Effective Hamiltonian for PrRu4P12 Showing Unconventional Charge Ordering

The origin and the nature of the charge ordering in PrRu 4 P 12 are studied theoretically by using a simple model. First, the mixing matrix elements between conduction electrons and Pr 4 f 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 Γ 1 is the CF ground state and Γ 4 (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 Γ 4 (2) becomes the ground state on one of the sublattices. The magnitude of the interaction between Γ 4 (2) triplets can be estimated within the present model; it turns out to be very weak, suggesting that Γ 4 (2) triplets behave as almost free even at low temperatures.