Analytical theory of pyrochlore cooperative paramagnets

TL;DR

This paper develops an analytical approach to understanding the broad crossover regime in pyrochlore spin liquids, revealing how local tetrahedral interactions influence correlations and structure factors near phase transitions.

Contribution

It introduces a method extending the high-temperature expansion using a single-tetrahedron Hamiltonian to analyze correlation buildup in pyrochlore systems.

Findings

Analytical insights into the crossover from spin liquid to paramagnet.

Identification of eigenspace structure effects on correlation development.

Observation of coexistence of scattering features near phase transitions.

Abstract

The pyrochlore lattice is associated with several potential and actual spin liquid phases as a result of its strong geometric frustration. At finite temperature, these can exhibit an unusually broad cross-over regime to a conventional paramagnet. Here, we study this regime analytically by showing how a single-tetrahedron Hamiltonian can extrapolate beyond the first term of a high-temperature expansion and yield insights into the build-up of correlations. We discuss how this unusual behaviour is brought about by the structure of the eigenspaces of the coupling matrix. Further interesting behaviour can appear for parameter values located near phase transitions: we find coexistence of $(111)$ rods and $(220)$ peaks in the structure factor, as observed in neutron scattering experiments on Yb$_2$Ti$_2$O$_7$.