- Email: [email protected]
CeCu2Si2: Renormalized band structure, quasiparticles and co-operative phenomena
PHYSICA
Physica B 186-188 (1993) 895-898 North-Holland
Cefu2Si2: Renormalized band structure, quasiparticles and co-operative phenomena Gertrud Zwicknagl and Uwe Pulst Max-Planck-lnstitut fiir Festkrrperforschung, Stuttgart, Germany The prototype heavy fermion compound CeCu2Si2 exhibits a rather complicated phase diagram at low temperatures. Recently, a number of phase transitions at temperatures above the superconducting Tc were discovered. These transitions seem to be correlated with the appearance of superconductivity. We calculate the quasiparticles in CeCuESi2 by means of the renormalized band structure method. The results for the Fermi surface suggest that the new phase transition may be driven by a topological transition in the system of the heavy quasiparticles. The heavy fermion compound CeCu2Si 2 exhibits a very complex phase diagram at low temperatures. Of particular interest here is the new phase transition discovered recently in as-grown single crystals [1]. The transition leads to pronounced anomalies in the elastic constants and, in addition, to changes in the observed Fermi surface cross sections. The experimental studies seem to suggest a close correlation between the new as yet undefined phase transition and the appearance of superconductivity which is found after an appropriate heat treatment. The present paper reports theoretical results on the Fermi surface and the quasiparticles in CeCu2Si z which are calculated by means of the renormalized band (RB) scheme. The formalism as well as applications were recently reviewed [2]. The method combines material-specific ab initio methods of electronic structure calculations and phenomenological Fermi liquid considerations. The quasiparticle bands are determined by solving a standard band structure problem for independent electrons moving in a periodic (nonlocal) potential. The actual computations were performed by means of the linear muffin tin orbital (LMTO) method adopting the atomic sphere approximation (ASA) [3]. The strong local correlations are accounted for by using properly modified phase shifts for the f-electrons at the lanthanide or actinide sites. The modifications account for the high effective masses and the crystalline electric field (CEF) splitting. The results can be directly compared with measured
Correspondence to: G. Zwicknagl, Max-Planck-Institut f/Jr Festk6rperforschung, 7000 Stuttgart 80, Germany.
de Haas-van Alphen (dHvA) data and can serve to interpret them. The compound CeCuaSi 2 crystallizes in the tetragonai ThCr2Si 2 structure. For our numerical studies we use the experimentally determined lattice parameters listed in ref. [4]. The RB calculations presented here adopt the CEF scheme determined by ref. [5]. Similar calculations have been carried out with the recent CEF data of ref, [6]. The detailed comparison will be published elsewhere [7]. The width of the quasiparticle band was adjusted so as to reproduce the linear coefficient of the specific heat y = 7 0 0 m J / mol K 2. The results for the Fermi surface can be summarized as follows: in CeCu2Si 2 one finds two separate sheets of the Fermi surface for heavy and light quasiparticles. The light quasiparticles have effective masses of the order of m* --- 5m e where m e is the bare electron mass. They can be considered as weakly renormalized conduction electrons and consequently, it is no surprise that the corresponding Fermi surface is rather similar to the LDA prediction as can be seen from fig. 1. The Fermi surface derived from our LDA band structure closely resembles the one determined by Harima and Yanase [8]. The observed Fermi surface cross sections [9] can be explained by both the renormalized band structure as well as by the LDA bands. There is, however, a characteristic difference between the Fermi surfaces for the light quasiparticles as derived from the two schemes: the LDA calculation predicts a small closed surface centered around the F-point. This surface, however, does not lead to signals in the dHvA-experiment although the corresponding cross sections are rather small and the masses are expected to be light.
0921-4526/93/$06.00 ~ 1993- Elsevier Science Publishers B.V. All rights reserved
896
G. Zwicknagl, U. Pulst / Fermi surface and quasiparticles in CeCu2Si 2
Fig. 1. Comparison of the Fermi surfaces for the light quasiparticles in CeCu2Si 2 as derived from (a) the L D A band structure and the renormalized bands (b).
