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Photoemission investigation on the temperature dependence of the valence fluctuations in Yb3Si5
Journal
of the Less-Common
Metals,
120
(1986)
Ll - L5
Ll
Letter Photoemission investigation on the temperature dependence of the valence fluctuations in Yb3Si5 I. ABBATI, Istituto
L. BRAICOVICH,
di Fisica
A. IANDELLI, Istituto (Received
de1 Politecnico, G. L. OLCESE
di Chimica
Fisica
B. De MICHELIS, 20133
Milan0
A. FASANA
and M. SANCROTTI
(Italy)
and A. PALENZONA
dell’Universitti,
16132
Genova
(Italy)
March 4,1986)
The study of valence fluctuations is of paramount importance in the physical metallurgy of rare earths compounds [ 11. In this connection some of us have reported in a previous paper [2] the valence fluctuations of ytterbium in silicon-rich compounds based on lattice parameters and magnetic susceptibilities. These methods although extremely useful are rather indirect; a better analysis can be made by combining these results with those of a more direct method such as photoemission spectroscopy. The aim of the present letter is to report the results of X-ray photoemission research on Yb3Si5 as a function of the temperature and to discuss them in conjunction with the magnetic susceptibility data of ref. 2. This is the first analysis of this kind for the Yb-Si system and gives a direct insight into the valence fluctuation mechanism. Among silicon-rich compounds Yb& has been chosen because it is the only system having a well-defined stoichiometry [2] in which all ytterbium ions are in equivalent sites. The other systems are YbS& _-x (x = 0.2), i.e. defect compounds. The results were obtained using Mg Ka radiation (hv = 1253.6 eV) and with a cylindrical mirror analyser in a system whose lay-out is given in ref. 3. The samples characterized by X-ray diffraction were prepared as described in detail in ref. 2 and were cleaned in the vacuum chamber of the apparatus (base pressure, 7 X lo-” Ton) by scraping with a diamond file. The sample holder could be resistively heated and cooled by circulating liquid nitrogen. The data were acquired using a computer to optimize the signal-to-noise ratio. X-ray photoemission has a rather high sensitivity to the bulk so that the surface gives only a minor effect; this is very convenient since the surface ytterbium is divalent owing to the lower coordination [ 41. The X-ray photoemission spectrum of Yb3Si5 at room temperature is given in Fig. 1; the dominant structures come from the 4f electrons and are the final state contributions from the ionization of the Yb2+ and of the Yb3+ configurations [5]. The two contributions are identified in the figure. 0022-5088/86/$3.50
0 Elsevier
Sequoia/Printed
in The Netherlands
L2
Fig. 1. X-ray photoem~~~on spectrum (Mg Kcu) of Yk@is P3 = v - 2 values as a function of temperature (upper part).
