# Influence of lattice structure on multipole interactions in $\Gamma_3$ non-Kramers doublet systems

## TL;DR

This paper investigates how different lattice structures influence multipole interactions in $ ext{f}^2$ ions with a $ ext{Gamma}_3$ non-Kramers doublet ground state, revealing structure-dependent quadrupole and octupole interactions.

## Contribution

It derives the specific multipole interactions for cubic, bcc, and fcc lattices using perturbation theory, highlighting the impact of lattice geometry on these interactions.

## Key findings

- Quadrupole interaction in simple cubic lattice
- Octupole interaction in bcc lattice
- Both quadrupole and octupole interactions in fcc lattice

## 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.