MULTIPLET STRUCTURES IN 4d-XAS OF CeO2 AND CeRh3

We show that differences in parameter values of the Anderson model obtained from an analysis of the Ce 3d core level spectra between CeRhs and CeO2 well explain a remarkable difference in the Ce 4d core photoabsorption spectrum between the two by introducing interactions given by the Slater integrals and spin-orbit ones. The purpose of this work is t o present an interpretation for the Ce 4d-core X-ray absorption spectrum (4d-XAS) in CeOz and CeRh3, which is consistent with those for other high energy spectroscopies, on the basis of the impurity Anderson model incorporated with spin-orbit interactions and those described by the Slater integrals. For metallic Ce compounds, Gunnarsson and Schonhamrner [I] have given a theoretical interpretation for the Ce 3d-core X-ray photoemission spectrum (3d-XPS), 3d-XAS and some other spectroscopies with the use of the Andemon model incorporated with a core hole attractive potential acting on 4f electrons [2]. As a result the spectra are found to be well explained by assuming that the number of 4f electrons in the ground state nf is larger than 0.8 for metallic systems such as CeRh3. Furthermore the contribution to the spectra of the states with electron-hole pairs in the conduction band is shown to be negligible as higher order terms of the 1/Nf expansion with Nf being the spin and orbital degeneracy of 4f state, if Nf is sufficiently large as in the case of Ce compounds; an interpretation for the spectra is shown to be possible on the basis common to metallic and insulating Ce compounds. For an insulator CeO2, an interpretation similar to that for metallic systems have been carried out for 3dXPS 13, 41, 3d-XAS and bremsstrahlung isochromat spectrum [5] and it is extended to the Ce 2p XAS [6]. As a result, various spectra except 4d-XAS of CeOz are found to be well explained by assuming that nf N 0.5 and the 4f-4f Coulomb interaction UE and the hybridization V between the 4f and valence band states are much larger than those for metallic systems. The difference in parameter values between metallic systems and the insulator CeOz is to be ascribed to that in the species of atom composing Ce compounds or whether metallic or insulating: the electronegativity of oxygen in CeO2 is expected to be higher than that of transition element atoms in metallic compounds, which means smaller (larger) nf in Ce02 (metallic systems) or higher (lower) 4f level zf in Ce02 (metallic systems). Larger Us in CeOz can be ascribed to an absence of screening due to conduction electrons. Larger hybridization may be due to a strong covalent bonding between Ce and 0 atoms in Ce02 [7]. One way to confirm quantitatively the difference in parameters is to estimate them by carrying out ab initio calculation as given for Ce 181. Another way may be to show that the difference well explains another spectrum. We adopt the latter in this work. The 4d-XAS in a prethreshold regio for Ce compounds is well known to exhibit complicated multiplet structure due to a smaller 4d-core hole spin-orbit interaction and larger 4f-4d Slater integrals [9]. The multiplet structure of metallic systems including CeRh3 (nf 0.75) is similar to that for a trivalent compound CeF3 (nf I ) , while in CeOz a narrowing of the spectrum is seen and it is quite dissimilar to that for CeF3 and is rather similar to that for La compound 110-121. This seems to provoke controversy about the 4f valency of CeO2 [lo, 111. We show that the difference in parameters well explain that in 4d-XAS between CeOz and CeRhs. Our Hamiltonian is composed of HI and HZ [13]: HI describes the Anderson model [I] with the 4f level ~ f , the conduction band, the hybridization matrix element V ( E ) between the 4f state and conduction band state with energy E , the 4f-4f Coulomb interaction Utf and the 4f-4d Coulomb interaction Uf, [2]. Hz describes the 4f-4f Slater integrals F2, F* and F6, the 4f-4d ones F2 , F4 , GI, G~ and G~ and the spin-orbit interaction in the 4f (4d) state with coupling coAstant [f (&); F0 is taken into account in the effective interactions Ue and Uk. We calculate the 4d-XAS due to the 4d -+ 4f dipole transition with the following assumption: i) the ground state is a superposition of ldlOfO) and idlofly) and the final state that of /d9f1) and (d9f2v) with y being a hole with f symmetry in the conduction band; ii) the lowest order approximation of th'e 1/Nf expansion [l]; iii) we replace the occupied conduction (or valence) band by a single level, which is taken as the origin of energy, (and V ( E ) by a parameter -V). A justification of the replacement as first order approximation will be given elsewhere; iv) we Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19888336 C8 740 JOURNAL DE PHYSIQUE adopt the common parameter values of Hz given in [9] for Ce. v) we use the parameter values of HI which are obtained from an analysis of the 3d core level spectra for each compound [4, 51 except Uf,. Figure 1 compares calculated 4d-XAS for dlOfO 4 d9f1 (a) and dlOfl -+ d9f2 (b) transitions (vertical lines) with experiments [l l] for LaF3 and CeF3 (solid curves), respectively. The final state multiplets converge t o the origin of figures l a or l b for Hz = 0 and dipole transition matrix elements are normalized so that the integrated intensity for dlofo -+ d9f1 is unity. Hereafter we mainly focus our attention to the prethreshold energy region with weak spectral intensity. In mixed valent systems, the two transitions dlOfO -+ d9f1 and dlOflv -+ d9f2v interfere with each other depending on nf, V and a typical energy difference between d9f1 and d9f2v multiplets El E2 with El = ef Ufc and E2 = 2E1 + Ufi [13, 141. Figure l c (If) shows a good agreement between experiments [lo, 11, 121 and calculated 4d-XAS for CeRh3 (CeO2) with assuming E I = -1.7, V = 0.38, Ue = 7.0 and Uf, = 10.0, i.e., nf = 0.75 and El E2 = 4.7 Fig. 1. Comparison of calculated 4d-XAS (vertical-lines) with experiments for LaF3, CeF3, CeRh3 (111 and CeOz [lo, 121 (solid curves with arbitrary units): d(e) shows the results with V = 0.6 eV (sf = -1.7 eV) with other pararneters fixed to those adopted in c(f); the origin of energy for c-f is taken to be E2 (see text). ( ~ f = +0.5, V = 0.76, UfF = 10.5 and Uf, = 10.5, i.e., nf = 0.46 and El Ez = -0.5) in units of eV except n f ; a smaller value of Ufc is adopted compared with the 3d core case. A prominent deviation of 4d-XAS in the prethreshold region for CeO2 from that for CeF3 and the suppression of d9f1 multiplet structure in CeRh3 are due to the above-mentioned interference. This is remarkable especially in CeO2 reflecting the situation nf0.5 and V = El-Ez(cf. nfw 0.8 and V << El-& in CeRh3). Figures Id and l e are results with the parameters of Hl intermediate between Ce-s and CeOz which give an aspect of the mechanism producing the difference between the two.