Fig. 2. Fermi surface of the heavy quasiparticles in CeCuzSi 2 as derived from the renormalized bands.
G. Zwicknagl, U. Pulst / Fermi surface and quasiparticles in CeCu2Si 2
897
)iii ¸¸ iii ii ¸
]
i
i
Fig. 3. CeCu:Si2: Change in the topology of the Fermi surface of the heavy quasiparticles when the f-valence is reduced from its initial value n t -~ 0.95 (a) to by 0.02 (b).
Of particular interest are the heavy quasiparticles of effective masses m * = 5 0 0 m ~ which are found on a separate sheet. The topology of this surface is rather different from the corresponding L D A result. As can be seen from fig. 2 the Fermi surface of the heavy quasiparticles mainly consists of columns along the tetragonal axis and small pockets. The crucial point is that the topology of this surface depends rather sensitively on the position of the Fermi energy. The band filling and hence the f-valence are critical quantities. Reducing the f-occupancy from the initial value of nf = 0.95 by 0.02, i.e. by --2% leads to changes in the topology as shown in fig. 3. As a result, the quasiparticle density of states (DOS) should exhibit rather pronounced structures in the immediate vicinity of the
Fermi energy which, in turn, can induce instabilities [10]. A n external magnetic field couples to the f-degrees of freedom. It leads to Zeeman splitting ---/x~,B of the heavy quasiparticle bands and hence can move the structures in the DOS relative to the Fermi energy. The effective moment P~e, of the f-states which reflects the C E F splitting depends on the direction of the external magnetic field. From the renormalized band calculation we determine the values of the critical magnetic fields for which the pronounced structures are moved to the Fermi energy. Due to CEF splitting of the f-states this critical value of the external magnetic field will depend upon its orientation. The calculation reported here also accounts for a slight broaden-
898
G. Zwicknagl, U. Pulst / Fermi surface and quasiparticles in CeCu2Si 2
Table 1 Comparison of the critical magnetic fields for field directions along the tetragonal axis (B~r,) and in the basal plane (B~ri,) as derived from the renormalized band structure and the corresponding experimental values. B~rit (T) ")
H~n , (T) b)
accrit
8.0
7
6.5
(T) ~)
References
H~, (T) b) 4
a) Renormalised bands. h) Experiment.
ing of the quasiparticle bands in the external field according to T * ( B ) = ~/(T*(0)) 2 + ( i t . B ) 2 .
This work was partially supported by Sonderforschungsbereich 252, D a r m s t a d t - F r a n k f u r t - M a i n z .
(1)
The explicit values of the critical fields B~rit and B~r . for field directions parallel to the c- and a-axes, respectively, are given in table 1. These values agree rather well with experiment. We therefore suggest that the observed new phase transition in CeCu2Si 2 may be driven by a topological transition in the system of the heavy quasiparticles.
[1] M. Lang, R. Modler, U. Ahlheim, R. Helfrich, P.H.P. Reinders, F. Steglich, W. Assmus, W. Sun, G. Bruls, D. Weber and B. L/ithi, Phys. Scripta T 39 (1991) 135. [2] G. Zwicknagl, Adv. Phys. 41 (1992) 203. [3] H.L. Skriver, The LMTO Method, Springer Series in Solid State Sciences No. 41 (Springer-Verlag, Berlin, 1984). [4] J. Sticht, N. d'Ambrumenil and J. Kfibler, Z. Phys. B 65 (1986) 149. [5] S. Horn, E. Holland-Moritz, M. Loewenhaupt, F. Steglich, H. Scheuer, A. Benoit and J. Flouquet, Phys, Rev. B 23 (1981) 3171. [6] E.A. Goremychkin and R. Osborn, preprint. [7] Uwe Pulst and Gertrud Zwicknagl, to be published. [8] Hisamoto Harima and Akira Yanase, J. Phys. Soc. Japan 60 (1991) 21. [9] M. Hunt, P. Meeson, P.A. Probst, P. Reinders, M. Springford, W. Assmus and W. Sun, J. Phys. C 2 (1990) 6859. [10] M.I. Kaganov and I.M. Lifshits, Sov. Phys. Usp. 22 (1979) 904.
