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4f photoemission spectra of light rare earths
Journal of Magnetism and Magnetic North-Holland, Amsterdam
4f PHOTOEMISSION Peter
Materials
271
478~48 (1985) 271-273
SPECTRA
OF LIGHT RARE EARTHS
S. RISEBOROUGH
Department of Physics, Polytechnic Institute of New York, 333 Jay Sireei, Brooklyn, NY 11201, USA
The 4f derived valence band photoemission spectra of Ce, Pr and Nd compounds are interpreted in terms of the presence of two types of screening channels; localized screening and diffuse screening. The effect of hybridization on these screening channels is investigated.
1. Introduction The valence band photoemission spectra of Ce and its compounds has long been the subject of considerable controversy [l-lo]. The controversy surrounds the interpretation of two peaks; one at the Fermi level and another approximately 2.5 eV below it. Recently, both resonant [3-51 and angle resolved photoemission [6] experiments have conclusively shown that both these peaks correspond to the emission of f electrons. Several mechanism [7-91 have been invoked to interpret the data, and are all equivocal. Recent photoemission experiments [11,12] on Pr and Nd compounds have shed new light onto the subject. These experiments suggest that the bi-modal 4f spectra is common to all of the light rare earth elements, completely independent of their magnetic properties. The experimental data [ll], displayed in fig. 1, shows the 4f spectra for an isomorphic series of rare earth compounds. In the Ce compounds, one peak lies at the Fermi level and the other is 2.5 eV below it. As one scans the series, from Ce through Pr to Nd, the two peaks move to lower energies but still maintain their energy separation at the constant value of 2.5 eV. Also one notices that the relative intensities of the two peaks change. The intensity of the peak closest to the Fermi energy diminishes across the series, there is a concomitant increase in intensity of the peak at lower binding energies. We shall show how the Anderson model [13], together with the screening mechanism for the f hole [8], can describe the experimental results.
0304-8853/85/$03.30 (North-Holland
Physics
0 Elsevier Science Publishers Publishing
Division)
B.V.
a
0
4 ENERGY
BELOW
EF (eV)
Fig. 1. The 4f derived valence band photoemission spectra the series RERu, in which RE = Ce, Pr and Nd [ll].
for
212
P.S. Riseborough
/ 4j spectra of light rare earfhs
2. Calculations and results
criterion
for bound
The f derived valence band photoemission spectra can be calculated directly from the f electron Green’s function. We shall treat the f-d Coulomb interaction via perturbation theory, and for mixed valence Ce, we shall use the unperturbed propagators as found from the l/N expansion method [14]. The lowest order, nontrivial, contribution of U, to the f electron self-energy is depicted diagramatically in fig. 2. In this lowest order process, the f hole in the final state of the photoemission causes the electrons in the conduction band to be redistributed amongst the d band states, through the formation of the electron-hole pairs. The perturbation theory results are expected to converge for the light rare earth metals, since the 12 fold conduction band contains at most only two or three electrons, and thus is approaching the low density limit. Treglia et al. [15] have shown that in such a limit, the method may reproduce results for all two peaked photoemission spectra of Pd, and is in agreement with the results of more exact calculations [16]. We calculate the self-energy due to the f-d screening interaction, in the local approximation [15]. Since both the hybridization [7] and the f-d screening interaction [8] can result in a bound state being split off from the bottom of the conduction band, we find that the criterion for bound state formation [17] is considerably reduced by the hybridization. If we model the quantity
lr31+
z+(y2/W)(2P-1/2P+l)a(P)
as
,,:s:l,{w2-~2}p+1’2>
W>(wl
i
b,
(2.1)
W
this expression p reflects the k dependence of the hybridization V(k).) then we find the approximate
(In
Fig. 2. The 4f hole in the final state interacts with the conduction band, producing a rearrangement of the d band occupation.
