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Coherence effects in photoemission from ordered Ce systems
Physica B 259—261 (1999) 1105—1106
Coherence effects in photoemission from ordered Ce systems Gertrud Zwicknagl Max-Planck-Institut fiir Physik Komplexer Systeme, Au}enstelle Stuttgart, Postfach 80 06 65, 70506 Stuttgart, Germany
Abstract The intensity dependence on the emission angle displayed by the Kondo peak in ordered Ce alloys reflects the effective coupling between the Ce 4f states. The renormalized band model for the f-derived excitations yields the momentum dependence of the effective coupling. Good qualitative descriptions of the experimental data are achieved for crystalline Ce/Pt and Ce/Be films. 1999 Elsevier Science B.V. All rights reserved. Keywords: Heavy fermions
Coherence effects can strongly influence the lowtemperature behavior of ordered Ce compounds. The resulting deviations from the universal behavior of dilute Kondo systems are observed in the thermodynamic and transport properties of many heavy-fermion compounds. The influence of coherence is evidenced, e.g., by the formation of heavy quasiparticle bands whose Fermi surfaces and effective masses have been determined by deHaas—van Alphen experiments [1,2,4,5]. More direct microscopic information can be gained from high-resolution photoemission experiments [3,6]. This paper (1) describes the results of a semi-phenomenological theory of heavy-fermion compounds which includes the effects of lattice periodicity and (2) provides a method for analyzing related experiments. The theory exploits the fact that the f-derived low-energy excitations acquire dispersion via the coupling to the weakly correlated conduction electrons which, in turn, can be reliably described by means of standard electronic structure methods. Figs. 1 and 2 illustrate the theoretical results for the momentum dependence of the f-spectral function of thin ordered Ce films on two different substrates. The occupied parts of the spectra exhibit negligible dispersion. The coherence effects are reflected in the pronounced momentum dependence of the intensity obtained for the Ce/Pt system. No momentum dependence is found for the Ce/Be system. The data are in good qualitative agreement with recent photoemission data [3,6].
The theory leading to the results shown in Figs. 1 and 2 is based on the renormalized band method [1,4] which successfully describes the quasiparticle excitations in heavy-fermion compounds. The theory procedes from a fully (Dirac) relativistic selfconsistent band structure calculation which yields the weakly correlated conduction bands. The strong local correlations, on the other hand, are accounted for by a resonant f-phase shift at the Ce sites. We calculate the band structure for Ce-compounds from which we deduce the surface-projected f-spectral function N o (k ; u)"1! Im G (k; u)2 N , , I p where 122 N denotes the average with respect to the I k-component perpendicular to the surface. This averaging allows us to simulate the loss of translational invariance perpendicular to the surface. The results for the Ce/Pt system were derived from the model compound CePt for which we adopted both the cubic CuAu and hexagonal SnNi structure while the Ce/Be spectra were calculated from CeBe . Renormalized phase shifts are introduced for the f-5/2 channels at the Ce sites negelecting crystalline electric field effects. The resonance widths ¹ *K30 K yield c(CePt )K100 mJ/ mol Ce K and c(CeBe )K113 mJ/mol Ce K for the coefficients of the linear specific heat, respectively.
0921-4526/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 0 9 8 1 - 8
1106
G. Zwicknagl / Physica B 259—261 (1999) 1105—1106
Fig. 1. Surface-projected f-spectral function of CePt in the hexagonal SnNi structure. k varies along the RM direction of the , (0 0 1) surface Brillouin zone. The data were convoluted with a Lorentzian of width 5 meV.
Fig. 2. Surface-projected f-spectral function of CeBe . k varies , along the RM direction of the (1 1 1) surface Brillouin zone. The data were convoluted with a Lorentzian of width 5 meV.
References
[4] G. Zwicknagl, Phys. Scripta T 49 (1993) 34. [5] H. Aoki, S. Uji, A.K. Albessard, Y. Onuki, J. Phys. Soc. Japan 61 (1992) 3457. [6] M. Garnier, D. Purdie, K. Breuer, M. Hengsberger, Y. Baer, Phys. Rev. B 58 (1998) 9697.
[1] G. Zwicknagl, Adv. Phys. 41 (1992) 203. [2] G.G. Lonzarich, J. Magn. Magn. Mater 76&77 (1988) 1. [3] M. Garnier, D. Purdie, K. Breuer, M. Hengsberger, Y. Baer, Phys. Rev. B 56 (1997) R11399.
