Effective Hamiltonian for PrRu4P12 showing unconventional charge ordering

The origin and the nature of the charge ordering in PrRu4P12 are studied theoretically by using a simple model. First, the mixing matrix elements between conduction electrons and Pr 4f states are examined to show that the magnitude of the mixing depends sensitively on the crystal-field (CF) levels. Then, taking the simplest case in which Γ1 is the CF ground state and Γ4(2) is a low-lying CF excited state in the normal phase, we derive an effective Hamiltonian for both the charge and spin degrees of freedom. As expected, it results in a two-sublattice charge ordering assisted by the nesting of conduction band, where Γ4(2) becomes the ground state on one of the sublattices. The magnitude of the interaction between Γ4(2) triplets can be estimated within the present model; it turns out to be very weak, suggesting that Γ4(2) triplets behave as almost free even at low temperatures. (author)