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Raman scattering on intermediate valent TmSe
Solid State Communications, Vol. 32, pp. 573—576. Pergamon Press Ltd. 1979. Printed in Great Britain. RAMAN SCATTERING ON INTERMEDIATE VALENT TmSe A. Treindi and P. Wachter Laboratonum für Festkorperphysik, ETH Zurich, 8093 Zurich, Switzerland (Received 11 June 1979 by A.R. Miedema) Defect induced first order resonance Raman spectra have been measured on cleaved single crystals of intermediate valent Tm~Se, where the Tm to Sc ratio x varied between 0.87 and 1.05. A softening of the zone boundary LO phonons linear in the degree of valence mixing was observed. On polished samples an additional scattering peak at 60 cm~was found. Its intensity varies with stoichiometry concomitant with the degree ofvalence mixing and it disappears in the trivalent Tm~87Se.
IN THE FIELD of rare earth (RE) compounds with intermediate valence much interest is focused presently on TmSe showing unique features in this class of materials. Recent investigations of structural, magnetic, thermal and transport properties of the system Tm~Se (where x denotesmixed the Tm to Secharacter ratio) established homogeneously valent of TrnSe, awith the valence of the Tm ions varying between + 3 in Tm 087Se and + 2.72 in Tm1 ~Se [1]. 13 of Tm2~ The twoofelectronic 4f and 4f125d Tm3~are configurations degenerate in energy at EF and form a hybridized new ground state. Interconfiguration fluctuations (ICF) are assumed to occur when this ground state is perturbed by either temperature or external excitations. Such a valence fluctuation can be expected to couple strongly to the longitudinal phonons because of the large difference in the ionic radii of Tm2~ and Tm3~.The material also exhibits an anomalously high static compressibility [1]. In this letter we report experimental results of our Raman investigation on Tm~Se with the same crystals which have been investigated in reference 1. In Table 1 we give the stoichiometry, lattice constant and average valence of the samples. The selection rules forbidding first order Raman scattering in f.c.c. crystals are lifted by the vacancies present in both cation and anion sublattices,3 with in their concentration varying between 7 x 1020 cm Tm 3 in Tm 1 0Se and 4 x l021 cm 0 87Se. The measured Raman spectra represent a weighted phonon density of states, as has been found in all metallic RE monochalcogenides investigated until now [2—4]. The measurements were done using our standard Raman setup with back scattering configuration (180° or oblique incidence); the samples were cleaved from single crystals and have been kept in He gas. Some of the samples have been polished to reduce the high
amount of background scattering from the imperfect cleavage surfaces. The general features of the experimental phonon spectra can be seen in Fig. 1(a) showing the room ternperature spectrum polished Tm0order 87Se.scattering The bands 1 areofdue to a first probelow cm by examining the Stokes to anti.Stokes cess as 220 verified ratio and their temperature dependence. There is a striking similarity between the spectra of Tm0 87Se and GdSe [3]. Accordingly we identify an acoustical band between 60 and 110 cmt, whereby the main contribution to the scattering amplitude comes from the high density of states of the TA and LA phonon branches at the zone boundary. We assign the band around 140cm’ to the TO branch and the band around 190 cm~to the LO branch with its peak corresponding to the phonons from the boundary of the BZ. This interpretation is also supported by measurements on TrnS (very similar to GdS [2, 3]), from where the band frequencies can be extrapolated to trivalent Tm 0 87Se according to the anion mass ratio. The scattering intensity depends on the defect concentration; in the cleaved samples of Tm~Se especially the A .band intensity is reduced by a factor of 6 on going from x = 0.87 to x = 1.0, whereas the intensity of the optic bands (see Fig. 2) is much less sensitive to the chemical remarkable feature of the spectracomposition. shown in Fig.The 2 ismost the decrease of the LO(L) frequency by varying x between 0.87 and 1.05. Lowering the temperature down to about 10 K did not reveal any additional phenomena. According to a qualitative polarization analysis the fully symmetric A ig scattering component is increasing with x. Polishing the samples leads to more depolarized spectra. In the spectra of polished samples (Fig. 1) the scattering intensity is generally higher than in cleaved samples. A surprising feature of these spectra is a peak located at 60 cm~,the
573
574
RAMAN SCATTERING ON INTERMEDIATE VALENT TmSe
Vol. 32, No.7
Table 1. Ciystallographic and valence data of the investigated samples of Tm~Sc (from reference 1) Tm to Se ratio Lattice constant (A) Valence n as deduced from a0
0.87 5.628 +3 190
0.97 5.662
wLo(L)[cm]
1.0 5.705
+ 2.89 181 ±2
±2
+2.75 178
1.05 5.7 15 + 2.72 176 ±2
±2
TO a)
-
I
TO HI’-
-
Tm
Se
087
LO
b)
-
_______
.
