Influence of lattice structure on multipole interactions in ${\Gamma }_3$ non-Kramers doublet systems

Abstract

We study the multipole interactions between $f^2$ ions with the ${\Gamma }_3$ non-Kramers doublet ground state under a cubic crystalline electric field. We construct the ${\Gamma }_3$ doublet state of the electrons with the total angular momentum $j=5/2$. By applying the second-order perturbation theory with respect to the intersite hopping, we derive the multipole interactions. We obtain a quadrupole interaction for a simple cubic lattice, an octupole interaction for a bcc lattice, and both quadrupole and octupole interactions for an fcc lattice. We also discuss general tendencies of the multipole interactions depending on the lattice structure by comparing the results with those for the ${\Gamma }_8$ quartet systems of $f^1$ ions.

arXiv comment7 pages, 2 figures, to be published in Phys. Rev. B

References in corpus (16)

• Heavy Fermion Superconductivity in the Quadrupole Ordered State of PrV2Al20
• Triple-q octupolar ordering in NpO_2
• Superconductivity in the Ferroquadrupolar State in the Quadrupolar Kondo Lattice PrTi${}_2$Al${}_{20}$
• Observation of Modulated Quadrupolar Structures in PrPb3
• Orbital dynamics in ferromagnetic transition metal oxides
• Simultaneous Superconducting and Antiferroquadrupolar Transitions in PrRh${}_2$Zn${}_{20}$
• Construction of microscopic model for f-electron systems on the basis of j-j coupling scheme
• Octupole Ordering Model for the Phase IV of CexLa1-xB6
• Detection of Neutron Scattering from Phase IV of Ce0.7La0.3B6: A Confirmation of the Octupole Order
• Microscopic theory of multipole ordering in NpO2
• Lattice Distortion and Octupole Ordering Model in CexLa1-xB6
• Analysis of f-p model for octupole ordering in NpO2
• Effective Crystalline Electric Field Potential in a j-j Coupling Scheme
• Multipole ordering in f-electron systems on the basis of a j-j coupling scheme
• Complex orbital state in manganites
• Orbital effects in manganites

Cited by in corpus (16)

• First-principles theory of magnetic multipoles in condensed matter systems
• Octupolar order in d-orbital Mott insulators
• Exchange interactions, Jahn-Teller coupling, and multipole orders in pseudospin one-half $5{\mathbf{d}}^2$ Mott insulators
• Two-channel Kondo Effect Emerging from Nd Ions
• Field-Induced Switching of Ferro-Quadrupole Order Parameter in PrTi2Al20
• Quadrupole Orders on the fcc Lattice
• Triple-$q$ quadrupole-octupole order scenario for PrV${}_2$Al${}_{20}$
• Quadrupole partial orders and triple-$q$ states on the face-centered cubic lattice
• Anisotropic Superconductivity Emerging from the Orbital Degrees of Freedom in a ${\Gamma }_3$ Non-Kramers Doublet System
• Mean-field Study of Antiferromagnetic and Antiferroquadrupolar Orderings in Tetragonal CeCoSi
• Kondo effect in the seven-orbital Anderson model hybridized with ${\Gamma }_8$ conduction electrons
• Nematic and time-reversal breaking superconductivities coexisting with quadrupole order in a ${\Gamma }_3$ system
• Quantum Critical Point between Two-Channel Kondo and Fermi-Liquid Phases
• Octupolar edge state in an $e_g$ orbital system on a square lattice
• Flat Surface State with Octupole Moment in an $e_g$ Orbital System on a Simple Cubic Lattice
• Microscopic Theory of ${\Gamma }_3$ Quadrupole Ordering in Pr Compounds on the Basis of a $j$-$j$ Coupling Scheme