Research: Pseudo-Goldstone gaps amd order-by-quantum disorder

Order-by-disorder is a phenomenon whereby ordinary magnetically ordered ground states are selected by fluctuations in frustrated magnets. It is nicely exemplified in certain materials - the easy-plane pyrochlore Er₂Ti₂O₇ among them. Since order-by-disorder lies on the border between conventional magnetism and more exotic physics it offers cases where the traditional tools of many-body physics are stretched almost to breaking point but still allow one to address important questions about the underlying mechanism and phenomenology.

In this paper, the focus is on one of the consequences of order-by-disorder:  that certain zero energy spin wave modes in the semiclassical theory - called pseudo-Goldstone modes - acquire anonzero energy gap, once fluctuations are included, that may be seen in experiments. It was thought that the pseudo-Goldstone energy gap first makes an appearance in calculations only after including the leading effect of interactions between the spin waves -  calculations that are somewhat involved. This paper uncovers a previously hidden feature of the perturbation theory showing the leading contribution to the pseudo-Goldstone energy gap can, in fact, be computed exactly from a simple intuitive formula that obviates the need to consider interactions. This is of practical significance since this key aspect of the physics can be computed much more readily using this result and the paper includes calculations in a great many known instances of order-by-disorder including experimental examples such as Er2Ti2O7.

J. G. Rau, P. A. McClarty, and R. Moessner,
Pseudo-Goldstone Gaps and Order-by-Quantum Disorder in Frustrated Magnets,
Phys. Rev. Lett. 121, 237201 (2018)