1
state formation
as
1+(ww)-(~2/w)~(P)
1 ’
where
a(p)
= 22Pf3(
p + 1)
qP+:)qP+;) r(2P
+
3)
(2.2)
In this expression V is a measure of the hybridization, 2 W is the conduction band width and E, is the position of the 4f level measured from the bottom of the conduction band. We see that when the f level is close to the lower band edge, the hybridization enhances the probability that a d band bound state is formed in the photoemission final state. Under such circumstances, the final state of the photoemission process may involve two possible screening channels [S]. In one screening channel, the bound state is filled by a conduction electron, and the d band continuum is filled up to the Fermi level. The wave function of the bound state is closely localized around the final state 4f hole. This is the local screening channel. In the other case, the bound state remains empty and the d band continuum is filled up to the Fermi level. The 4f hole is screened by the electrons in the itinerant conduction band states. This is the diffuse screening channel. From conservation of energy considerations one finds that the kinetic energy of the photo emitted electron corresponding to the locally screened final state is higher than that associated with the diffusely screened final state. The energy difference is that required to take an electron out of the bound state below the bottom of the conduction band and place it at the fermi level. This energy separation, must therefore be slightly greater than the width of the occupied portion of the lanthanide conduction band. Since joint photoemission/BIS experiments [18] suggests that for all the lanthanide metals this energy is roughly 2 to 3 eV, we expect that the energy separation between the two 4f peaks should remain almost constant at this value. The relative intensity of the two peaks is governed by the overlap between the initial state and the two final states of the photoemission process. For large hybridization, the locally screeened peak dominates, while for smaller hybridization the diffusely screened peak becomes intenser. In this way, we correlate the experimentally observed decrease in the intensity of the locally screened peak [ll] with the decrease of hybridization, presumably caused by the lanthanide contraction.
P.S. Riseborough / 4f spectra of light rare earths
References [l] B. Johansson, Phil. Mag. 30 (1977) 469. [?] L.I. Johansson, J.W. Allen, T. Gustafsson, I. Lindau and S.B. Hagstrom, Solid State Commun. 28 (1978) 53. [3] A. Franciosi, J.H. Weaver, N. Martensson and M. Croft, Phys. Rev. B24 (1982) 3651. [4] N. Martensson, B. Reihl and R.D. Parks, Solid State Commun. 41 (1982) 573. (51 R.D. Parks, N. Martensson and B. Reihl, in: Valence Instabilities eds. P. Wachter and H. Boppart (North-Holland, Amsterdam, 1982). [6] D.M. Wieliczka, C.G. Olson and D.W. Lynch, Phys. Rev. B29 (1983) 3028. [7] 0. Gunnarsson and K. Schonhammer, Phys. Rev. Lett 50 (1983) 604; Phys. Rev. B28 (1983) 4220. [P] S.H. Liu and K.M. Ho, Phys. Rev. B26 (1982) 7052, B28 (1983) 4220.
273
[9] M. Schliiter and C.M. Varma, Helvetica Phys. Acta 56 (1983) 147. (lo] P.S. Riseborough, to be published. [ll] R.D. Parks, S. Raaen, M.L. den Boer, Y.S. Chang and G.P. Williams, Phys. Rev. Lett. 52 (1984) 2176. [12] D.M. Wieliczka, C.G. Olson and D.W. Lynch, Phys. Rev. Lett. 52 (1984) 2180. [13] P.W. Anderson, Phys. Rev. 124 (1961) 41. [14] F.C. Zhang and T.K. Lee, Phys. Rev. B28 (1983) 33. [15] G. Treglia, F. Ducastelle and D. Spanjaard, J. de Phys. 41 (1980) 281, 43 (1982) 341. 1161 L.C. Davis and L.A. Feldkamp, Solid State Commun. 34 (1980); J. Appl. Phys. 50 (1979) 1944. [17] A.C. Hewson and P.S. Riseborough, Solid State Commun. 22 (1977) 379. [18] J.K. Lang. Y. Baer and P.A. Cox, J. Phys. Fll (1981) 121.
