Spin-orbital wave excitations in orbitally degenerate exchange model with multipolar interactions

Elementary excitations in the multipole ordered state, which models the phase III in CeB₆, are investigated by means of a generalized Holstein-Primakoff formalism. When different kinds of nearest-neighbor exchange interactions between multipoles are comparable to each other, orbital-flip excitations exhibit almost one-dimensional dispersion along the k_z axis. With high symmetry of the interactions, zero modes appear due to the macroscopic degeneracy of the ground state. The next-nearest-neighbor Γ_4u2-type interaction, which stabilizes the magnetic order of the phase III in CeB₆, lifts the degeneracy and leads to gapfull excitation spectrum. When the next-nearest-neighbor Γ_5u-type interaction exists simultaneously, the spectrum shows softening at Γ and Z points. These excitations may be probed by neutron scattering and ultrasonic measurements.