Tm09 Se
HTm 10 Se
a)
300 K
Tm087Se
>-
___
c
...
(I)
z.
~
...Tm095e
..
-••.~
-.
W -
T~
d
Tm~~Se
—
Tm105Se U
-
20
100 Frequency
shift
200 (cm*
Fig. 1. Room temperature Raman spectra of mechanically polished Tm~Se.Intensity is normalized on contents of upper 400 of 512 channels. intensity of which is strongly correlated with the stoichiometry of the compound. To make this correlation better visible we have normalized in Fig. 1 the integrated intensity. Variation of the temperature down to 10K has no effect on the position or width (FWHM 10 cm~)of this first order peak. In integer trivalent GdSe and LaSe, serving as a reference material, we have never observed a similar feature, comparing as well polished and cleaved crystals or variation in stoichiometry [3]. However, in Tm~Se the stoichiometry variation yields the unique possibility to change the degree of valence mixing in the same compound3~ [1]. ionsThus and it Tm0 is this 87Secomposition contains only which integer is in valent Tm similar to GdSe or LaSe. Significantly the all respects 60 cm’ peak is absent in cleaved or polished samples of this composition.
Tm105Se
(J)
120
160
FREQUENCY
200
SHIFT
cm~
Fig. 2. TO and LO Raman bands of cleaved samples of Tm~Se(x = 0.87, 0.97, 1.0 and 1.05) at room temperature. Laser wavelength Sl4nm, symmetry component (XX). The change in intermediate valence goes concomitant with the variation of stoichiometry (see Table 1) and the 60 cm~peak grows with increasing valence mixing. Since this peak has not been found in cleaved samples of any composition (though it would be difficult to be observed there due to the high scattering background at this low frequency) we conclude that it is surface induced and the connection with intermediate valence is probably indirect via the anomalously high compressibility of these materials [1]. In these extremely soft compounds polishing of the surface than encountered induces a much usually. larger Theirregularity observed peak of the could lattice represent a local mode from this disturbed surface region. On the other hand, the energy of this peak has the right order of magnitude expected for fluctuation
Vol. 32, No.7
RAMAN SCATTERING ON INTERMEDIATE VALENT TmSe
575
When we relate the LO-frequency to the volume of the ~
Gd
0 85Se
Fig. 3. Peak position of the LO band of cleaved Tm~Se, of GdSe and of LaSe versus lattice constant. The straight line is an extrapolation to the hypothetical divalent TmSe. The LO(L) frequency of the divalent YbSe is calculated from the zone center frequency (170 cm_i) and an estimated LO dispersion.
unit cell we get an effective Grueneisen parameter = din ~/d ln V = 14.3, a value which clearly reflects the anomaly of the observed phonon softening. Normal 7-values are always of the order of 1 when the change of volume is due to real or chemical pressure (change of substituents) without associated electronic transitions. 2~Se to experimentally the hypotheticalknown Tm (a = For 5.94an A)extrapolation we refer to the Yb2~Se.Its LO(L)-frequency is calculated from the LO(I’) value of w = 170 cm~[9] under the assumption that LO mode dispersion in YbSe is similar as in other divalent RE chalcogenides. The resulting 140 ±10 cm~ are also given in Fig. 3; apparently the LO-frequencies of the intermediate valent Tm~ Se lie well on the straight line connecting the pure di- and trivalent limiting points. When we compare the LO(L)-phonon frequencies of the integer valent Tm 0 87Se, GdSe and laSe, spanning practically the whole RE series, we realize that the change in lattice constant due to the change in ionic radius of the RE ion (lanthanide contraction) has only a small effect on the phonon frequencies. Comparing LaSe and Tm0 87Se, we get y = 3a/c~dw/da 1.4. For this comparison we can neglect the slight vanation of the atomic masses within the La series, because in the LO-phonon mode at the zone boundary only the Se ions are moving and the RE ions are at rest.
