PHYSICAL REVIEW B VOLUME 51, NUMBER 8 15 FEBRUARY 1995-II Electronic structure and optical response of L-Cepds A. Vega, * S. Bouarab, and M. A. Khan Institut de Physique et Chimie des Materiauz de Strasbourg, 28 rue du Loess, 67087 Strasbourg, France (Received 26 July 1994; revised manuscript received 7 October 1994) A theoretical study of the electronic structure and the related optical response of L-CePd5 is reported. The charge distribution is calculated self-consistently within the linear mufBn-tin-orbital method in the atomic-sphere approximation. The exchange and correlation potential is treated in the local-density approximation. The origin of the different electronic states is discussed in terms of the hybridization between the Ce and Pd orbitals, and is illustrated by means of the /-projected local density of states at each inequivalent atom within the unit cell. The different electronic population at each inequivalent site is analyzed as a function of the local coordination number as well as by considering the chemical character of the neighboring atoms. The different absorption peaks obtained in the imaginary part of the dielectric function and in the real part of the optical conductivity are traced back to particular interband transitions. A comparison of the present results with those for other Ce-Pd alloys is made. I. INTRODUCTION In the past years, a considerable effort has been in- vested both &om the experimental and theoretical points of view in order to understand the electronic properties and, in particular, the optical response in the Ce-Pd in- termetallic compounds. Most of the exciting properties exhibited by the ordered Ce-Pd alloys are due to the 4f states of Ce, which are in the vicinity of the Fermi energy (E~) and, thus, strongly hybridize with the conduction 4d band of the neighboring Pd atoms. The relative po- sition of the resulting electronic states depends not only on the concentration of Ce and Pd in the corresponding alloy, but also in the particular geometrical arrangement of the atoms, and confers to these materials a fluctuat- ing valence character. Moreover, the geometrical order in these materials has been observed to vary as a function of the annealing temperature and pressure. This has an influence in properties like the electrical resistivity which increases significantly with pressure. Spectroscopic measurements have been performed for CePd3 by Allen et at. and Peterman et at. from which the valence-band photoemission spectra have been ob- tained. The empty states have been observed through bremsstrahlung isochromat spectroscopy (BIS) by Hille- brecht et aE. With respect to CePd7, the same prop- erties have been studied through BIS, core level x-ray- photoemission spectroscopy and x-ray-absorption spec- troscopy by Beaurepaire et al. Besides, measurements of magnetic susceptibility and specific heat have been recently reported for this system. The theoretical calculations for these compounds through the linear aug- mented plane wave (LAPW) method (Refs. 13 and 14) and through linear muffin-tin orbital (LMTO) (Refs. 15 and 9) present a rather good agreement with the above experimental observations. In the case of CePd5, most of the experimental efforts have been devoted to the study of the electrical resistivity and the crystal structure ' as a function of the annealing temperature. However, up to now, no experimental results concerning the electronic structure and optical properties are available for this sys- tem. In order to have a unified picture over the Ce-Pd alloys, these properties deserve to be also investigated in Cepd5. It is the aim of this work to present a detailed theoretical study of the electronic and optical properties of this alloy, and to compare the general trends obtained with those for CePd3 and CePd7. The rest of the paper is organized as follows. After a brief account, in Sec. II, of the crystal structure of CePd5, we will present in Sec. III the theoretical model used for the calculations. The discussion of the results for the electronic distribution and optical response is reported in Secs. IV and V, respectively. Section VI summarizes the results. II. GEOMETRICAL STRUCTURE The crystal structure of CePd5 has been recently an- alyzed through x-ray diffraction by Kuwano et al. ' It is revealed that this compound has two phases, one stable at low temperature (L-CePds), and the other at high temperature (H-CePds). The structure of L CePd5 is regarded as orthorhombic with lattice parame- ters a = 0. 5700 nm, 6 = 0. 4062 nm and c = 0.8461 nm. The numbers of cerium and palladium sites in the unit cell are two and ten, respectively. In Fig. 1, the unit cell is illustrated and the coordinates of the twelve atoms are given. By taking into account the different local environ- ment of each atom, i.e. , the local coordination number and the chemical character of the neighboring sites, five different types of atoms can be found within the unit cell. The two Ce atoms are equivalent (type 1) and there are four types of Pd atoms: types 2, 4, and 5 with two atoms in each case, and type 3 with four atoms. 0163-1829/95/51(8)/4823(7)/$06. 00 51 4823 1995 The American Physical Society