Research: Infinite-range interactions and irrational magnetic moments in a classical spin liquid

Classical spin liquids (CSLs) are highly correlated, yet disordered, phases of magnetic matter. They have a few exotic properties which distinguish them from ordinary paramagnets.

Firstly, when clusters of magnetic vacancies are introduced into a CSL, they add a contribution to the magnetic susceptibility which looks like a completely free spin with a fractional magnetic moment.

Secondly, the correlations of CSLs, are described by gauge theories, like those which describe the fundamental forces of nature. The most-studied CSLs are those described by the gauge theory of electromagnetism, but more recently examples have been discovered described by “rank-2” versions of electromagnetism, where electric and magnetic fields are matrices of vectors.

In this work we make two important developments to the theory of CSLs. Firstly, we show that the fractional magnetic moments can have irrational size, and their size may be tuned by tuning microscopic parameters of the Hamiltonian. Secondly, we work out the effective interactions between vacancy clusters in a rank-2 spin liquid, which are mediated by the underlying gauge theory. We show that these interactions do not decay with distance: they are equally strong whether the vacancies are near or far.

R. Flores-Calderon, O. Benton, R. Moessner,
Irrational Moments and Signatures of Higher-Rank Gauge Theories in Diluted Classical Spin Liquids,
Phys. Rev. Lett. 133, 106501 (2024) (arXiv)