) which permits relaxation processes within the 1±3/2> doub— let ground state, A possible interpretation of the Tl/2 temperature dependence of the spectral width at high temperatures following a constant 4) thatis below value at low temperatures based some on the characteristic temperature T, the f dcc— prediction of Varuia(1 trons of an intermediate valence system can
be described as a Fermi liquid having a temperature independent spectral width and that above this tempera cure the Femi liqu transforms to a classical liquid with a spectral width proportional to Tl/2. Although
Vol. 36, No. 6
this description is fairly attractive and appears valid, a literal classical liquid nomenclature is riot completely satisfactory. This is because for a classical liquid the spectral shape is a Gaussian with the spectral width not only proportional to T~/2 but also increasing linearly with The q—dependence for the classical liquid, however, arises through the probability of spatial displacement of the nuclei whereas the rare earth f electrons remain localized and should therefore show the q—dependence appropriate to the 4f form factor, as observed. In summary, the riresent measurements of the quasi—elastic Spectral component of the compound CeAI3 reveal an apparently Constant spectral width below I K but which increases as TI~’2 at higher temperatures. These first observations of such a temperature dependence for an intermediate valence system are consistent with the prediction that the 4f electrons behave as a Fermi liquid at low temperatures and undergo transformation to a classical liquid type behaviour above some characteristic valence fluctuation temtera— ture. Finally we point out that the q depen—
dence of integrated intensity of the quasi the 4f1 magnetic form factor) appears (corrected almost q mdc— elastic scattering for pendent : no tendency toward ferromagnetic short range correlations is detected. We acknowledge helpful discussions with F. U. N. U.ildane. U. Sherri ngton. B. W. Southern and C.M. Varma. We have also benefited from discussions and correspondence with K.W. Becker and P. Fulde.
Re fe ronces (I) Valence Instabilities and Related
(2)
(3)
(4)
(5)
(6) (7)
(8)
Narrow—Band Phenomena, Editor: R.D. Parks (Plenum, New York 1977). W.E. Gardner, J. Penfold, T.F. Smith and I.R. Harris, J. Phys. F: Metal Phys. 2, 133 (1972). F.E. Maranzana. Phys. Rev. Lett. 25, 239 (1970). K.H.J. Buschow, H.J. Van Daal, F.E. Maranzana and P.8. Van Aken, Phys. Rev. 83, 1662 (1971). B. Barbara, G.X. Boucherle, J.L. Buevoz, M.F. Rossignol and J. Schweizer, Solid State Communication 24, 481 (1977). W.C.M. Mattens, R.A. Elenbaas and F.R. do Boor, Communications on Physics 2, 147 (1977). K. Andres. J.E. Graebner and U.R. Ott. Phys. Rev. Lett. 35, 1779 (1975). M. Ribault, A. Benoit, J. Flouquet, J. Palleau. J. Physiqiie—Lettres 40, 413 (1979). E. Holland—Merits, N. Loewenhaupt,
(9)
(10)
(II)
(12) (13) (14)
(15)
W. Schmatz and D.K. Wohlleben, I’liys. Rev. Lett. 38, 983 (1977). S.M. Shapiro, J.D. Axe, R.J. Birgeneau, L.M. Lawrence and R.D. Parks, Phys. Rev. B 16, 2225 (1977). A.P. Murani, K. Knorr and K.H.J. Buschow, in Crystal Field Effects in Metals and Alloys, Editor: A. Furrer (Plenum New York 1977), pp. 268—72. P.A. Alckseev, I.P. Sadikov, l.A. Markova, E.M. Savitskii, V.F. Terekho and 0.1). Chistyakov, Soy. Phys. Solid State 18, 1466 (1976). VU. Becker, P. Fulde and J. Keller, z. Physik B 28, 9 (197/). B. Coqblin and J.R. Schrieffer, ~‘hys. Rev. IRS 845 (1969). C.M. V~Frna, in the extended abstracts of the US—Japanese Seminar on Mixed Valence Compounds, Sendai, Japan, October 1977, and private communication. J.R.D. Copley and S.W. Lovesey, Reports on Progress in Physics 38, 461 (1975).
TEMPERATURE DEPENDENCE OF THE SPECTRAL WIDTH IN THE INTERMEDIATE VALENCE COMPOUND CeA1 3 1~, K.H.J. Buschow~,A. Benoit~, and 3. Flouquet~ A.P. Murani~, K. Knorr a) Institut Laue—Langevin, BP 156 X, b) Institut für Physik, Univ. Mainz, c) Philips Research Lab., Eindhoven, d) Centre de Recherches sur lea Très Grenoble—Cedex, France.