flower part] and measured
The homogeneous (dynamic) mixed valence behaviour is apparent from the presence of the 2+ and 3+ configurations in a system in which all ytterbium sites are equivalent. The relative weight of the 3+ and 2+ configurations are given by the areas of the two multiplets corrected for the occupaucy. An accurate fitting, described in ref. 4, of a wider set of photoemission spectra taken using synchrotron radiation and using X-rays including the present ones gives the bulk valence u = 2.52 + 0.02. The dependence of u on the temperature is defined even better than the absolute values; we can give meaning to variations with the temperature as low as 2% 3% because of the very good statistics (each spec~m was counted for several hours in each run). The temperature dependence of the weight p3 (p3 is defined as tt - 2) is given in Fig, 1 (upper part). Values at temperatures above 375 K are not given because of surface segregation of divalent ytterbium. Already at 375 K some segregation takes place (about l/3 of a monolayer) and a minor correction to the data has been made. The argument runs along the following lines. (i) The relevant qualitative result is the weak dependence of the valence on the temperature. A first approximate analysis in a Curie-Weiss scheme of the su~e~~b~~ty data of ref. 2 gave a decrease in p3 of around 49% from 300 K to 100 K while the present, more direct, observation gives a variation of around 16%. The weak temperature dependence shows that thermal fluctuations are not the only origin of the valence fluctuations. This has been explained for other compounds [6,7] as the consequence of the quantum fluctuations between the 2+ and the 3+ conf~g~ations which contribute a term independent of the temperature. (ii) The relative rok of thermal and quantum ~u~tuations can be discussed on the basis of the joint analysis of the susceptibilities (from ref. 2) and the measured p3 values, by using the interconfiguration fluctuation
L3
model [6, 71 which has been used successfully in this temperature range for Y bPd& [ 81. In this model the weight of the 3+ configuration is 8
p3 = 8 + exp(E,fT*) and the susceptibility per mole of ytterbium is given by x(T) =A$
A _ V4.54L(.B12 3K B
where EB is the Boltzmann constant, pg the Bohr magneton and N the Avogadro number. In these expressions E, is the separation in energy between the ionic states of the 4fr3 and 4f14 configurations, and the Boltzmann factor is calculated in accordance with
Here T is the temperature and I’ is a measure of the mixing width of the two configurations and introduces a term in the partion function, independent of the temperature, Le. it takes into account the qu~tum fluctuations between the two ~onfig~ations. The value I”/Ex = Tf is often called the characteristic fluctuation temperature and is a measure of the mixing width. The simultaneous fitting of x and p3 uersus temperature by means of the above expressions is much more restrictive than the fitting of only one of the two curves and gives reliable information on the parameters E, and Z’f. We have defined two regions around the measured x from ref. 2 and around the present p3, which account for the experimental uncertainties and we have made a computer fit. A rough evaluation of the Pauli paramagnetism shows that it is negligible beyond any doubt; this has been done both using the free electron model and using the analog to a related system (Si-Ca) for which the electron density of states are available [ 91. The values of x and p3, or even x alone, cannot be fitted with E, and Tf independent of temperature. In effect these parameters must depend on the temperature [ 71; in particular in a more expanded system (at higher temperate) the 2+ config~ation tends to be more favourable than in a compressed system. As the simplest approx~ation we have assumed that the temperature dependence is attributed only to E,, which is taken to be linearly dependent on T*. We have found a satisfactory fit (Fig. 2) with the following values: Tf = 167 K, E,(lOO) = 450 K and E,(300) = 700 K. (iii) Tf is higher than in the ternary silicides investigated previously. In the present case Tf = 167 K against 100 K in YbPd2Siz [8] and 110 K in YbCuzSi2 [6] ; this value comes from a new fitting of the measurements of ref. 8 where the data were fitted with a different tentative definition of T*. The increase in Tf with respect to the above ternary silicides is relevant to physical metallurgy; the increase in the silicon content of the molecule together with the known fact that the bond with silicon is among the
I
0
I
I
”
”
500
TI”KI
I
1000
Fig. 2. Fitting of the measured pa (upper part) and x (lower part) with the interconfiguration fluctuation model.
