Multipole ordering inf-electron systems on the basis of aj−jcoupling scheme

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 (f f σ) 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 (f f σ). 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 Γ3g 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 Γ2u antiferrooctupole 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 Γ5u octupole ordering.

Hidden order and multipolar exchange striction in a correlated f -electron system

“…There is a multitude of possible high-rank odd order parameters realizable within the = 9/2 ground-state multiplet of Np 4+ ( = 3, 5, 7; i.e., octupolar, triakontadipolar, etc.). A lot of effort has been directed over the last two decades ( 21 , 23 , 24 , 26 – 29 ) to identify a possible primary order able to reconcile various experimental facts. In particular, assumption of a triakontadipolar antiferromagnetic (AF) 3 order of the symmetry was shown ( 24 , 25 , 30 ) to lead to the best agreement with X-ray scattering and inelastic neutron scattering (INS) spectra.…”

Key Role of Hybridization between Actinide 5<i>f</i> and Oxygen 2<i>p</i> Orbitals for Electronic Structure of Actinide Dioxides

“…In fact, the octupole ordering has been strongly suggested by 17 O-NMR experiment [13] and also by inelastic neutron scattering study [14]. As for the microscopic origin of such higher-order multipole ordering, it has been shown that octupole order is stabilized by the orbitaldependent superexchange interaction, and obtained by the second-order perturbation of 5f electron hopping in the Г 8 degenerate Hubbard model on a fcc lattice [15][16][17]. Recently, significant contribution of dotriacontapole moment has been also pointed out [18,19].…”

Quadrupolar spin liquid, octupolar Kondo coupling and odd-frequency superconductivity in an exactly solvable model

“…The spin-orbit coupling splits the energy levels into a higher-energy j eff = 1 2 doublet and the low-lying j eff = 3 2 quadruplet [9]. Alternatively, we may consider rare earth ions which have a quartet ground state in an octahedral crystal field [25,26].…”

“…The higher value of j eff allows for multipolar interactions which can promote hidden multipolar orders or even quantum spin-orbital liquid phases [19][20][21][22][23]. Multipolar interactions also play an important role in rare-earth systems [24][25][26][27][28], where electrons in the fshell are much more localized and have stronger spinorbit coupling than d electrons in transition metal compounds. Indeed, rare-earth magnets analogous to j eff = 1 2 Kitaev materials have been proposed recently [29][30][31].…”