Monopole holes in a partially ordered spin liquid

TL;DR

This paper explores the coexistence of magnetic order and spin liquid behavior in a dipolar spin system, introducing the concept of monopole holes as topological defects analogous to electron holes.

Contribution

It introduces the concept of monopole holes in a partially ordered spin liquid, extending the understanding of topological defects in systems with coexisting order and fluctuations.

Findings

Monopole holes are effectively coupled via Coulomb interactions.

Long-range order acts like a filled valence band, while the Coulomb spin liquid resembles an empty conduction band.

Dipolar interactions lift degeneracy by increasing flippable plaquettes, akin to a quantum dimer model.

Abstract

If spin liquids have been famously defined by what they are not, i.e. ordered, the past years have seen the frontier between order and spin liquid starting to fade, with a growing number of materials whose low-temperature physics cannot be explained without co-existence of (partial) magnetic order and spin fluctuations. Here we study an example of such co-existence in the presence of magnetic dipolar interactions, related to spin ice, where the order is long range and the fluctuations support a Coulomb gauge field. Topological defects are effectively coupled via energetic and entropic Coulomb interactions, the latter one being stronger than for the spin-ice ground state. Depending on whether these defects break the divergence-free condition of the Coulomb gauge field or the long-range order, they are respectively categorized as monopoles - as in spin ice - or monopole holes, in analogy with electron holes in semiconductors. The long-range order plays the role of a fully-occupied valence band, while the Coulomb spin liquid can be seen as an empty conducting band. These results are discussed in the context of other lattices and models which support a similar co-existence of Coulomb gauge field and long-range order. We conclude this work by explaining how dipolar interactions lift the spin liquid degeneracy at very low energy scale by maximizing the number of flippable plaquettes, in light of the equivalent quantum dimer model.