Energetic selection of ordered states in a model of the Er2Ti2O7 frustrated pyrochlore XY antiferromagnet

Abstract

We consider the possibility that the discrete long-range ordered states of Er2Ti2O7 are selected energetically at the mean field level as an alternative scenario that suggests selection via thermal fluctuations. We show that nearest neighbour exchange interactions alone are not sufficient for this purpose, but that anisotropies arising from excited single ion crystal field states in Er2Ti2O7, together with appropriate anisotropic exchange interactions, can produce the required long range order. However, the effect of the single ion anisotropies is rather weak so we expect thermal or quantum fluctuations, in some guise, to be ultimately important in this material. We reproduce recent experimental results for the variation of magnetic Bragg peak intensities as a function of magnetic field.

8 pages. 7 figures. Version to be published for Proceedings of HFM2008 Conference. Slight modifications compared to Version #1

References in corpus (4)

• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Dynamically-Induced Frustration as a Route to a Quantum Spin Ice State in Tb2Ti2O7 via Virtual Crystal Field Excitations and Quantum Many-Body Effects
• Structural distortion and the spin liquid state in Tb2Ti2O7
• Partial order from disorder in a classical pyrochlore antiferromagnet

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• Bosonic Many-body Theory of Quantum Spin Ice
• Order by Disorder and Energetic Selection of the Ground State in the XY Pyrochlore Antiferromagnet Er2Ti2O7. An Inelastic Neutron Scattering Study
• Effect of Chemical Pressure on the Crystal Electric Field States of Erbium Pyrochlore Magnets
• Order-by-disorder near criticality in $XY$ pyrochlore magnets
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• Local Susceptibility of the Yb2Ti2O7 Rare Earth Pyrochlore Computed from a Hamiltonian with Anisotropic Exchange
• Magnetic dilution and domain selection in the XY pyrochlore antiferromagnet Er${}_2$Ti${}_2$O${}_7$
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• Realization of fractonic quantum phases in the breathing pyrochlore lattice
• 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
• Higher-Rank Spin Liquids and Spin Nematics from Competing Orders in Pyrochlore Magnets
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• Magnetic field tuning of crystal field levels and vibronic states in Spin-ice Ho${}_2$Ti${}_2$O${}_7$ observed in far-infrared reflectometry
• Intertwined Magnetic Dipolar and Electric Quadrupolar Correlations in the Pyrochlore Tb${}_2$Ge${}_2$O${}_7$