Quantum order by disorder in frustrated diamond lattice antiferromagnets

TL;DR

This paper develops a quantum theory for frustrated diamond lattice antiferromagnets, revealing a phase diagram with multiple ordered phases and matching experimental specific heat data, supporting the presence of spiral orderings.

Contribution

It introduces a quantum fluctuation-driven phase diagram for frustrated diamond lattice antiferromagnets, predicting specific spiral orderings consistent with experimental data.

Findings

Six phases with coplanar spiral orderings identified.

Excellent agreement between theoretical specific heat and experimental data.

Prediction of $(k,k,0)$-spiral ordering in several compounds.

Abstract

We present a quantum theory of frustrated diamond lattice antiferromagnets. Considering quantum fluctuations as the predominant mechanism relieving spin frustration, we find a rich phase diagram comprising of six phases with coplanar spiral ordering in addition to the N\'eel phase. By computing the specific heat of these ordered phases, we obtain a remarkable agreement between $(k,k,0)$-spiral ordering and the experimental specific heat data for the diamond lattice spinel compounds MnSc$_2$S$_4$, Co$_3$O$_4$ and CoRh$_2$O$_4$, i.e. specific heat data is a strong evidence for $(k,k,0)$-spiral ordering in all of these materials. This prediction can be tested in future neutron scattering experiments on Co$_3$O$_4$ and CoRh$_2$O$_4$, and is consistent with existing neutron scattering data on MnSc$_2$S$_4$. Based on this agreement we infer a monotonically increasing relationship between frustration and the strength of quantum fluctuations.