strongest [ 10 J suggests that the overlap integrals between nearby atoms can increase with a corresponding increase in the mixing width, i.e. the importance of quantum. fluctuations with respect to thermal fluctuations. There is a good qualitative connection between the metallurgical trends and the spectroscopy of 4f states. The values of E, agree with those of related compounds. Our fitting of the x of YbAl, [6] gives E,(300) = 660 K. The E, values are in the range (2 - 10 kcal (g atom Yb))‘) [lo, 111. In conclusion a combined discussion of the mixed valence measured versus temperature with photoemission and of the magnetic susceptibility suggest the great relevance of quantum fluctuations in originating the homogeneous (dynamic) mixed valence in Yb3Si5. We have also shown a satisfactory connection between physical metallurgy and the trends of quantum fluctuations in the silicides investigated to date. This work has been supported by the Consiglio Nazionale delle Ricerche (CNR) of Italy through the Progetto Finalizzato Chimica Fine e Secondaria. The photoemission equipment was made available by the GNSM of the CNR and by the CISM of the Ministero della Publica Istruzione. 1 L. M. Falicov, W. Hanke and M. P. Maple (eds.), Valence Fluctuations in Solids, North Holland, Amsterdam, 1981. 2 A. Iandelli, A. Palenzona and G. L. Olcese, J. Less-Common Met., 64 (1979) 213. 3 I. Abbati, L. Braicovich, A. Fasana, C. M. Bertoni, F. Manghi and C. Calandra, Phys. Rev. B, 23 (1981) 6448. 4 I. Abbati, L. Braicovich, U. de1 Pennino, A. Iandelli, G. L. Olcese, A. Palenzona, C. Carbone, J. Nogami, J. J. Yeh and I. Lindau, Physica B, 130 (1985) 141. 5 M. Campagna, G. K. Wertheim and Y. A. Baer, in L. Ley and M. Cardona (eds.), Photoemission in Solids II, Springer, Berlin, 1979, p. 217.
L5 6 B. C. Sales and D. K. Wohlleben, Phys. Rev. Lett., 35 (1975) 1240. 7 W. Franz, F. Steglich, W. Zell, D. Wohlleben and F. Pobell, Phys. Rev. Lett., 45 (1980) 64. 8 E. V. Sampathkumaran, J. N. Frank, G. Kalkowski, G. Kaindl, M. Domke and G. Wortmann, Phys. Rev. B, 29 (1984) 5702. 9 J. H. Weaver, A. Franciosi and V. L. Moruzzi, Phys. Rev. B, 29 (1984) 3293. 10 A. Iandelli and A. Palenzona, in K. A. Gschneidner, Jr., and L. Eyring (eds.), Handbook on the Physics and Chemistry of Rare Earths, Vol. 2, North-Holland, Amsterdam, 1979, p. 1. 11 K. A. Gschneidner, Jr., J. Less-Common Met., 17 (1969) 13.
of the Less-Common
Metals,
120
(1986)
Ll - L5
Ll
Letter Photoemission investigation on the temperature dependence of the valence fluctuations in Yb3Si5 I. ABBATI, Istituto
L. BRAICOVICH,
di Fisica
A. IANDELLI, Istituto (Received
de1 Politecnico, G. L. OLCESE
di Chimica
Fisica
B. De MICHELIS, 20133
Milan0
A. FASANA
and M. SANCROTTI
(Italy)
and A. PALENZONA
dell’Universitti,
16132
Genova
(Italy)
March 4,1986)
The study of valence fluctuations is of paramount importance in the physical metallurgy of rare earths compounds [ 11. In this connection some of us have reported in a previous paper [2] the valence fluctuations of ytterbium in silicon-rich compounds based on lattice parameters and magnetic susceptibilities. These methods although extremely useful are rather indirect; a better analysis can be made by combining these results with those of a more direct method such as photoemission spectroscopy. The aim of the present letter is to report the results of X-ray photoemission research on Yb3Si5 as a function of the temperature and to discuss them in conjunction with the magnetic susceptibility data of ref. 2. This is the first analysis of this kind for the Yb-Si system and gives a direct insight into the valence fluctuation mechanism. Among silicon-rich compounds Yb& has been chosen because it is the only system having a well-defined stoichiometry [2] in which all ytterbium ions are in equivalent sites. The other systems are YbS& _-x (x = 0.2), i.e. defect compounds. The results were obtained using Mg Ka radiation (hv = 1253.6 eV) and with a cylindrical mirror analyser in a system whose lay-out is given in ref. 3. The samples characterized by X-ray diffraction were prepared as described in detail in ref. 2 and were cleaned in the vacuum chamber of the apparatus (base pressure, 7 X lo-” Ton) by scraping with a diamond file. The sample holder could be resistively heated and cooled by circulating liquid nitrogen. The data were acquired using a computer to optimize the signal-to-noise ratio. X-ray photoemission has a rather high sensitivity to the bulk so that the surface gives only a minor effect; this is very convenient since the surface ytterbium is divalent owing to the lower coordination [ 41. The X-ray photoemission spectrum of Yb3Si5 at room temperature is given in Fig. 1; the dominant structures come from the 4f electrons and are the final state contributions from the ionization of the Yb2+ and of the Yb3+ configurations [5]. The two contributions are identified in the figure. 0022-5088/86/$3.50
0 Elsevier
Sequoia/Printed
in The Netherlands
L2
Fig. 1. X-ray photoem~~~on spectrum (Mg Kcu) of Yk@is P3 = v - 2 values as a function of temperature (upper part).
