Odd-Parity Multipoles by Staggered Magnetic Dipole and Electric Quadrupole Orderings in CeCoSi

TL;DR

This paper explores the theoretical possibility of odd-parity multipole orderings in CeCoSi, revealing hidden multipoles associated with magnetic and electric orderings and their potential experimental signatures.

Contribution

It introduces a microscopic mean-field analysis showing how specific odd-parity multipoles emerge in CeCoSi's staggered magnetic and electric orderings, a novel insight.

Findings

Magnetic quadrupole induced by magnetic dipole ordering for large crystal-field splitting.

Electric toroidal quadrupole emerges from electric quadrupole ordering for small crystal-field splitting.

Predicted magneto-electric and elastic-electric effects related to odd-parity multipoles.

Abstract

We investigate a possibility of odd-parity multipole orderings in a locally noncentrosymmetric tetragonal compound CeCoSi. By performing symmetrical and microscopic mean-field analyses on a two-orbital tight-binding model, we propose potential odd-parity multipoles hidden in staggered antiferromagnetic and antiferroquadrupole orderings in CeCoSi. We show that $3z^2-r^2$ type of the magnetic quadrupole is induced by the staggered magnetic dipole ordering for a large crystal-field splitting between two orbitals, while $xy$ type of the electric toroidal quadrupole is emergent by the staggered electric quadrupole ordering for a small crystal-field splitting. Furthermore, we discuss a magneto-electric effect and elastic-electric effect due to the odd-parity multipoles, which will be useful to identify order parameters in CeCoSi.