frequencies (60 cm~= 7.4 meV = 1.8 x 1012 Hz) and agrees surprisingly well with the linewidth of 7 meV of a quasielastic line in neutron scattering attributed to a fluctuation time [5]. Another possibility shall shortly be mentioned, namely an attribution to an f—d acoustic mode. In a two Fermi-liquid model [6] with heavy 4f electrons and light d electrons a coherent out of phase motion off and d electrons is possible in which the much lighter electrons screen the ions so that the ion plasrron oscillations are replaced by the LA modes [7]. In addition reflectivity measurements on TmSe in the far infrared have also revealed a anomalous peak in the optical conductivity near 7 meV photon energy [8]. However, this being the first time that such an anomaly has been observed, further experiments on other intermediate valence compounds have to be performed for better understanding. In Fig. 3 we have plotted the experimental LO(L). frequency of Tm~Seand of some integer valent RE selenides vs the lattice constant. We find for Tm~Se a linear decrease of the LO-frequency with decreasing valence [which is as usual assumed to vary linear with the lattice constant according to reference (1)] with dw/dn = 50 cm’, where ii is the valence of the Tm ions,
Therefore we conclude, that in Tm~Seit is not simply the blowing up of the lattice due to an increase in the ionic diameter of the Tm ions with decreasing valence which is responsible for the softening of the LO(L)-phonons. On the other hand it can also be excluded experimentally, that variation of stoichiometry (connected with a high defect concentration) is the reason of the observed phonon shift. In Fig. 3 we also show experimental points for Gd0 85Se and Gdi 0Se, which practically have identical LO-phonon frequencies and lattice constants. A similar variation of stoichiometry in the integer valent Gd~Swith x between 0.7 and 1.0 does also not result in a LO-frequency shift [2], and leads only to a negligible small variation of the lattice constants. We come to the conclusion, that the observed LO-phonon renormalization is mainly of electronic nature, due to the f-d hybridization in the intermedi. ate valent Tm~Seseries. In a simple model the valence mixing can be interpreted as a partial transfer of charge from the delocalized 5d.band into more localized 4f- levels, reducing the positive charge of the ion core from + 3e in Tm0 87Se to + 2.72e in Tm 105Se and thereby reducing the2 effective Coulomb force between and ions. This view is consistent withthe the Tm” fact,+ that the Se
~
~mO87~
-
—
La Se
\
•—
Tm~9Se\Tm10Se j~Tm1 \ 05 Se
\ o
\ \
S
T Tm~Se00Se
56
57
5.8
LATTICE CONSTANT
5,9
60
61
(A)
—
—
—
576
RAMAN SCATTERING ON INTERMEDIATE VALENT TmSe
Vol. 32, No.7
the phonon frequencies of the intermediate valent. crystals coincide with the interpolation line of the 2+ and 3+ integer valent compounds. It could be interpreted as the LO-phonons “seeing” a static intermediate valence,
the intermediate valent phase the TO and LO(L) peaks can no longer be separated. The observed increase of the A ig scattering component within the Tm~Se series can also be understood as a result off—d hybridization. In pure trivalent Tm0,87Se
Hereby one must assume that the LO-phonons at the zone boundary are not screened by the Sd electrons, as it is the case for integer valent compounds like GdS [2] and GdSe [3J,where the occupied part of the Sd. band and 4flevels are well separated in energy. But this static picture, where we treat the 4f and the Sd electrons separately, is13 only limitedconfigurvalue in andof4f125d the case of TmSe. Here the 4f ations are degenerate and hybridize into a new ground state. Interconfiguration fluctuations lead to drastic changes of the ion volumes and therefore couple strongly to the phonons. For symmetry reasons this coupling and
the initial states of the scattering process have mainly 5d character. The 4f partition in the initial states increases with the degree of valence mixing in Tm~Se. From Raman experiments on other RE chalcogenides it has been deduced, that the A lg scattering component is absent when the initial state are pure Sd, whereas it predominates when the Raman ground state is 4f [2]. Acknowledgements areBatlogg gratefulfor tohelpful E. Kaldis for providing the samples, We to B. discussions and to H.P. Staub for technical assistance.
