Ordering in a frustrated pyrochlore antiferromagnet proximate to a spin liquid

TL;DR

This paper investigates possible low-temperature ordered phases in a pyrochlore antiferromagnet near a quantum spin liquid state, identifying nine phases with symmetry breaking and proposing a field theory for the critical transition.

Contribution

It provides a comprehensive analysis of ordered phases near a U(1) quantum spin liquid in pyrochlore systems, including a symmetry-based classification and a field theory for the phase transition.

Findings

Identified nine possible ordered phases with enlarged unit cells.

Connected the simplest phase to previously studied magnetization plateau states.

Proposed a field theory describing the critical transition from spin liquid to ordered phase.

Abstract

We perform a general study of spin ordering on the pyrochlore lattice with a 3:1 proportionality of two spin polarizations. Equivalently, this describes valence bond solid conformations of a quantum dimer model on the diamond lattice. We determine the set of likely low temperature ordered phases, on the assumption that the ordering is weak, i.e the system is close to a ``U(1)'' quantum spin liquid in which the 3:1 proportionality is maintained but the spins are strongly fluctuating. The nature of the 9 ordered states we find is determined by a ``projective symmetry'' analysis. All the phases exhibit translational and rotational symmetry breaking, with an enlarged unit cell containing 4 to 64 primitive cells of the underlying pyrochlore. The simplest of the 9 phases is the same ``R'' state found earlier in a theoretical study of the ordering on the magnetization plateau in the $S=3/2$ materials \cdaf and \hgaf. We suggest that the spin/dimer model proposed therein undergoes a direct transition from the spin liquid to the R state, and describe a field theory for the universal properties of this critical point, at zero and non-zero temperatures.