Geometrically Frustrated Quadrupoles on the Pyrochlore Lattice and Generalized Spin Liquids

Frustrated magnetic insulators based on rare-earth f-electron elements are generically strongly spin-orbit coupled and exhibit highly anisotropic multipolar interactions. The common approach to simplify modeling such a complex systems is to project onto a low-energy crystal field doublet, deriving an effective-spin-1/2 Hamiltonian, replacing the complicated multipoles with effective dipoles. For many of the most enigmatic materials, particularly the non-Kramers pyrochlore compounds, the ground state doublet has mixed multipole character.

In this talk, I discuss recent progress in going beyond the effective dipolar Hamiltonian by studying the behavior of frustrated quadrupolar degrees of freedom. Using the pyrochlore lattice as a model system, we showcase novel phenomena in frustrated quadrupolar materials, building on intuition gained from the dipolar case and drawing anlogies to unixial and biaxial nematic liquids. We demonstrate generalized order-by-disorder ground state selection, as well as generalized spin liquids that realize emergent tensor gauge theories up to rank three, associated with fracton topological order.

Our findings have implications extending well beyond the pyrochlore and rare-earth contexts: we analyze the behavior of quadrupolar operators across different effective spin quantum numbers and show that their properties depend sensitively on spin magniutde, with S=1, 3/2, and 2 being special cases, while S>2 quadrupoles smoothly approach the infinite-S limit.