Order by virtual crystal field fluctuations in pyrochlore XY antiferromagnets

Jeffrey G. Rau, Sylvain Petit, and Michel J. P. Gingras
Phys. Rev. B 93, 184408 – Published 10 May 2016

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 ψ2 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 comment on possible tests of this scenario and discuss implications for other order-by-disorder candidates in rare-earth magnets.

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  • Received 18 September 2015

DOI:https://doi.org/10.1103/PhysRevB.93.184408

©2016 American Physical Society

Authors & Affiliations

Jeffrey G. Rau1, Sylvain Petit2, and Michel J. P. Gingras1,3,4,5,6

  • 1Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
  • 2CEA, Centre de Saclay, DSM/IRAMIS/Laboratoire Leon Brillouin, F-91191 Gif-sur-Yvette, France
  • 3Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
  • 4Canadian Institute for Advanced Research, 180 Dundas Street West, Suite 1400, Toronto, Ontario M5G 1Z8, Canada
  • 5Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada
  • 6TRIUMF, Theory Group, 4004 Wesbrook Mall, Vancouver, British Columbia V6T 2A3, Canada

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Vol. 93, Iss. 18 — 1 May 2016

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