the corresponding frequency renormalization is largest for LO-phonons at the boundary of the BZ with wavevectors along the (111) direction. This phonon mode is a fully symmetrical vibration of the Se ions against the Tm ions at rest, corresponding to a periodic compression of the Tm According to a theory outhned by Bennemann et aL [10, 11] this coupling leads to a softening of the LO(L)-frequency with dw N(EF), where dw is the frequency shift and N(EF) is the electronic density of states at the Fermi level. N(EF) is expected to be very large in the intermediate valence state. This theory can quantitatively explain the phonon softening in Sm-mixed valent compounds [10]. A similar calculation\ for Tm~ Se ~
would need independent experimental data for N(EF) which are missing. Using the model of Bennemann it can be deduced reversely from our measurements, that N(EF) increases linearly with the degree of valence mixing. Recent neutron scattering experiments revealed that in Sm 0,75Y0,25S the phonon softening lowers the LO branch even below the TO branch [12]. However, our Raman experiments on TmSe give only evidence that in
—
1.
2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
REFERENCES B. Batlogg, H.R. Ott, E. Kaldis, W. Thoni & P. Wachter, Phys. Rev. B19, 247 (1979); H.R. Ott, B. Batlogg, E. Kaldis & P. Wachter, /. AppL Phys. 49, 2118 (1978); B. Batlogg, E. Kaldis & H.R. Ott, Phys. Lett. 62A,P.270 (1977). E. Anastassakis, G. Güntherodt, Grunberg, M. Cardona, H. Hackfort & W. Zinn, Phys. Rev. B16, 3504 (1977). A. Treindl & P. Wachter,Phys. Lett. 64A, 147 (1977). G. Güntherodt, R. Merlin, A. Frey & M. Cardona, Solid State Commun. 27, 551 (1978). M. Lowenhaupt & E. Holland-Moritz, J. Magnetism and Magnetic Materials 9, 50 (1978). C.M. Varma, Solid State Commun. 30, 537 (1979). C.M.Varma,Rev.ModemPhys. 48, 219 (1976). B. Batlogg, Thesis ETH 1979, Phys. Rev. (to be published). J. Vitins, J. Magnetism and Magnetic Materials 5, 212 (1977). K.H. Bennemann & M. Avignon (to be published). S.K.Ghatak&K.H. Bennemann,J. Phys. F8,57l (1978). H.A. Mook, R.M. Nicklow, T. Penney, F. Holtzberg & W.M. Shafer,Phys..Rev. 18B, 2925 (1978).
IN THE FIELD of rare earth (RE) compounds with intermediate valence much interest is focused presently on TmSe showing unique features in this class of materials. Recent investigations of structural, magnetic, thermal and transport properties of the system Tm~Se (where x denotesmixed the Tm to Secharacter ratio) established homogeneously valent of TrnSe, awith the valence of the Tm ions varying between + 3 in Tm 087Se and + 2.72 in Tm1 ~Se [1]. 13 of Tm2~ The twoofelectronic 4f and 4f125d Tm3~are configurations degenerate in energy at EF and form a hybridized new ground state. Interconfiguration fluctuations (ICF) are assumed to occur when this ground state is perturbed by either temperature or external excitations. Such a valence fluctuation can be expected to couple strongly to the longitudinal phonons because of the large difference in the ionic radii of Tm2~ and Tm3~.The material also exhibits an anomalously high static compressibility [1]. In this letter we report experimental results of our Raman investigation on Tm~Se with the same crystals which have been investigated in reference 1. In Table 1 we give the stoichiometry, lattice constant and average valence of the samples. The selection rules forbidding first order Raman scattering in f.c.c. crystals are lifted by the vacancies present in both cation and anion sublattices,3 with in their concentration varying between 7 x 1020 cm Tm 3 in Tm 1 0Se and 4 x l021 cm 0 87Se. The measured Raman spectra represent a weighted phonon density of states, as has been found in all metallic RE monochalcogenides investigated until now [2—4]. The measurements were done using our standard Raman setup with back scattering configuration (180° or oblique incidence); the samples were cleaved from single crystals and have been kept in He gas. Some of the samples have been polished to reduce the high
