Order by virtual crystal field fluctuations in pyrochlore XY antiferromagnets

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.

16 pages, 6 figures

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• Experimental Insights into Ground State Selection of Quantum XY Pyrochlores
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• Magnetic dilution and domain selection in the XY pyrochlore antiferromagnet Er${}_2$Ti${}_2$O${}_7$
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• Upper branch magnetism in quantum magnets: Collapses of excited levels and emergent selection rules
• A neutron scattering measurement of crystalline-electric fields in magnesium rare-earth selenide spinels
• Control of effective free energy landscape in a frustrated magnet by a field pulse
• Pseudo-Spin Versus Magnetic Dipole Moment Ordering in the Isosceles Triangular Lattice Material K${}_3$Er(VO${}_4$)${}_2$
• Field induced phase diagram of the XY pyrochlore antiferromagnet Er${}_2$Ti${}_2$O${}_7$
• Experimental evidence for field induced emergent clock anisotropies in the XY pyrochlore Er${}_2$Ti${}_2$O${}_7$
• Order-by-disorder without quantum zero-point fluctuations in the pyrochlore Heisenberg ferromagnet with Dzyaloshinskii-Moriya interactions
• Multi-phase competition in quantum $XY$ pyrochlore antiferromagnet CdYb${}_2$Se${}_4$: zero and applied magnetic field study
• Beyond Single Tetrahedron Physics of Breathing Pyrochlore Compound Ba3Yb2Zn5O11
• Traversing the pyrochlore stability diagram; microwave-assisted synthesis and discovery of mixed B-site Ln${}_2$InSbO${}_7$ family
• Monte Carlo study on the detection of classical order by disorder in real antiferromagnetic Ising pyrochlores
• Anisotropic excitonic magnetism from discrete ${\mathrm{C}}_4$ symmetry in CeRhIn${}_5$
• LiHoF4 as a spin-half non-standard quantum Ising system
• Intertwined Magnetic Dipolar and Electric Quadrupolar Correlations in the Pyrochlore Tb${}_2$Ge${}_2$O${}_7$
• Low-temperature high-frequency dynamic magnetic susceptibility of classical spin-ice Dy${}_2$Ti${}_2$O${}_7$
• Phononic enhancement and detection of hidden spin-nematicity and dynamics in quantum magnets
• Programmable order by disorder effect and underlying phases through dipolar quantum simulators