Electronic states in1∕1Cd6Yband1∕1Cd6Ca: Relativistic, correlation, and structural effects

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The electronic structure of the rational approximants $1∕1$ ${\mathrm{Cd}}_{6}\mathrm{Yb}$ and $1∕1$ ${\mathrm{Cd}}_{6}\mathrm{Ca}$ to the stable icosahedral ${\mathrm{Cd}}_{5.7}\mathrm{Yb}$ and ${\mathrm{Cd}}_{5.7}\mathrm{Ca}$ quasicrystals is studied by the full-potential linear augmented plane-wave method. A comparison is made between several structural models. We show that the (relativistic) spin-orbit (SO) interaction and electronic correlations that are not described by the usual local density approximation are essential for an accurate description of the electronic structure. In particular, we show that the SO interaction is responsible for a splitting of the Cd $4d$ and Yb $4f$ peaks, and that the experimental peak positions can be reproduced by including a Hubbard $U$ term in the Hamiltonian [$U(\mathrm{Cd})=5.6\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, $U(\mathrm{Yb})=3.1\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$]. Our results show very good agreement with a photoemission (PE) spectrum of $1∕1$ ${\mathrm{Cd}}_{6}\mathrm{Yb}$ [R. Tamura, Y. Murao, S. Takeuchi, T. Kiss, T. Yokoya, and S. Shin, Phys. Rev. B 65, 224207 (2002)] and a $350\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ PE spectrum of $1∕1$ ${\mathrm{Cd}}_{6}\mathrm{Ca}$, which we present in this paper.