38042 Grenoble—Cedex, France 6500 Mainz, RFA The Netherlands Basses Temperatures, CNRS, BP 166 X, 38042
Rece~ued4 Aaga~s.t 1980 by E.F.
‘t.tauI~
We report measurements of the quasi—elastic spectral component of the compound CeAl 3 in the temperature range 60 mK < T < 125 K. At low temperatures, below 1 K, the quasi—elastic spectral width is effectively constant but increases as Tl/2 at higher tetnperatures.One possible interpretation of this behaviour is that it reflects the transformation of the f electrons from a Fermi liquid at low temperatures to a classical liquid at higher temperatures.
2 at low resistivity temperatures.(6) y( 1620 mJ/mole K) very and the increasing Neutron as scattering T measurements have recently been reported on several interme— diate valence systems. In CePd 3 a broad quasi— elastic spectrum of half width 20 meV is observed which remains essentially tempeç~— alloys also show ture independent below 9) room temperature.’ broad quasi—elastic spectra (half width Measurements on Ce—Th~ ~ 20 meV), but upon cooling the alloys under—
Some of the rare earth metals and inter— metallic also Sm, Eu compounds and Tm often involving showCeanomalous and Yb and thermal and magnetic properties which in recent years have been classified as the intermediate valence or mixed valence beha— viour.(U In some systems the effects of intermediate valency are fairly strong, and are accompanied by anhigh unmistakably large noticeable at relatively temperatures anomaly in the lattice parameters of the systems. For example CePd 3, a well acclaimed intermediate valence system, shows an appro— ximately temperature independent suscepti— bility (a broad shallow maximum at ISO K) and has lattice parameters çg~respondingto an average valency of 3~45•~’) In other systems such as CeAI2 and CeAl~, for example, the lattice parameter anomaly is very much smaller and the physical properties of the compounds at higher temperatures are accoun— table simply in t9rms of the Kondo effect of the Ce~~+ ~ At low temperatures the compound CeAl2 orders magnetically 4) CeAI with a complex magnetic structure.( 3, on the other hand, shows a magnetic behaviour which is a scaled down 2), YbAlCu~5), and compounds many others. version of th~tobserved in the suchlow At as temperatures CePd3¼ the magnetic suscepti— biliry, for example, deviates strongly from a Curie—Weiss behaviour observed at high temperatures, goes through a broad maximum around 0.7 K~6) (as compared with 27 K for YbAlCu(5) and 150 K for CePd 2) and becomes essentially temperature inaependent 3)( as T * 0 K. Thermal expansion measurements of the compound CeAI 3 show a negative coef— ficient around the temperature of the maximum in the susceptibility ; below 300 mK the thermal expansion is negative and linear in of ‘He~ ). Other remarkable tem~er~ure as observed for low the temperature liquid phase properties of this compound include a very large linear specific heat coefficient
go a second—order structural phase transi— tion to the ct-phase. The magnetic scattering is found to persist even in this phase but the quasi—elastic spectrum is very much broader (half width ~, 70 meV). In the following we report what we believe are the first systematic measure— ments of the spectral width of the quasi— elastic scattering in an intermediate valence system over a wide—enough reduced temperature range (relative to some characteristic tem— perature Te associated with valence fluctua— tions) which permit a meaningful determina— tion of the temperature dependence of the spectral width. This is possible because the characteristic temperature T0 is low for systems investigated far thisof temperature CeA13 (~ I K) whereas sofor most the other is quite high (> 100 K) so that measurements up to several hundred degrees or more need to be made to cover the same reduced tempera— ture range. The measurements were made on the cold source time—of—flight spectrometer 1N5 at the Institute Laue—Langevin, usi~gneutrons of incident energy 3.5 meV (4.8 A), with an overall elastic energy resolution of 230 ~jeV. The temperature range covered in the measu— rements is between 60 mK and 125 K, the low 3He” dilution refrigerator temperatur~sbeing obtained by the and use the of higher the He temperatures by the use of a normal He4 cryostat. The time—of—flight spectra normalised
523
524
THE INTERMEDIATE VALENCE COMPOUND CeAI
3
relative to vanadit~standard and corrected for background (cryostat) scattering and self—shielding were converted into S(q,w) and are shown in Fig. I for one detector angle and for several representative tempe— for CeAl At low temperatures the spectra ratures. 3 show the central elastic peak as well as a quasi—elastic scattering contribu— tion which is seen only in neutron energy loss (+ ye w). As the temperature increases more to 10 symmetric K the quasi—elastic and at higher scattering temperatures becomes we
Vol. 36, No. 6
see additional, progressively increasing inelastic structure which becomes visible through up scattering of neutrons (i.e. neutron energy gain) from the higher lying 10,II). crystal field states as these become populated( We express the neutron scattering cross—section for a polycrystalline para— magnetic sample with crystal field split N(X!.~) ~— S(q,w) (I) magnetic 2c states as —d — d~dw mc 0 with
12
$=24.6°
S(q,w)a[
2(q)(a
1...eXp~_(0,kT)][x(~)1J av F 8
0f0(q,W)
n
4~ -
+ ~
~
a~f~(q,w±w~~)}
where the symbols have their usual meanings. The first term inside the curly brackets, 8
i.e. f,(q,w), represents the quasi—elastic spectral function centered about zero energy transfer and the second term is the summation over the inelastic excitations between crystal field states of the system. The constants a0, aa (ci—I,n) are the normalized temperature dependent probability factors. The solid lines in figure I are the result of fits to the data in the energy range —2.5 .~ u~2.5 meV, using Lorentzian form for the central mode spectral function f~(q,w). Over this energy range the q— variation for a given detector angle e is such that the variation of intensity through the 4f form factor F(q) is a maximum of 3 1 at
—
b)
______
7
C)
74. ‘I
10K
________________________
8
6
______
d)
C. 20K
~‘.
