Multipole Orders and Fluctuations in Strongly Correlated Electron Systems

In this paper we review experimental and theoretical results on higher electronic multipoles in solids with strong correlations. Recent experiments and their theoretical interpretation have confirmed the ordering of octupoles and even higher multipoles in rare-earth and actinide compounds with f electrons. The concept of multipoles is critically examined in point groups where spherical tensors of different ranks mix. Using a phenomenological approach, we demonstrate how linear and nonlinear couplings of different multipoles lead to rich phase diagrams and anomalies in physical observables. As actual representative systems, we first consider CexLa1-xB6, for which resonant X-ray scattering probed the octupole order for the first time, and NpO2, where quadrupoles induced by the octupole order have been observed. We then consider a class of compounds called skutterudites its the most convenient system for systematic study. Particular emphasis is placed on the ordering of scalar components from fourth-rank tensors (hexadecapoles) and sixth-rank tensors (hexacontatetrapoles). A comparison of a skutterudite PrFe4P12 and URu2Si2 is made, where much fewer carriers remain in the ordered states than in the disordered phase. The even number (two) off electrons per site in Pr3+ or U4+ makes the system free front the Kramers degeneracy, in contrast to standard models for Mott transitions. Hence, it is pointed out that multipole orders, particularly the scalar order, should provide a new route for studying the dichotomy between the itinerant and localized behaviors of electrons.