Multipole ordering in f-electron systems on the basis of a j-j coupling scheme

TL;DR

This paper models multipole ordering in f-electron systems on different lattice structures using a j-j coupling scheme, revealing distinct ordered states for sc, bcc, and fcc lattices through mean-field analysis.

Contribution

It introduces a microscopic modeling approach for multipole orderings in f-electron systems based on lattice-dependent effective models derived from a j-j coupling scheme.

Findings

sc lattice exhibits b3_{3g} antiferro-quadrupole and ferromagnetic transitions

bcc lattice shows b3_{2u} antiferro-octupole and ferromagnetic phases

fcc lattice undergoes a single transition to b3_{5u} octupole order

Abstract

We investigate microscopic aspects of multipole ordering in f-electron systems with emphasis on the effect of lattice structure. For the purpose, first we construct f-electron models on three kinds of lattices, simple cubic (sc), bcc, and fcc, by including f-electron hopping through (ff\sigma) bonding in a tight-binding approximation on the basis of a j-j coupling scheme. Then, an effective model is derived in the strong-coupling limit for each lattice structure with the use of second-order perturbation theory with respect to (ff\sigma). By applying mean-field theory to such effective models, we find different types of multipole ordered state depending on the lattice structure. For the sc lattice, a \Gamma_{3g} antiferro-quadrupole transition occurs at a finite temperature and as further lowering temperature, we find another transition to a ferromagnetic state. For the bcc lattice, a \Gamma_{2u} antiferro-octupole ordering occurs first, and then, a ferromagnetic phase transition follows it. Finally, for the fcc lattice, we find a single phase transition to the longitudinal triple-q \Gamma_{5u} octupole ordering.