Microscopic analysis of multipole susceptibility of actinide dioxides: A scenario of multipole ordering in AmO${}_2$

By evaluating multipole susceptibility of a seven-orbital impurity Anderson model with the use of a numerical renormalization group method, we discuss possible multipole states of actinide dioxides at low temperatures. In particular, here we point out a possible scenario for multipole ordering in americium dioxide. For Am${}^{4+}$ ion with five $5f$ electrons, it is considered that the ground state is ${\mathrm{\Gamma }}_7^{-}$ doublet and the first excited state is ${\mathrm{\Gamma }}_8^{-}$ quartet, but we remark that the $f^5$ ground state is easily converted due to the competition between spin-orbit coupling and Coulomb interactions. Then, we find that the ${\mathrm{\Gamma }}_8^{-}$ quartet can be the ground state of AmO${}_2$ even for the same crystalline electric field potential. In the case of ${\mathrm{\Gamma }}_8^{-}$ quartet ground state, the numerical results suggest that high-order multipoles such as quadrupole and octupole can be relevant to AmO${}_2$.