Order by virtual crystal field fluctuations in pyrochlore XY antiferromagnets

TL;DR

This paper demonstrates that virtual crystal field fluctuations play a significant and competitive role in the order-by-disorder mechanism in pyrochlore XY antiferromagnets, particularly in Er2Ti2O7, challenging previous assumptions about their insignificance.

Contribution

The study reveals that virtual crystal field fluctuations are substantial and can rival quantum fluctuations in selecting the ground state, with implications for understanding order-by-disorder in rare-earth magnets.

Findings

Virtual crystal field fluctuations are significant in Er2Ti2O7.

The experimentally observed psi2 state is explained by these fluctuations.

The excitation gap and spin-wave spectrum are accurately reproduced.

Abstract

Conclusive evidence of order by disorder is scarce in real materials. Perhaps one of the strongest cases presented has been for the pyrochlore XY antiferromagnet Er2Ti2O7, with the ground state selection proceeding by order by disorder induced through the effects of quantum fluctuations. This identification assumes the smallness of the effect of virtual crystal field fluctuations that could provide an alternative route to picking the ground state. Here we show that this order by virtual crystal field fluctuations is not only significant, but competitive with the effects of quantum fluctuations. Further, we argue that higher-multipolar interactions that are generically present in rare-earth magnets can dramatically enhance this effect. From a simplified bilinear-biquadratic model of these multipolar interactions, we show how the virtual crystal field fluctuations manifest in Er2Ti2O7 using a combination of strong coupling perturbation theory and the random phase approximation. We find that the experimentally observed psi2 state is indeed selected and the experimentally measured excitation gap can be reproduced when the bilinear and biquadratic couplings are comparable while maintaining agreement with the entire experimental spin-wave excitation spectrum. Finally, we comments on possible tests of this scenario and discuss implications for other order-by-disorder candidates in rare-earth magnets.