Order-by-Disorder in the XY Pyrochlore Antiferromagnet Revisited

Abstract

We investigate the properties of the XY pyrochlore antiferromagnet with local <111> planar anisotropy. We find the ground states and show that the configurational ground state entropy is subextensive. By computing the free energy due to harmonic fluctuations and by carrying out Monte Carlo simulations, we confirm earlier work indicating that the model exhibits thermal order-by-disorder leading to low temperature long-range order consisting of discrete magnetic domains. We compute the spin wave spectrum and show that thermal and quantum fluctuations select the same magnetic structure. Using Monte Carlo simulations, we find that the state selected by thermal fluctuations in this XY pyrochlore antiferromagnet can survive the addition of sufficiently weak nearest-neighbor pseudo-dipolar interactions to the spin Hamiltonian. We discuss our results in relation to the Er2Ti2O7 pyrochlore antiferromagnet.

13 pages, 6 figures

References in corpus (15)

• Why spin ice obeys the ice rules
• Definitive Evidence for Order-by-Quantum-Disorder in Er2Ti2O7
• Quantum order by disorder and accidental soft mode Er2Ti2O7
• Is the Yb2Ti2O7 pyrochlore a quantum spin ice?
• Rods of Neutron Scattering Intensity in Yb2Ti2O7: Compelling Evidence for Significant Anisotropic Exchange in a Magnetic Pyrochlore Oxide
• Structural distortion and the spin liquid state in Tb2Ti2O7
• Magnetic ordering in Gd2Sn2O7: the archetypal Heisenberg pyrochlore antiferromagnet
• Magnetic order, magnetic correlations and spin dynamics in the pyrochlore antiferromagnet Er2Ti2O7
• Energetic selection of ordered states in a model of the Er2Ti2O7 frustrated pyrochlore XY antiferromagnet
• Partial order from disorder in a classical pyrochlore antiferromagnet
• Thermodynamic properties of the Yb2Ti2O7 pyrochlore as a function of temperature and magnetic field: validation of a quantum spin ice exchange Hamiltonian
• Phase Transition and Thermal Order-by-Disorder in the Pyrochlore Quantum Antiferromagnet Er2Ti2O7: a High-Temperature Series Expansion Study
• Evidence for gapped spin-wave excitations in the frustrated Gd2Sn2O7 pyrochlore antiferromagnet from low-temperature specific heat measurements
• Low temperature specific heat and possible gap to magnetic excitations in the Heisenberg pyrochlore antiferromagnet Gd2Sn207
• Palmer-Chalker correlations in the XY pyrochlore antiferromagnet Er2Sn2O7

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