Valence state and magnetism of Yb$_{7}$Co$_{4}$InGe$_{12}$.

Ytterbium (Yb) compounds exhibit unusual physical properties due to the Yb f-electrons, which play an active role in bonding, giving rise to intermediate valence, heavy-fermion or Kondo behavior. Many physical characteristics of the Yb systems are related to the fact that Yb can have two valence states: nonmagnetic divalent Yb$^{2+}$ (f$^{14})$ and magnetic trivalent Yb$^{3+}$ (f$^{13})$. We have synthesized a new Yb containing quaternary Yb$_{7}$Co$_{4}$InGe$_{12}$. XPS and magnetic susceptibility measurements indicate that all Yb are all trivalent. To understand the Yb valency in this compound, we have carried out \textit{ab initio }electronic structure calculations within density functional theory using FP-LAPW method. The electronic structure is obtained using LSDA with on-site Coulomb correlation potential (LSDA+U) included for both 4f electrons of Yb and 3d electrons of Co. As a one ``f-hole'' analogue of many Ce compounds$^{1, 2}$, we find that all the Yb atoms are trivalent, in agreement with XPS and magnetic susceptibility measurements. $^{1}$A. I. Liechtenstein, V. P. Antropov, and B. N Harmon, Phys. Rev. B 49, 10770 (1994). $^{2}$E. Bauer, Adv. Phys. 40, 417 (1991).