Electronic higher multipoles in solids

This tutorial review discusses basic features of electronic multipoles and their ordering phenomena. Starting with classification of electric and magnetic higher multipoles under spherical symmetry, we proceed to two representative cases with strong spin-orbit interaction. First, staggered octupole orders in Ce_1-xLa_xB₆ and SmRu₄P₁₂ are discussed using the crystalline electric field states. Secondly, a scalar component of even higher multipoles in Pr skutterudites is studied where ordering of fourth-rank tensor (hexadecapole) and sixth-rank one (hexacontatetrapole) has been observed. Possibility of a reentrant transition from the multipole ordered state is discussed. Briefly mentioned are multipole aspects of Pomeranchuk instability of itinerant electrons and collective motion of nucleus. It is argued that the multipoles provide a new framework to study the metal-insulator transition.