Classical symmetry enriched topological orders and distinct monopole charges for dipole-octupole spin ices

TL;DR

This paper distinguishes between dipolar and octupolar spin ices by analyzing magnetic monopole charges, providing a classical method to identify different symmetry enriched topological orders in pyrochlore materials.

Contribution

It predicts that dipolar spin ice has finite magnetic monopole charges while octupolar spin ice has zero charge, offering a classical diagnostic tool for topological order.

Findings

Dipolar spin ice monopoles carry finite magnetic charge.

Octupolar spin ice monopoles have zero magnetic charge.

This distinction can resolve debates on Ce$_2$Sn$_2$O$_7$'s nature.

Abstract

Distinct symmetry enriched topological orders often do not have classical distinctions. Motivated by the recent progress on the pyrochlore spin ice materials based on the dipole-octupole doublets, we argue that the dipolar spin liquid and the octupolar spin liquid can be distinguished through the magnetic charges of the magnetic monopoles in the classical spin ice regime. It is observed and predicted that the long-range dipole-dipole interaction renders the magnetic monopole of the dipolar spin ice a finite magnetic charge via the dumbbell picture even in the classical regime. For the octupolar spin ice, however, a zero magnetic charge is expected from this mechanism in the classical regime. We expect this smoking-gun observation to resolve the debate on the nature of Ce$_2$Sn$_2$O$_7$, and more broadly, this work may inspire further experiments and thoughts on the Ce-pyrochlore spin liquids, Nd-pyrochlore antiferromagnets, Er-based spinels, and the distinct properties of the emergent quasiparticles in various symmetry enriched topological phases.