Two-channel Kondo Effect Emerging from Nd Ions

We discuss Kondo phenomena in a seven-orbital impurity Anderson model hybridized with ${\mathrm{\Gamma }}_8$ conduction electrons by employing a numerical renormalization group method. In particular, we focus on the case with three local $f$ electrons, corresponding to a Nd${}^{3+}$ ion. For realistic values of Coulomb interactions, spin-orbit coupling, cubic crystalline electric field potentials, and hybridization, we find a residual entropy of $0.5\log 2$, a characteristic of two-channel Kondo phenomena, for the wide range of parameters of the local ${\mathrm{\Gamma }}_6$ ground state. This is considered to be the magnetic two-channel Kondo effect, consistent with the result from an extended $s$-$d$ model constructed on the basis of the $j$-$j$ coupling scheme. Finally, we briefly discuss candidates of Nd compounds to observe the two-channel Kondo effect.