Quantum Order by Disorder in Frustrated Diamond Spinel Antiferromagnets

We study the effect of quantum fluctuations on the frustrated diamond lattice antiferromagnet where frustration arises from the presence of second neighbor interactions. Such an antiferromagnet describes the magnetic properties of spinel AB$_2$X$_4$ where magnetic ions are located on A-sites. We compare the resulting phase diagram of the quantum model and that of its classical counterpart, and discuss the difference/similarity between the quantum and thermal order by disorder phenomena. Implications for experiments on CoRh$_2$O$_4$, Co$_3$O$_4$ and MnSc$_2$S$_4$ will be discussed.