Multipolar order and excitations in rare-earth boride Kondo systems

We review the cubic rare-earth boride series which displays diverse electronic states like localized 4f electron multiplets split by the crystal electric field (CEF), itinerant heavy-fermion quasiparticle bands of the Kondo lattice as well as gapped Kondo insulator or mixed-valent semiconductor states. Fairly exotic states may appear due to the 'hidden' order of multipoles carried by degenerate CEF multiplets, in addition to magnetic order present in many RB6 (R = rare earth) compounds. Most prominent are CeB6 and its La-diluted alloys which exhibit antiferro-quadrupolar and octupolar ordering enabled by the cubic G8 quartet state. The associated collective excitations are multipolar waves with a dispersion characteristic for the underlying order and accessible by inelastic neutron scattering. This localized multipolar-moment picture of R-borides is complemented by the itinerant Kondo-lattice approach. Collective spin exciton modes inside the hybridization gap around symmetry points of the Brillouin zone may appear. This has been observed in heavy-fermion metal CeB6 and in particular in the Kondo insulators YbB12 and SmB6. The latter is also the prime candidate for a strongly correlated topological insulator.