Optical evidence of 4 f -band formation in CeN Anna Delin Condensed Matter Theory Group, Physics Department, Uppsala University, S-751 21 Uppsala, Sweden P. M. Oppeneer Max-Planck Research Group ‘‘Electron Systems,’’ University of Technology, D-01062 Dresden, Germany M. S. S. Brooks European Commission, European Institute for Transuranium Elements, Postfach 2340, D-76125 Karlsruhe, Germany T. Kraft Max-Planck Research Group ‘‘Electron Systems,’’ University of Technology, D-01062 Dresden, Germany J. M. Wills Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 Bo ¨ rje Johansson and Olle Eriksson Condensed Matter Theory Group, Physics Department, Uppsala University, S-751 21 Uppsala, Sweden Received 7 February 1997 We report ab initio calculations of the ground state and optical properties of CeN, which show that the 4 f electrons in CeN are itinerant and that the intra-atomic 4 f -Coulomb interaction is largely screened. A coherent 4 f band of width 2 eV is formed, from which an accurate description of the optical spectrum is obtained. The lattice parameter, linear specific heat coefficient, and magnetic susceptibility are also well reproduced. While CeN was previously classified to be a mixed valence compound, our results show that the more appropriate picture is that of a 4 f -band material. S0163-18299751916-3 CeN is an interesting compound that was previously clas- sified to be an archetypal mixed valence compound where- fore it has attracted considerable attention. 1–6 The common situation found in most 4 f materials is that the occupied 4 f states are well localized and contain an integer number of electrons. This is the standard model of the lanthanides. Mixed valency occurs when the 4 f level is very close to or even degenerate with the Fermi level. The originally local- ized 4 f states then may start to hybridize with the conduction-band states and may acquire a width in the meV range. 7 Thus, the 4 f states are still mainly localized, and hybridization can be treated as a small perturbation. 7,8 The resulting ground-state electronic configuration of the lan- thanide will not be the 4 f n  5 d 6 s 6 p  l configuration, or the 4 f n -1  5 d 6 s 6 p  l +1 configuration, but rather an intermediate of these two. A necessary condition for mixed valency to occur is of course that the energy difference between these two configurations is effectively zero. There exists also another possibility for the 4 f electrons in that these may become itinerant. In this case, the 4 f states can be described within band theory as ordinary Bloch states. The band picture differs distinctly from the intermediate va- lence picture mentioned above. We note, however, that the term ‘‘mixed valent’’ is sometimes used in a wider but less accurate sense to denote f electron materials in which hy- bridized f bands are formed in the vicinity of E F . In the following, when using the term mixed valency we shall use it exclusively in the stricter meaning. As compared to the normal, integer valence rare-earth compounds, mixed valency expresses itself in an unusual behavior of various physical properties such as anomalous lattice parameters, compressibility, elastic constants ( c 12 is sometimes negative, thermal expansion coefficients, and magnetic susceptibility. In many cases, e.g., the well-known compounds SmS, SmB 6 , and TmSe, the mixed valency con- cept has proven to be extremely fruitful in explaining the palette of anomalous properties observed in these 4 f materials. 7–9 On the basis of its unusual physical properties, it has frequently been argued that CeN is a mixed valent. 1–6 However, a more recent analysis of photoemission spectros- copy PES and inverse photoemission spectroscopy IPES spectra using Gunnarsson-Scho ¨ nhammer GS analysis 10 has revealed that the energy difference between uncoupled f 0 and f 1 configurations is much larger than the hybridization strength. 11 This result suggests that CeN is in fact not a mixed valent. Instead, Patthey et al. propose that CeN is a narrow-band material. 11 In this paper, we show that the model where the Ce-4 f states are treated as normal Bloch states reproduces in great detail the optical spectrum of CeN. The 4 f -band approach, moreover, explains the anomalous lattice constant and pro- vides good agreement with experimental data for the mag- netic susceptibility and the electronic specific heat. In addi- tion to these findings in support of the band model, from a comparison with Ce metal, we argue that the necessary con- dition for mixed valency is not satisfied in CeN. The identi- fication of itinerant 4 f electrons in CeN is unusual in com- parison to the behavior typically found in the other Ce monopnictides, where the occupied 4 f electron is localized and the intra-atomic 4 f -Coulomb repulsion is important for explaining the optical spectra. 12 PHYSICAL REVIEW B 15 APRIL 1997-II VOLUME 55, NUMBER 16 55 0163-1829/97/5516/101734/$10.00 R10 173 © 1997 The American Physical Society