flower part] and measured
The homogeneous (dynamic) mixed valence behaviour is apparent from the presence of the 2+ and 3+ configurations in a system in which all ytterbium sites are equivalent. The relative weight of the 3+ and 2+ configurations are given by the areas of the two multiplets corrected for the occupaucy. An accurate fitting, described in ref. 4, of a wider set of photoemission spectra taken using synchrotron radiation and using X-rays including the present ones gives the bulk valence u = 2.52 + 0.02. The dependence of u on the temperature is defined even better than the absolute values; we can give meaning to variations with the temperature as low as 2% 3% because of the very good statistics (each spec~m was counted for several hours in each run). The temperature dependence of the weight p3 (p3 is defined as tt - 2) is given in Fig, 1 (upper part). Values at temperatures above 375 K are not given because of surface segregation of divalent ytterbium. Already at 375 K some segregation takes place (about l/3 of a monolayer) and a minor correction to the data has been made. The argument runs along the following lines. (i) The relevant qualitative result is the weak dependence of the valence on the temperature. A first approximate analysis in a Curie-Weiss scheme of the su~e~~b~~ty data of ref. 2 gave a decrease in p3 of around 49% from 300 K to 100 K while the present, more direct, observation gives a variation of around 16%. The weak temperature dependence shows that thermal fluctuations are not the only origin of the valence fluctuations. This has been explained for other compounds [6,7] as the consequence of the quantum fluctuations between the 2+ and the 3+ conf~g~ations which contribute a term independent of the temperature. (ii) The relative rok of thermal and quantum ~u~tuations can be discussed on the basis of the joint analysis of the susceptibilities (from ref. 2) and the measured p3 values, by using the interconfiguration fluctuation
L3
model [6, 71 which has been used successfully in this temperature range for Y bPd& [ 81. In this model the weight of the 3+ configuration is 8
p3 = 8 + exp(E,fT*) and the susceptibility per mole of ytterbium is given by x(T) =A$
A _ V4.54L(.B12 3K B
where EB is the Boltzmann constant, pg the Bohr magneton and N the Avogadro number. In these expressions E, is the separation in energy between the ionic states of the 4fr3 and 4f14 configurations, and the Boltzmann factor is calculated in accordance with
Here T is the temperature and I’ is a measure of the mixing width of the two configurations and introduces a term in the partion function, independent of the temperature, Le. it takes into account the qu~tum fluctuations between the two ~onfig~ations. The value I”/Ex = Tf is often called the characteristic fluctuation temperature and is a measure of the mixing width. The simultaneous fitting of x and p3 uersus temperature by means of the above expressions is much more restrictive than the fitting of only one of the two curves and gives reliable information on the parameters E, and Z’f. We have defined two regions around the measured x from ref. 2 and around the present p3, which account for the experimental uncertainties and we have made a computer fit. A rough evaluation of the Pauli paramagnetism shows that it is negligible beyond any doubt; this has been done both using the free electron model and using the analog to a related system (Si-Ca) for which the electron density of states are available [ 91. The values of x and p3, or even x alone, cannot be fitted with E, and Tf independent of temperature. In effect these parameters must depend on the temperature [ 71; in particular in a more expanded system (at higher temperate) the 2+ config~ation tends to be more favourable than in a compressed system. As the simplest approx~ation we have assumed that the temperature dependence is attributed only to E,, which is taken to be linearly dependent on T*. We have found a satisfactory fit (Fig. 2) with the following values: Tf = 167 K, E,(lOO) = 450 K and E,(300) = 700 K. (iii) Tf is higher than in the ternary silicides investigated previously. In the present case Tf = 167 K against 100 K in YbPd2Siz [8] and 110 K in YbCuzSi2 [6] ; this value comes from a new fitting of the measurements of ref. 8 where the data were fitted with a different tentative definition of T*. The increase in Tf with respect to the above ternary silicides is relevant to physical metallurgy; the increase in the silicon content of the molecule together with the known fact that the bond with silicon is among the
I
0
I
I
”
”
500
TI”KI
I
1000
Fig. 2. Fitting of the measured pa (upper part) and x (lower part) with the interconfiguration fluctuation model.
