Quantum order by disorder or virtual crystal-field selection in Er_2Ti_2O_7? · revision history

Revision 2

Accepted · core change · record

Changes against revision 1:

Title · changed
Revision 1: Quantum order by disorder or virtual crystal-field selection in Er2Ti2O7?
Revision 2: Quantum order by disorder or virtual crystal-field selection in $\mathrm{Er_2Ti_2O_7}$?
Plain · changed
Revision 1: Er2Ti2O7 orders into one particular spin pattern although its main interactions treat a whole continuous family equally. Both quantum fluctuations and virtual excitations to higher atomic energy levels can pick that pattern, and their relative share is unsettled.
Revision 2: $\mathrm{Er_2Ti_2O_7}$ orders into one particular spin pattern although its main interactions treat a whole continuous family equally. Both quantum fluctuations and virtual excitations to higher atomic energy levels can pick that pattern, and their relative share is unsettled.
Precise · changed · core
Revision 1: For Er2Ti2O7 with anisotropic nearest-neighbor exchange $(J_{zz}, J_{pm}, J_{pmpm}, J_{zpm})$ fitted to neutron data, compute the energy splitting between the $\psi_2$ and $\psi_3$ states and the pseudo-Goldstone gap produced by (a) quantum zero-point fluctuations within the ground doublet and (b) virtual crystal-field excitations, and compare with the measured gap. An answer gives the fraction of the measured gap due to each mechanism.
Revision 2: For $\mathrm{Er_2Ti_2O_7}$ with anisotropic nearest-neighbor exchange $(J_{zz}, J_{pm}, J_{pmpm}, J_{zpm})$ fitted to neutron data, compute the energy splitting between the $\psi_2$ and $\psi_3$ states and the pseudo-Goldstone gap produced by (a) quantum zero-point fluctuations within the ground doublet and (b) virtual crystal-field excitations, and compare with the measured gap. An answer gives the fraction of the measured gap due to each mechanism.
Settled by
A calculation including both spin-wave zero-point energy and second-order crystal-field corrections, with exchange fitted to the full neutron spectrum, compared with the measured gap.
Kind
well-posed
Answer type
value
References
(empty)
Literature status
partially-resolved
Status note
A pseudo-Goldstone gap was observed (Ross et al., PRL 2014) as order by disorder predicts; Rau et al. (PRL 2016) showed virtual crystal-field fluctuations give a comparable selection.
Posed since
2012

Decisions