Physica B 186-188 (1993) 895-898 North-Holland
Cefu2Si2: Renormalized band structure, quasiparticles and co-operative phenomena Gertrud Zwicknagl and Uwe Pulst Max-Planck-lnstitut fiir Festkrrperforschung, Stuttgart, Germany The prototype heavy fermion compound CeCu2Si2 exhibits a rather complicated phase diagram at low temperatures. Recently, a number of phase transitions at temperatures above the superconducting Tc were discovered. These transitions seem to be correlated with the appearance of superconductivity. We calculate the quasiparticles in CeCuESi2 by means of the renormalized band structure method. The results for the Fermi surface suggest that the new phase transition may be driven by a topological transition in the system of the heavy quasiparticles. The heavy fermion compound CeCu2Si 2 exhibits a very complex phase diagram at low temperatures. Of particular interest here is the new phase transition discovered recently in as-grown single crystals [1]. The transition leads to pronounced anomalies in the elastic constants and, in addition, to changes in the observed Fermi surface cross sections. The experimental studies seem to suggest a close correlation between the new as yet undefined phase transition and the appearance of superconductivity which is found after an appropriate heat treatment. The present paper reports theoretical results on the Fermi surface and the quasiparticles in CeCu2Si z which are calculated by means of the renormalized band (RB) scheme. The formalism as well as applications were recently reviewed [2]. The method combines material-specific ab initio methods of electronic structure calculations and phenomenological Fermi liquid considerations. The quasiparticle bands are determined by solving a standard band structure problem for independent electrons moving in a periodic (nonlocal) potential. The actual computations were performed by means of the linear muffin tin orbital (LMTO) method adopting the atomic sphere approximation (ASA) [3]. The strong local correlations are accounted for by using properly modified phase shifts for the f-electrons at the lanthanide or actinide sites. The modifications account for the high effective masses and the crystalline electric field (CEF) splitting. The results can be directly compared with measured
Correspondence to: G. Zwicknagl, Max-Planck-Institut f/Jr Festk6rperforschung, 7000 Stuttgart 80, Germany.
de Haas-van Alphen (dHvA) data and can serve to interpret them. The compound CeCuaSi 2 crystallizes in the tetragonai ThCr2Si 2 structure. For our numerical studies we use the experimentally determined lattice parameters listed in ref. [4]. The RB calculations presented here adopt the CEF scheme determined by ref. [5]. Similar calculations have been carried out with the recent CEF data of ref, [6]. The detailed comparison will be published elsewhere [7]. The width of the quasiparticle band was adjusted so as to reproduce the linear coefficient of the specific heat y = 7 0 0 m J / mol K 2. The results for the Fermi surface can be summarized as follows: in CeCu2Si 2 one finds two separate sheets of the Fermi surface for heavy and light quasiparticles. The light quasiparticles have effective masses of the order of m* --- 5m e where m e is the bare electron mass. They can be considered as weakly renormalized conduction electrons and consequently, it is no surprise that the corresponding Fermi surface is rather similar to the LDA prediction as can be seen from fig. 1. The Fermi surface derived from our LDA band structure closely resembles the one determined by Harima and Yanase [8]. The observed Fermi surface cross sections [9] can be explained by both the renormalized band structure as well as by the LDA bands. There is, however, a characteristic difference between the Fermi surfaces for the light quasiparticles as derived from the two schemes: the LDA calculation predicts a small closed surface centered around the F-point. This surface, however, does not lead to signals in the dHvA-experiment although the corresponding cross sections are rather small and the masses are expected to be light.
0921-4526/93/$06.00 ~ 1993- Elsevier Science Publishers B.V. All rights reserved
896
G. Zwicknagl, U. Pulst / Fermi surface and quasiparticles in CeCu2Si 2
Fig. 1. Comparison of the Fermi surfaces for the light quasiparticles in CeCu2Si 2 as derived from (a) the L D A band structure and the renormalized bands (b).
Fig. 2. Fermi surface of the heavy quasiparticles in CeCuzSi 2 as derived from the renormalized bands.