amount of background scattering from the imperfect cleavage surfaces. The general features of the experimental phonon spectra can be seen in Fig. 1(a) showing the room ternperature spectrum polished Tm0order 87Se.scattering The bands 1 areofdue to a first probelow cm by examining the Stokes to anti.Stokes cess as 220 verified ratio and their temperature dependence. There is a striking similarity between the spectra of Tm0 87Se and GdSe [3]. Accordingly we identify an acoustical band between 60 and 110 cmt, whereby the main contribution to the scattering amplitude comes from the high density of states of the TA and LA phonon branches at the zone boundary. We assign the band around 140cm’ to the TO branch and the band around 190 cm~to the LO branch with its peak corresponding to the phonons from the boundary of the BZ. This interpretation is also supported by measurements on TrnS (very similar to GdS [2, 3]), from where the band frequencies can be extrapolated to trivalent Tm 0 87Se according to the anion mass ratio. The scattering intensity depends on the defect concentration; in the cleaved samples of Tm~Se especially the A .band intensity is reduced by a factor of 6 on going from x = 0.87 to x = 1.0, whereas the intensity of the optic bands (see Fig. 2) is much less sensitive to the chemical remarkable feature of the spectracomposition. shown in Fig.The 2 ismost the decrease of the LO(L) frequency by varying x between 0.87 and 1.05. Lowering the temperature down to about 10 K did not reveal any additional phenomena. According to a qualitative polarization analysis the fully symmetric A ig scattering component is increasing with x. Polishing the samples leads to more depolarized spectra. In the spectra of polished samples (Fig. 1) the scattering intensity is generally higher than in cleaved samples. A surprising feature of these spectra is a peak located at 60 cm~,the
573
574
RAMAN SCATTERING ON INTERMEDIATE VALENT TmSe
Vol. 32, No.7
Table 1. Ciystallographic and valence data of the investigated samples of Tm~Sc (from reference 1) Tm to Se ratio Lattice constant (A) Valence n as deduced from a0
0.87 5.628 +3 190
0.97 5.662
wLo(L)[cm]
1.0 5.705
+ 2.89 181 ±2
±2
+2.75 178
1.05 5.7 15 + 2.72 176 ±2
±2
TO a)
-
I
TO HI’-
-
Tm
Se
087
LO
b)
-
_______
.
Tm09 Se
HTm 10 Se
a)
300 K
Tm087Se
>-
___
c
...
(I)
z.
~
...Tm095e
..
-••.~
-.
W -
T~
d
Tm~~Se
—
Tm105Se U
-
20
100 Frequency
shift
200 (cm*
Fig. 1. Room temperature Raman spectra of mechanically polished Tm~Se.Intensity is normalized on contents of upper 400 of 512 channels. intensity of which is strongly correlated with the stoichiometry of the compound. To make this correlation better visible we have normalized in Fig. 1 the integrated intensity. Variation of the temperature down to 10K has no effect on the position or width (FWHM 10 cm~)of this first order peak. In integer trivalent GdSe and LaSe, serving as a reference material, we have never observed a similar feature, comparing as well polished and cleaved crystals or variation in stoichiometry [3]. However, in Tm~Se the stoichiometry variation yields the unique possibility to change the degree of valence mixing in the same compound3~ [1]. ionsThus and it Tm0 is this 87Secomposition contains only which integer is in valent Tm similar to GdSe or LaSe. Significantly the all respects 60 cm’ peak is absent in cleaved or polished samples of this composition.
Tm105Se
(J)
120
160
FREQUENCY
200
SHIFT
cm~
Fig. 2. TO and LO Raman bands of cleaved samples of Tm~Se(x = 0.87, 0.97, 1.0 and 1.05) at room temperature. Laser wavelength Sl4nm, symmetry component (XX). The change in intermediate valence goes concomitant with the variation of stoichiometry (see Table 1) and the 60 cm~peak grows with increasing valence mixing. Since this peak has not been found in cleaved samples of any composition (though it would be difficult to be observed there due to the high scattering background at this low frequency) we conclude that it is surface induced and the connection with intermediate valence is probably indirect via the anomalously high compressibility of these materials [1]. In these extremely soft compounds polishing of the surface than encountered induces a much usually. larger Theirregularity observed peak of the could lattice represent a local mode from this disturbed surface region. On the other hand, the energy of this peak has the right order of magnitude expected for fluctuation
Vol. 32, No.7
RAMAN SCATTERING ON INTERMEDIATE VALENT TmSe
575
When we relate the LO-frequency to the volume of the ~
Gd
0 85Se
Fig. 3. Peak position of the LO band of cleaved Tm~Se, of GdSe and of LaSe versus lattice constant. The straight line is an extrapolation to the hypothetical divalent TmSe. The LO(L) frequency of the divalent YbSe is calculated from the zone center frequency (170 cm_i) and an estimated LO dispersion.
