Multipole Orders and Fluctuations in Strongly Correlated Electron Systems

Abstract

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 Ce x La 1Àx B 6 , for which resonant X-ray scattering probed the octupole order for the first time, and NpO 2 , where quadrupoles induced by the octupole order have been observed. We then consider a class of compounds called skutterudites as 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 PrFe 4 P 12 and URu 2 Si 2 is made, where much fewer carriers remain in the ordered states than in the disordered phase. The even number (two) of f electrons per site in Pr 3þ or U 4þ makes the system free from 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.

Magnetic field dependence of the neutron spin resonance inCeB6

“…2. It is remarkable that the magnon is more intense around the Γ (110) point than at the equivalent Γ (001) or Γ (000) positions [49], suggesting an anomalous nonmonotonic behavior of the dynamic form factor that is characteristic of multipolar moments (for conventional dipolar moments, it would decrease monotonically with |Q|) [50][51][52]. A magnetic field of 2.5 T [ Fig.…”

Cluster multipole theory for anomalous Hall effect in antiferromagnets

“…III, we introduce CMP moments as order parameters defined for a cluster of atoms, which is a natural generalization of the local magnetic moments for atoms. The CMP characterizes the non-collinear AFM structure as analogous to the atomic magnetic multipole moments characterizing the local magnetic distribution [24][25][26][27][28][29] . We show that the AHE of Mn 3 Ir and Mn 3 Z is associated with the cluster octupole moments which belong to the same symmetry with the magnetic dipole moments.…”

Electric Octupole Order in Bilayer Ruthenate Sr3Ru2O7

“…Exotic quantum phases induced by the spin-orbit coupling have been attracting recent interest in various fields of condensed matter physics, owing to their fascinating phenomena such as noncentrosymmetric superconductivity, 1 chiral magnetism, 2, 3 multipole order, 4 multiferroics, 5 spintronics, 6,7 and topological quantum phases. [8][9][10] Intriguing properties appear in the electronic structure, transport, optics, magnetic excitation, and so forth, as a result of the spin-orbit coupling and symmetry breaking.…”

“…Although various high-rank multipole orders have been proposed for d-and f-electron systems, 4 previous studies have focused on the even-parity multipole, such as the electric quadruple and the magnetic octupole. We can define the counterpart, namely, the odd-parity multipole.…”