Coherence effects in photoemission from ordered Ce systems Gertrud Zwicknagl Max-Planck-Institut fiir Physik Komplexer Systeme, Au}enstelle Stuttgart, Postfach 80 06 65, 70506 Stuttgart, Germany
Abstract The intensity dependence on the emission angle displayed by the Kondo peak in ordered Ce alloys reflects the effective coupling between the Ce 4f states. The renormalized band model for the f-derived excitations yields the momentum dependence of the effective coupling. Good qualitative descriptions of the experimental data are achieved for crystalline Ce/Pt and Ce/Be films. 1999 Elsevier Science B.V. All rights reserved. Keywords: Heavy fermions
Coherence effects can strongly influence the lowtemperature behavior of ordered Ce compounds. The resulting deviations from the universal behavior of dilute Kondo systems are observed in the thermodynamic and transport properties of many heavy-fermion compounds. The influence of coherence is evidenced, e.g., by the formation of heavy quasiparticle bands whose Fermi surfaces and effective masses have been determined by deHaas—van Alphen experiments [1,2,4,5]. More direct microscopic information can be gained from high-resolution photoemission experiments [3,6]. This paper (1) describes the results of a semi-phenomenological theory of heavy-fermion compounds which includes the effects of lattice periodicity and (2) provides a method for analyzing related experiments. The theory exploits the fact that the f-derived low-energy excitations acquire dispersion via the coupling to the weakly correlated conduction electrons which, in turn, can be reliably described by means of standard electronic structure methods. Figs. 1 and 2 illustrate the theoretical results for the momentum dependence of the f-spectral function of thin ordered Ce films on two different substrates. The occupied parts of the spectra exhibit negligible dispersion. The coherence effects are reflected in the pronounced momentum dependence of the intensity obtained for the Ce/Pt system. No momentum dependence is found for the Ce/Be system. The data are in good qualitative agreement with recent photoemission data [3,6].
The theory leading to the results shown in Figs. 1 and 2 is based on the renormalized band method [1,4] which successfully describes the quasiparticle excitations in heavy-fermion compounds. The theory procedes from a fully (Dirac) relativistic selfconsistent band structure calculation which yields the weakly correlated conduction bands. The strong local correlations, on the other hand, are accounted for by a resonant f-phase shift at the Ce sites. We calculate the band structure for Ce-compounds from which we deduce the surface-projected f-spectral function N o (k ; u)"1! Im G (k; u)2 N , , I p where 122 N denotes the average with respect to the I k-component perpendicular to the surface. This averaging allows us to simulate the loss of translational invariance perpendicular to the surface. The results for the Ce/Pt system were derived from the model compound CePt for which we adopted both the cubic CuAu and hexagonal SnNi structure while the Ce/Be spectra were calculated from CeBe . Renormalized phase shifts are introduced for the f-5/2 channels at the Ce sites negelecting crystalline electric field effects. The resonance widths ¹ *K30 K yield c(CePt )K100 mJ/ mol Ce K and c(CeBe )K113 mJ/mol Ce K for the coefficients of the linear specific heat, respectively.
0921-4526/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 0 9 8 1 - 8
1106
G. Zwicknagl / Physica B 259—261 (1999) 1105—1106
Fig. 1. Surface-projected f-spectral function of CePt in the hexagonal SnNi structure. k varies along the RM direction of the , (0 0 1) surface Brillouin zone. The data were convoluted with a Lorentzian of width 5 meV.
Fig. 2. Surface-projected f-spectral function of CeBe . k varies , along the RM direction of the (1 1 1) surface Brillouin zone. The data were convoluted with a Lorentzian of width 5 meV.
References
[4] G. Zwicknagl, Phys. Scripta T 49 (1993) 34. [5] H. Aoki, S. Uji, A.K. Albessard, Y. Onuki, J. Phys. Soc. Japan 61 (1992) 3457. [6] M. Garnier, D. Purdie, K. Breuer, M. Hengsberger, Y. Baer, Phys. Rev. B 58 (1998) 9697.
[1] G. Zwicknagl, Adv. Phys. 41 (1992) 203. [2] G.G. Lonzarich, J. Magn. Magn. Mater 76&77 (1988) 1. [3] M. Garnier, D. Purdie, K. Breuer, M. Hengsberger, Y. Baer, Phys. Rev. B 56 (1997) R11399.