4f PHOTOEMISSION Peter
Materials
271
478~48 (1985) 271-273
SPECTRA
OF LIGHT RARE EARTHS
S. RISEBOROUGH
Department of Physics, Polytechnic Institute of New York, 333 Jay Sireei, Brooklyn, NY 11201, USA
The 4f derived valence band photoemission spectra of Ce, Pr and Nd compounds are interpreted in terms of the presence of two types of screening channels; localized screening and diffuse screening. The effect of hybridization on these screening channels is investigated.
1. Introduction The valence band photoemission spectra of Ce and its compounds has long been the subject of considerable controversy [l-lo]. The controversy surrounds the interpretation of two peaks; one at the Fermi level and another approximately 2.5 eV below it. Recently, both resonant [3-51 and angle resolved photoemission [6] experiments have conclusively shown that both these peaks correspond to the emission of f electrons. Several mechanism [7-91 have been invoked to interpret the data, and are all equivocal. Recent photoemission experiments [11,12] on Pr and Nd compounds have shed new light onto the subject. These experiments suggest that the bi-modal 4f spectra is common to all of the light rare earth elements, completely independent of their magnetic properties. The experimental data [ll], displayed in fig. 1, shows the 4f spectra for an isomorphic series of rare earth compounds. In the Ce compounds, one peak lies at the Fermi level and the other is 2.5 eV below it. As one scans the series, from Ce through Pr to Nd, the two peaks move to lower energies but still maintain their energy separation at the constant value of 2.5 eV. Also one notices that the relative intensities of the two peaks change. The intensity of the peak closest to the Fermi energy diminishes across the series, there is a concomitant increase in intensity of the peak at lower binding energies. We shall show how the Anderson model [13], together with the screening mechanism for the f hole [8], can describe the experimental results.
0304-8853/85/$03.30 (North-Holland
Physics
0 Elsevier Science Publishers Publishing
Division)
B.V.
a
0
4 ENERGY
BELOW
EF (eV)
Fig. 1. The 4f derived valence band photoemission spectra the series RERu, in which RE = Ce, Pr and Nd [ll].
for
212
P.S. Riseborough
/ 4j spectra of light rare earfhs
2. Calculations and results
criterion
for bound
The f derived valence band photoemission spectra can be calculated directly from the f electron Green’s function. We shall treat the f-d Coulomb interaction via perturbation theory, and for mixed valence Ce, we shall use the unperturbed propagators as found from the l/N expansion method [14]. The lowest order, nontrivial, contribution of U, to the f electron self-energy is depicted diagramatically in fig. 2. In this lowest order process, the f hole in the final state of the photoemission causes the electrons in the conduction band to be redistributed amongst the d band states, through the formation of the electron-hole pairs. The perturbation theory results are expected to converge for the light rare earth metals, since the 12 fold conduction band contains at most only two or three electrons, and thus is approaching the low density limit. Treglia et al. [15] have shown that in such a limit, the method may reproduce results for all two peaked photoemission spectra of Pd, and is in agreement with the results of more exact calculations [16]. We calculate the self-energy due to the f-d screening interaction, in the local approximation [15]. Since both the hybridization [7] and the f-d screening interaction [8] can result in a bound state being split off from the bottom of the conduction band, we find that the criterion for bound state formation [17] is considerably reduced by the hybridization. If we model the quantity
lr31+
z+(y2/W)(2P-1/2P+l)a(P)
as
,,:s:l,{w2-~2}p+1’2>
W>(wl
i
b,
(2.1)
W
this expression p reflects the k dependence of the hybridization V(k).) then we find the approximate
(In
Fig. 2. The 4f hole in the final state interacts with the conduction band, producing a rearrangement of the d band occupation.