unit cell we get an effective Grueneisen parameter = din ~/d ln V = 14.3, a value which clearly reflects the anomaly of the observed phonon softening. Normal 7-values are always of the order of 1 when the change of volume is due to real or chemical pressure (change of substituents) without associated electronic transitions. 2~Se to experimentally the hypotheticalknown Tm (a = For 5.94an A)extrapolation we refer to the Yb2~Se.Its LO(L)-frequency is calculated from the LO(I’) value of w = 170 cm~[9] under the assumption that LO mode dispersion in YbSe is similar as in other divalent RE chalcogenides. The resulting 140 ±10 cm~ are also given in Fig. 3; apparently the LO-frequencies of the intermediate valent Tm~ Se lie well on the straight line connecting the pure di- and trivalent limiting points. When we compare the LO(L)-phonon frequencies of the integer valent Tm 0 87Se, GdSe and laSe, spanning practically the whole RE series, we realize that the change in lattice constant due to the change in ionic radius of the RE ion (lanthanide contraction) has only a small effect on the phonon frequencies. Comparing LaSe and Tm0 87Se, we get y = 3a/c~dw/da 1.4. For this comparison we can neglect the slight vanation of the atomic masses within the La series, because in the LO-phonon mode at the zone boundary only the Se ions are moving and the RE ions are at rest.
frequencies (60 cm~= 7.4 meV = 1.8 x 1012 Hz) and agrees surprisingly well with the linewidth of 7 meV of a quasielastic line in neutron scattering attributed to a fluctuation time [5]. Another possibility shall shortly be mentioned, namely an attribution to an f—d acoustic mode. In a two Fermi-liquid model [6] with heavy 4f electrons and light d electrons a coherent out of phase motion off and d electrons is possible in which the much lighter electrons screen the ions so that the ion plasrron oscillations are replaced by the LA modes [7]. In addition reflectivity measurements on TmSe in the far infrared have also revealed a anomalous peak in the optical conductivity near 7 meV photon energy [8]. However, this being the first time that such an anomaly has been observed, further experiments on other intermediate valence compounds have to be performed for better understanding. In Fig. 3 we have plotted the experimental LO(L). frequency of Tm~Seand of some integer valent RE selenides vs the lattice constant. We find for Tm~Se a linear decrease of the LO-frequency with decreasing valence [which is as usual assumed to vary linear with the lattice constant according to reference (1)] with dw/dn = 50 cm’, where ii is the valence of the Tm ions,
Therefore we conclude, that in Tm~Seit is not simply the blowing up of the lattice due to an increase in the ionic diameter of the Tm ions with decreasing valence which is responsible for the softening of the LO(L)-phonons. On the other hand it can also be excluded experimentally, that variation of stoichiometry (connected with a high defect concentration) is the reason of the observed phonon shift. In Fig. 3 we also show experimental points for Gd0 85Se and Gdi 0Se, which practically have identical LO-phonon frequencies and lattice constants. A similar variation of stoichiometry in the integer valent Gd~Swith x between 0.7 and 1.0 does also not result in a LO-frequency shift [2], and leads only to a negligible small variation of the lattice constants. We come to the conclusion, that the observed LO-phonon renormalization is mainly of electronic nature, due to the f-d hybridization in the intermedi. ate valent Tm~Seseries. In a simple model the valence mixing can be interpreted as a partial transfer of charge from the delocalized 5d.band into more localized 4f- levels, reducing the positive charge of the ion core from + 3e in Tm0 87Se to + 2.72e in Tm 105Se and thereby reducing the2 effective Coulomb force between and ions. This view is consistent withthe the Tm” fact,+ that the Se
~
~mO87~
-
—
La Se
