Physica B 312–313 (2002) 304–306 Heavy fermions in UPt 3 G. Zwicknagl a, *, A.N. Yaresko b , P. Fulde c a Institut fuer Mathematische Physik, TU Braunschweig, Mendelssohnstr. 3, 38116 Braunschweig, Germany b MPI fuer Chemische Physik fester Stoffe, Dresden, Germany c MPI fuer Physik komplexer Systeme, Dresden, Germany Abstract Quantum chemical calculations on molecules containing U ions as well as recent experiments on UPd 2 Al 3 show that some of the 5f states may be itinerant while others remain localized. Based on these findings we present a theory for the origin of the heavy quasi-particles in UPt 3 : The latter are described as f-derived band states with effective masses renormalized by intra-atomic excitations of the localized f electrons. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Heavy fermions; U compounds The central result of the present paper is that in UPt 3 we deal with localized as well as delocalized 5f electrons and that the coupling of the two subsystems results in heavy fermions. The coexistence of localized and delocalized 5f states in U-based heavy-fermion com- pounds is suggested by recent neutron inelastic scatter- ing experiments on UPd 2 Al 3 [1]. In the present paper, we consider two of the 5f electrons as localized, in agreement with the absence of any Kramers doublets in cases where a CEF splitting of U states has been observed. As a consequence, the heavy quasi-particles whose Fermi surfaces have been observed in deHaas– vanAlphen experiments should be derived from a single U 5f electron per U site which hybridizes with the conduction states. Following this track of thought, we calculated the band-structure by solving the Dirac equation starting from the self-consistent LDA potentials [2] but exclud- ing the U 5f j ¼ 5 2 ; j z ¼ 7 5 2 and j z ¼ 7 1 2 states from forming bands. The localized 5f orbitals are accounted for in the self-consistent density and, concomitantly, in the potential seen by the conduction electrons. The intrinsic bandwidth of the itinerant U 5f j ¼ 5 2 ; j z ¼ 7 3 2 electrons is taken from the LDA calculation while the position of the corresponding band-center C is chosen such that the density distribution of the conduction states as obtained within LDA remains unchanged. The f occupancy per U atom for the delocalized 5f electrons amounts to n f = 0.65 indicating that we are dealing with a mixed valent situation. The calculated dH–vA frequencies agree rather well with the observed ones [3] as shown in Fig. 1. The theoretical branch labelled A was detected in recent experiments [4]. The observed effective masses and calculated band masses for the large G-centered orbit are listed in Table 1 for selected directions of the magnetic field. The enhancement of the observed effective masses m n over the ones calculated within the present theory m b is of the order of 10. It can be quantitatively explained by the interaction of the itinerant 5f states with the localized f 2 configuration as we shall show below. We next turn to the discussion of the localized U 5f states. The multiplet structure of the localized f 2 states is calculated by diagonalizing the Coulomb matrix. The spin–orbit splitting is rather large and therefore a jj - coupling scheme is used. This simplification gives six 2- particle states built from j j ¼ 5 2 ; j z ¼ 7 5 2 S and j j ¼ 5 2 ; j z ¼ 7 1 2 S: The resulting eigenstates are generally no longer eigenstates of the total angular momentum J 2 ; but remain eigenstates of J z : The Coulomb matrix *Corresponding author. Tel.: +49-531-391-8186; fax: +49- 531-391-5206. E-mail address: G.Zwicknagl@tu-bs.de (G. Zwicknagl). 0921-4526/02/$-see front matter r 2002 Elsevier Science B.V. All rights reserved. PII:S0921-4526(01)01336-9