1
state formation
as
1+(ww)-(~2/w)~(P)
1 ’
where
a(p)
= 22Pf3(
p + 1)
qP+:)qP+;) r(2P
+
3)
(2.2)
In this expression V is a measure of the hybridization, 2 W is the conduction band width and E, is the position of the 4f level measured from the bottom of the conduction band. We see that when the f level is close to the lower band edge, the hybridization enhances the probability that a d band bound state is formed in the photoemission final state. Under such circumstances, the final state of the photoemission process may involve two possible screening channels [S]. In one screening channel, the bound state is filled by a conduction electron, and the d band continuum is filled up to the Fermi level. The wave function of the bound state is closely localized around the final state 4f hole. This is the local screening channel. In the other case, the bound state remains empty and the d band continuum is filled up to the Fermi level. The 4f hole is screened by the electrons in the itinerant conduction band states. This is the diffuse screening channel. From conservation of energy considerations one finds that the kinetic energy of the photo emitted electron corresponding to the locally screened final state is higher than that associated with the diffusely screened final state. The energy difference is that required to take an electron out of the bound state below the bottom of the conduction band and place it at the fermi level. This energy separation, must therefore be slightly greater than the width of the occupied portion of the lanthanide conduction band. Since joint photoemission/BIS experiments [18] suggests that for all the lanthanide metals this energy is roughly 2 to 3 eV, we expect that the energy separation between the two 4f peaks should remain almost constant at this value. The relative intensity of the two peaks is governed by the overlap between the initial state and the two final states of the photoemission process. For large hybridization, the locally screeened peak dominates, while for smaller hybridization the diffusely screened peak becomes intenser. In this way, we correlate the experimentally observed decrease in the intensity of the locally screened peak [ll] with the decrease of hybridization, presumably caused by the lanthanide contraction.
P.S. Riseborough / 4f spectra of light rare earths
References [l] B. Johansson, Phil. Mag. 30 (1977) 469. [?] L.I. Johansson, J.W. Allen, T. Gustafsson, I. Lindau and S.B. Hagstrom, Solid State Commun. 28 (1978) 53. [3] A. Franciosi, J.H. Weaver, N. Martensson and M. Croft, Phys. Rev. B24 (1982) 3651. [4] N. Martensson, B. Reihl and R.D. Parks, Solid State Commun. 41 (1982) 573. (51 R.D. Parks, N. Martensson and B. Reihl, in: Valence Instabilities eds. P. Wachter and H. Boppart (North-Holland, Amsterdam, 1982). [6] D.M. Wieliczka, C.G. Olson and D.W. Lynch, Phys. Rev. B29 (1983) 3028. [7] 0. Gunnarsson and K. Schonhammer, Phys. Rev. Lett 50 (1983) 604; Phys. Rev. B28 (1983) 4220. [P] S.H. Liu and K.M. Ho, Phys. Rev. B26 (1982) 7052, B28 (1983) 4220.
273
[9] M. Schliiter and C.M. Varma, Helvetica Phys. Acta 56 (1983) 147. (lo] P.S. Riseborough, to be published. [ll] R.D. Parks, S. Raaen, M.L. den Boer, Y.S. Chang and G.P. Williams, Phys. Rev. Lett. 52 (1984) 2176. [12] D.M. Wieliczka, C.G. Olson and D.W. Lynch, Phys. Rev. Lett. 52 (1984) 2180. [13] P.W. Anderson, Phys. Rev. 124 (1961) 41. [14] F.C. Zhang and T.K. Lee, Phys. Rev. B28 (1983) 33. [15] G. Treglia, F. Ducastelle and D. Spanjaard, J. de Phys. 41 (1980) 281, 43 (1982) 341. 1161 L.C. Davis and L.A. Feldkamp, Solid State Commun. 34 (1980); J. Appl. Phys. 50 (1979) 1944. [17] A.C. Hewson and P.S. Riseborough, Solid State Commun. 22 (1977) 379. [18] J.K. Lang. Y. Baer and P.A. Cox, J. Phys. Fll (1981) 121.