\
•—
Tm~9Se\Tm10Se j~Tm1 \ 05 Se
\ o
\ \
S
T Tm~Se00Se
56
57
5.8
LATTICE CONSTANT
5,9
60
61
(A)
—
—
—
576
RAMAN SCATTERING ON INTERMEDIATE VALENT TmSe
Vol. 32, No.7
the phonon frequencies of the intermediate valent. crystals coincide with the interpolation line of the 2+ and 3+ integer valent compounds. It could be interpreted as the LO-phonons “seeing” a static intermediate valence,
the intermediate valent phase the TO and LO(L) peaks can no longer be separated. The observed increase of the A ig scattering component within the Tm~Se series can also be understood as a result off—d hybridization. In pure trivalent Tm0,87Se
Hereby one must assume that the LO-phonons at the zone boundary are not screened by the Sd electrons, as it is the case for integer valent compounds like GdS [2] and GdSe [3J,where the occupied part of the Sd. band and 4flevels are well separated in energy. But this static picture, where we treat the 4f and the Sd electrons separately, is13 only limitedconfigurvalue in andof4f125d the case of TmSe. Here the 4f ations are degenerate and hybridize into a new ground state. Interconfiguration fluctuations lead to drastic changes of the ion volumes and therefore couple strongly to the phonons. For symmetry reasons this coupling and
the initial states of the scattering process have mainly 5d character. The 4f partition in the initial states increases with the degree of valence mixing in Tm~Se. From Raman experiments on other RE chalcogenides it has been deduced, that the A lg scattering component is absent when the initial state are pure Sd, whereas it predominates when the Raman ground state is 4f [2]. Acknowledgements areBatlogg gratefulfor tohelpful E. Kaldis for providing the samples, We to B. discussions and to H.P. Staub for technical assistance.
the corresponding frequency renormalization is largest for LO-phonons at the boundary of the BZ with wavevectors along the (111) direction. This phonon mode is a fully symmetrical vibration of the Se ions against the Tm ions at rest, corresponding to a periodic compression of the Tm According to a theory outhned by Bennemann et aL [10, 11] this coupling leads to a softening of the LO(L)-frequency with dw N(EF), where dw is the frequency shift and N(EF) is the electronic density of states at the Fermi level. N(EF) is expected to be very large in the intermediate valence state. This theory can quantitatively explain the phonon softening in Sm-mixed valent compounds [10]. A similar calculation\ for Tm~ Se ~
would need independent experimental data for N(EF) which are missing. Using the model of Bennemann it can be deduced reversely from our measurements, that N(EF) increases linearly with the degree of valence mixing. Recent neutron scattering experiments revealed that in Sm 0,75Y0,25S the phonon softening lowers the LO branch even below the TO branch [12]. However, our Raman experiments on TmSe give only evidence that in
—
1.
2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
REFERENCES B. Batlogg, H.R. Ott, E. Kaldis, W. Thoni & P. Wachter, Phys. Rev. B19, 247 (1979); H.R. Ott, B. Batlogg, E. Kaldis & P. Wachter, /. AppL Phys. 49, 2118 (1978); B. Batlogg, E. Kaldis & H.R. Ott, Phys. Lett. 62A,P.270 (1977). E. Anastassakis, G. Güntherodt, Grunberg, M. Cardona, H. Hackfort & W. Zinn, Phys. Rev. B16, 3504 (1977). A. Treindl & P. Wachter,Phys. Lett. 64A, 147 (1977). G. Güntherodt, R. Merlin, A. Frey & M. Cardona, Solid State Commun. 27, 551 (1978). M. Lowenhaupt & E. Holland-Moritz, J. Magnetism and Magnetic Materials 9, 50 (1978). C.M. Varma, Solid State Commun. 30, 537 (1979). C.M.Varma,Rev.ModemPhys. 48, 219 (1976). B. Batlogg, Thesis ETH 1979, Phys. Rev. (to be published). J. Vitins, J. Magnetism and Magnetic Materials 5, 212 (1977). K.H. Bennemann & M. Avignon (to be published). S.K.Ghatak&K.H. Bennemann,J. Phys. F8,57l (1978). H.A. Mook, R.M. Nicklow, T. Penney, F. Holtzberg & W.M. Shafer,Phys..Rev. 18B, 2925 (1978).