to aims—2.5
—~
8
e)
99~g...1~.74 .,<<~
1.24125K O.
<
2.5 meV we have achieved two
mentary TOF spectro— meter neutrons ofanother higher incident energyusing ofexperiment 12.5 meV on where crystal field exci—
.
~.
~
0 ________________________________________..
—7.5
—50
—2.5
0
2.5
c.~(meV) Fig. I
w
contribution due to crystal field states. We have verified this by carrying out a supple—
0.552
-10.0
<
a) excluded any phonon contribution which lies mainly above 10 meV and is negligible below, as seen from our measurements on a LaA13 sample and b) excluded almost completely, any inelastic
__________
8
the ends of the range, which we have ignored. A similar fitting procedure using a Gaussian form for f,(q,w) was found to give distinctly poorer fits. In limiting the range of the fit
S(q,u) vs w (with q varying) obtai— ned from the TOF spectra for the CeAl 3 sample at a series of tempe— ratures. The continuous curves represent fits to the data over the energy range — 2.5 < w < 2.5 meV using the Lorentzian form for the quasi—elastic spectral function f0(q,w). The assymmetry of the spectra is due to the detailed balance factor.
in tations energy are gain. observed both energy loss andq In Fig. 2 we show the inhalf-width r vs obtained from the least—square fits to the central quasi—elastic spectral component for the whole range of temperatures studied where the circled points for q — 0.8 are the results of fits to the constant—q data obtained using the cubic spline interpolation technique. The large scatter at low q’s is due to poorer statistics resulting from the smaller number of detectors which could be positioned at some of these low angles within a given q—resolution width. In Fig. 3 we plot the temperature ~epen— dence of the half—width for q — 0.55 A on a linear temperature scale. In the figure we also plot the same data points on a tempera—
Vol. 36, No. 6
THE INTERMEDIATE VALENCE COMPOUND CeAI
3
525
0
0
3.0
-
20
-
1.0
-
0
I
I
0.2
0.4
0.6
I
I
0.8
1.0
1)
1.2
q(~’-
The half—width r (half—width at half— height) vs q at a series of temperatures for the CeAl 3 sample obtained from the Lorentzian fits to the central mode of the spectra. The scatter among the data points give an indication of the error bars. The circled point for q — 0.8 A~ are obtained from fits to the interpolated constant—q data. The continuous curves are drawn to guide the eye.
Fig. 2
4.0 a,
3.0
= 0.55
-
Th/2 (K1t2)
2
II
0
25
4 I
I
6 I
50 T (K) half—yidth r vs
8
II
75
10
100
Fig. 3 : The T and T for q — 0.55 A~. The continuous curve through12the scale datarepresents points plotted the best on straight line through the 4 K and the T~ higher temperature points.