G. Zwicknagl, U. Pulst / Fermi surface and quasiparticles in CeCu2Si 2
897
)iii ¸¸ iii ii ¸
]
i
i
Fig. 3. CeCu:Si2: Change in the topology of the Fermi surface of the heavy quasiparticles when the f-valence is reduced from its initial value n t -~ 0.95 (a) to by 0.02 (b).
Of particular interest are the heavy quasiparticles of effective masses m * = 5 0 0 m ~ which are found on a separate sheet. The topology of this surface is rather different from the corresponding L D A result. As can be seen from fig. 2 the Fermi surface of the heavy quasiparticles mainly consists of columns along the tetragonal axis and small pockets. The crucial point is that the topology of this surface depends rather sensitively on the position of the Fermi energy. The band filling and hence the f-valence are critical quantities. Reducing the f-occupancy from the initial value of nf = 0.95 by 0.02, i.e. by --2% leads to changes in the topology as shown in fig. 3. As a result, the quasiparticle density of states (DOS) should exhibit rather pronounced structures in the immediate vicinity of the
Fermi energy which, in turn, can induce instabilities [10]. A n external magnetic field couples to the f-degrees of freedom. It leads to Zeeman splitting ---/x~,B of the heavy quasiparticle bands and hence can move the structures in the DOS relative to the Fermi energy. The effective moment P~e, of the f-states which reflects the C E F splitting depends on the direction of the external magnetic field. From the renormalized band calculation we determine the values of the critical magnetic fields for which the pronounced structures are moved to the Fermi energy. Due to CEF splitting of the f-states this critical value of the external magnetic field will depend upon its orientation. The calculation reported here also accounts for a slight broaden-
898
G. Zwicknagl, U. Pulst / Fermi surface and quasiparticles in CeCu2Si 2
Table 1 Comparison of the critical magnetic fields for field directions along the tetragonal axis (B~r,) and in the basal plane (B~ri,) as derived from the renormalized band structure and the corresponding experimental values. B~rit (T) ")
H~n , (T) b)
accrit
8.0
7
6.5
(T) ~)
References
H~, (T) b) 4
a) Renormalised bands. h) Experiment.
ing of the quasiparticle bands in the external field according to T * ( B ) = ~/(T*(0)) 2 + ( i t . B ) 2 .
This work was partially supported by Sonderforschungsbereich 252, D a r m s t a d t - F r a n k f u r t - M a i n z .
(1)
The explicit values of the critical fields B~rit and B~r . for field directions parallel to the c- and a-axes, respectively, are given in table 1. These values agree rather well with experiment. We therefore suggest that the observed new phase transition in CeCu2Si 2 may be driven by a topological transition in the system of the heavy quasiparticles.
[1] M. Lang, R. Modler, U. Ahlheim, R. Helfrich, P.H.P. Reinders, F. Steglich, W. Assmus, W. Sun, G. Bruls, D. Weber and B. L/ithi, Phys. Scripta T 39 (1991) 135. [2] G. Zwicknagl, Adv. Phys. 41 (1992) 203. [3] H.L. Skriver, The LMTO Method, Springer Series in Solid State Sciences No. 41 (Springer-Verlag, Berlin, 1984). [4] J. Sticht, N. d'Ambrumenil and J. Kfibler, Z. Phys. B 65 (1986) 149. [5] S. Horn, E. Holland-Moritz, M. Loewenhaupt, F. Steglich, H. Scheuer, A. Benoit and J. Flouquet, Phys, Rev. B 23 (1981) 3171. [6] E.A. Goremychkin and R. Osborn, preprint. [7] Uwe Pulst and Gertrud Zwicknagl, to be published. [8] Hisamoto Harima and Akira Yanase, J. Phys. Soc. Japan 60 (1991) 21. [9] M. Hunt, P. Meeson, P.A. Probst, P. Reinders, M. Springford, W. Assmus and W. Sun, J. Phys. C 2 (1990) 6859. [10] M.I. Kaganov and I.M. Lifshits, Sov. Phys. Usp. 22 (1979) 904.