Itinerant magnetic multipole moments of rank five, triakontadipoles, as the hidden order in URu$_{2}$Si$_{2}$

TL;DR

This paper predicts a hidden order in URu$_{2}$Si$_{2}$ characterized by rank five magnetic multipole moments, specifically triakontadipoles, which break time reversal symmetry without producing magnetic moments.

Contribution

It introduces a novel theoretical identification of high-rank magnetic multipole moments as the hidden order parameter in URu$_{2}$Si$_{2}$ using LDA+$U$ calculations and multipole tensor analysis.

Findings

Identification of rank five multipole moments as the hidden order

Demonstration of multipole moments coexisting with magnetic moments in actinides

Analysis of time reversal symmetry breaking due to multipole moments

Abstract

A broken symmetry ground state without any magnetic moments has been calculated by means of local-density-approximation to density functional theory plus a local exchange term, the so-called LDA+$U$ approach, for URu$_{2}$Si$_{2}$. The solution is analysed in terms of a multipole tensor expansion of the itinerant density matrix and is found to be a non-trivial magnetic multipole. Analysis and further calculations show that this type of multipole enters naturally in time reversal breaking in presence of large effective spin-orbit coupling and co-exists with magnetic moments for most magnetic actinides