12
II
125
526
THE INTERMEDIATE VALENCE COMPOUND CeAI
3
ture scale proportional to Thl’2. On this plot the data points at higher temperatures (4 K upwards) lie on a reasonable straight line but the lower temperature points below ~ I K show saturation to a constant temperature— independent width. We estimate the values of a — 1/2 for the Tm power law to be accurate to within a maximum possible error of ±0.1. The existence of quasi—elastic scatte— ring and the temperature dependence of its line width in CeAl1 is puzzling. At low temperatures (T < ~O K) and for the usual exchange Hamiltonian, the quasi—elastic scattering is predominantly due to nag— netic dipole transitions within the crystaL field ground state. In a perfect 1±3/2> ground state dipole transitions are forbidden. For this reason the theoretical treatment of Becker et al. (12) on the linewidth problem can not be quantitatively applied to the present system and the strong k—f interaction may oeed to be treated using the Coqblin— Schrieffer Hamiltonian (13) which permits relaxation processes within the 1±3/2> doub— let ground state, A possible interpretation of the Tl/2 temperature dependence of the spectral width at high temperatures following a constant 4) thatis below value at low temperatures based some on the characteristic temperature T, the f dcc— prediction of Varuia(1 trons of an intermediate valence system can
be described as a Fermi liquid having a temperature independent spectral width and that above this tempera cure the Femi liqu transforms to a classical liquid with a spectral width proportional to Tl/2. Although
Vol. 36, No. 6
this description is fairly attractive and appears valid, a literal classical liquid nomenclature is riot completely satisfactory. This is because for a classical liquid the spectral shape is a Gaussian with the spectral width not only proportional to T~/2 but also increasing linearly with The q—dependence for the classical liquid, however, arises through the probability of spatial displacement of the nuclei whereas the rare earth f electrons remain localized and should therefore show the q—dependence appropriate to the 4f form factor, as observed. In summary, the riresent measurements of the quasi—elastic Spectral component of the compound CeAI3 reveal an apparently Constant spectral width below I K but which increases as TI~’2 at higher temperatures. These first observations of such a temperature dependence for an intermediate valence system are consistent with the prediction that the 4f electrons behave as a Fermi liquid at low temperatures and undergo transformation to a classical liquid type behaviour above some characteristic valence fluctuation temtera— ture. Finally we point out that the q depen—
dence of integrated intensity of the quasi the 4f1 magnetic form factor) appears (corrected almost q mdc— elastic scattering for pendent : no tendency toward ferromagnetic short range correlations is detected. We acknowledge helpful discussions with F. U. N. U.ildane. U. Sherri ngton. B. W. Southern and C.M. Varma. We have also benefited from discussions and correspondence with K.W. Becker and P. Fulde.
Re fe ronces (I) Valence Instabilities and Related
(2)
(3)
(4)
(5)
(6) (7)
(8)
Narrow—Band Phenomena, Editor: R.D. Parks (Plenum, New York 1977). W.E. Gardner, J. Penfold, T.F. Smith and I.R. Harris, J. Phys. F: Metal Phys. 2, 133 (1972). F.E. Maranzana. Phys. Rev. Lett. 25, 239 (1970). K.H.J. Buschow, H.J. Van Daal, F.E. Maranzana and P.8. Van Aken, Phys. Rev. 83, 1662 (1971). B. Barbara, G.X. Boucherle, J.L. Buevoz, M.F. Rossignol and J. Schweizer, Solid State Communication 24, 481 (1977). W.C.M. Mattens, R.A. Elenbaas and F.R. do Boor, Communications on Physics 2, 147 (1977). K. Andres. J.E. Graebner and U.R. Ott. Phys. Rev. Lett. 35, 1779 (1975). M. Ribault, A. Benoit, J. Flouquet, J. Palleau. J. Physiqiie—Lettres 40, 413 (1979). E. Holland—Merits, N. Loewenhaupt,
(9)
(10)
(II)
(12) (13) (14)
(15)
W. Schmatz and D.K. Wohlleben, I’liys. Rev. Lett. 38, 983 (1977). S.M. Shapiro, J.D. Axe, R.J. Birgeneau, L.M. Lawrence and R.D. Parks, Phys. Rev. B 16, 2225 (1977). A.P. Murani, K. Knorr and K.H.J. Buschow, in Crystal Field Effects in Metals and Alloys, Editor: A. Furrer (Plenum New York 1977), pp. 268—72. P.A. Alckseev, I.P. Sadikov, l.A. Markova, E.M. Savitskii, V.F. Terekho and 0.1). Chistyakov, Soy. Phys. Solid State 18, 1466 (1976). VU. Becker, P. Fulde and J. Keller, z. Physik B 28, 9 (197/). B. Coqblin and J.R. Schrieffer, ~‘hys. Rev. IRS 845 (1969). C.M. V~Frna, in the extended abstracts of the US—Japanese Seminar on Mixed Valence Compounds, Sendai, Japan, October 1977, and private communication. J.R.D. Copley and S.W. Lovesey, Reports on Progress in Physics 38, 461 (1975).