strongest [ 10 J suggests that the overlap integrals between nearby atoms can increase with a corresponding increase in the mixing width, i.e. the importance of quantum. fluctuations with respect to thermal fluctuations. There is a good qualitative connection between the metallurgical trends and the spectroscopy of 4f states. The values of E, agree with those of related compounds. Our fitting of the x of YbAl, [6] gives E,(300) = 660 K. The E, values are in the range (2 - 10 kcal (g atom Yb))‘) [lo, 111. In conclusion a combined discussion of the mixed valence measured versus temperature with photoemission and of the magnetic susceptibility suggest the great relevance of quantum fluctuations in originating the homogeneous (dynamic) mixed valence in Yb3Si5. We have also shown a satisfactory connection between physical metallurgy and the trends of quantum fluctuations in the silicides investigated to date. This work has been supported by the Consiglio Nazionale delle Ricerche (CNR) of Italy through the Progetto Finalizzato Chimica Fine e Secondaria. The photoemission equipment was made available by the GNSM of the CNR and by the CISM of the Ministero della Publica Istruzione. 1 L. M. Falicov, W. Hanke and M. P. Maple (eds.), Valence Fluctuations in Solids, North Holland, Amsterdam, 1981. 2 A. Iandelli, A. Palenzona and G. L. Olcese, J. Less-Common Met., 64 (1979) 213. 3 I. Abbati, L. Braicovich, A. Fasana, C. M. Bertoni, F. Manghi and C. Calandra, Phys. Rev. B, 23 (1981) 6448. 4 I. Abbati, L. Braicovich, U. de1 Pennino, A. Iandelli, G. L. Olcese, A. Palenzona, C. Carbone, J. Nogami, J. J. Yeh and I. Lindau, Physica B, 130 (1985) 141. 5 M. Campagna, G. K. Wertheim and Y. A. Baer, in L. Ley and M. Cardona (eds.), Photoemission in Solids II, Springer, Berlin, 1979, p. 217.
L5 6 B. C. Sales and D. K. Wohlleben, Phys. Rev. Lett., 35 (1975) 1240. 7 W. Franz, F. Steglich, W. Zell, D. Wohlleben and F. Pobell, Phys. Rev. Lett., 45 (1980) 64. 8 E. V. Sampathkumaran, J. N. Frank, G. Kalkowski, G. Kaindl, M. Domke and G. Wortmann, Phys. Rev. B, 29 (1984) 5702. 9 J. H. Weaver, A. Franciosi and V. L. Moruzzi, Phys. Rev. B, 29 (1984) 3293. 10 A. Iandelli and A. Palenzona, in K. A. Gschneidner, Jr., and L. Eyring (eds.), Handbook on the Physics and Chemistry of Rare Earths, Vol. 2, North-Holland, Amsterdam, 1979, p. 1. 11 K. A. Gschneidner, Jr., J. Less-Common Met., 17 (1969) 13.