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Abstract
It is shown that quadrupole susceptibility can be detected in Gd compounds contrary to our textbook knowledge that Gd$^{3+}$ ion induces pure spin moment due to the Hund's rules in an $LS$ coupling scheme. The ground-state multiplet of Gd$^{3+}$ is always characterized by $J$=7/2, where $J$ denotes total angular momentum, but in a $j$-$j$ coupling scheme, one $f$ electron in $j$=7/2 octet carries quadrupole moment, while other six electrons fully occupy $j$=5/2 sextet, where $j$ denotes one-electron total angular momentum. For realistic values of Coulomb interaction and spin-orbit coupling, the ground-state wavefunction is found to contain significant amount of the $j$-$j$ coupling component. From the evaluation of quadrupole susceptibility in a simple mean-field approximation, we point out a possibility to detect the softening of elastic constant in Gd-based filled skutterudites.
Highlights
Multipole phenomena have attracted much attention in the research field of strongly correlated f -electron systems.1–3 In general, multipole indicates spin-orbital complex degree of freedom, which is considered to be active in f electron materials due to the strong spin-orbit coupling of f electrons
For Gd3+ ion, the ground state in the j-j coupling scheme is characterized by J=7/2, but it is composed of fully occupied j=5/2 sextet and one electron in j=7/2 octet, where j indicates one-electron total angular momentum
It is true that from a symmetry viewpoint, we can continue to use the Stevens operator even if we deviate from the LS coupling scheme, since the ground state multiplet is always characterized by the same total angular momentum when we change U and/or λ
Summary
Multipole phenomena have attracted much attention in the research field of strongly correlated f -electron systems. In general, multipole indicates spin-orbital complex degree of freedom, which is considered to be active in f electron materials due to the strong spin-orbit coupling of f electrons. In an LS coupling scheme, due to the Hund’s rules, electron configuration is determined so as to maximize total spin angular momentum S, indicating S=7/2 for Gd3+. In the LS coupling scheme, there is no CEF splitting in the ground-state multiplet and we cannot expect to observe the response of higher-rank multipole in Gd-based compounds. For Gd3+ ion, the ground state in the j-j coupling scheme is characterized by J=7/2, but it is composed of fully occupied j=5/2 sextet and one electron in j=7/2 octet, where j indicates one-electron total angular momentum. With the use of the CEF parameters determined from PrOs4Sb12,5–7 we evaluate the quadrupole susceptibility for Gd-based filled skutterudite compounds and discuss the detection of the softening of elastic constant.
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