Quadrupole and lattice effects of orbitally degenerate 4f-electron systems

The quadrupole orderings and lattice effects in 4f-electron systems with orbital degeneracy in rare earth compounds have been investigated by ultrasonic and thermal expansion measurements. A ferroquadrupole (FQ) O_xy-type ordering associated with a trigonal distortion in HoB₆ with a Γ₅ ground state is presented. The trigonal distortion in ordered phase IV Ce_xLa_1−xB₆ (x = 0.75 and 0.70) with a Γ₈ ground state indicates O_xy-type FQ ordering in phase IV. In both systems, HoB₆ and Ce_xLa_1−xB₆, C₄₄ anomalies are observed. In tetragonal HoB₂C₂, an ordered phase IV appears near a tetra-critical point, where the antiferroquadrupole phase II and antiferromagnetic phase III compete with each other. Noticeable ultrasonic attenuation and softening of elastic constants in phase IV of HoB₂C₂ due to quadrupole fluctuation with a slow relaxation time τ ∼ 7 × 10⁻⁹ s are found.