Theory of paramagnetic scattering in highly frustrated magnets with long-range dipole-dipole interactions: The case of the Tb2Ti2O7, pyrochlore antiferromagnet

Abstract

Highly frustrated antiferromagnets composed of magnetic rare-earth moments are currently attracting much experimental and theoretical interest. Rare-earth ions generally have small exchange interactions and large magnetic moments. This makes it necessary to understand in detail the role of long-range magnetic dipole-dipole interactions in these systems, in particular in the context of spin-spin correlations that develop in the paramagnetic phase, but are often unable to condense into a conventional long-range magnetic ordered phase. This scenario is most dramatically emphasized in the frustrated pyrochlore antiferromagnet material Tb2Ti207 which does not order down to 50 mK despite an antiferromagnetic Curie-Weiss temperature Tcw ~ -20 K. In this paper we report results from mean-field theory calculations of the paramagnetic elastic neutron-scattering in highly frustrated magnetic systems with long-range dipole-dipole interactions, focusing on the Tb2Ti207 system. Modeling Tb2Ti207 as an antiferromagnetic <111> Ising pyrochlore, we find that the mean-field paramagnetic scattering is inconsistent with the experimentally observed results. Through simple symmetry arguments we demonstrate that the observed paramagnetic correlations in Tb2Ti207 are precluded from being generated by any spin Hamiltonian that considers only Ising spins, but are qualitatively consistent with Heisenberg-like moments. Explicit calculations of the paramagnetic scattering pattern for both <111> Ising and Heisenberg models, which include finite single-ion anisotropy, support these claims. We offer suggestions for reconciling the need to restore spin isotropy with the Ising like structure suggested by the single-ion properties of Tb3+.

arXiv commentRevtex4, 18 pages, 3 eps figures (2 color figures). Change in title and emphasis on Tb2Ti2O7 only. Spin-ice material removed, to appear in a later publication

References in corpus (26)

• Spin Ice State in Frustrated Magnetic Pyrochlore Materials
• Emergent excitations in a geometrically frustrated magnet
• Dipolar Interactions and Origin of Spin Ice in Ising Pyrochlore Magnets
• Properties of a classical spin liquid: the Heisenberg pyrochlore antiferromagnet
• Low-temperature properties of classical, geometrically frustrated antiferromagnets
• Local spin resonance and spin-Peierls-like phase transition in a geometrically frustrated antiferromagnet
• Superconductivity at 1 K in Cd2Re2O7
• Spin Correlations in Ho${}_2$Ti${}_2$O${}_7$: a Dipolar Spin Ice System
• Magnetic and Thermodynamic Properties of the Collective Paramagnet-Spin Liquid Pyrochlore Tb2Ti2O7
• Static Critical Behavior of the Spin-Freezing Transition in the Geometrically Frustrated Pyrochlore Antiferromagnet Y2Mo2O7
• First Order Transition in the Spin Dynamics of Geometrically Frustrated Yb2Ti2O7
• Order induced by dipolar interactions in a geometrically frustrated antiferromagnet
• Order in the Heisenberg Pyrochlore: The Magnetic Structure of Gd2Ti2O7
• Muon Spin Relaxation Investigation of the Spin Dynamics of Geometrically Frustrated Antiferromagnets Y2Mo2O7 and Tb2Mo2O7 Static Critical Behavior of the Spin-Freezing
• Multiple Field-Induced Phase Transitions in a Geometrically-Frustrated Dipolar Magnet - Gd2Ti2O7
• Neutron scattering study of dipolar spin ice Ho_2Sn_2O_7: Frustrated pyrochlore magnet
• Static Correlation and Dynamical Properties of Tb3+-moments in Tb2Ti2O7 -Neutron Scattering Study-
• Understanding Paramagnetic Spin Correlations in the Spin-Liquid Pyrochlore Tb2Ti2O7
• Short-range Magnetic interactions in the Spin-Ice compound Ho${}_2$Ti${}_2$O${}_7$
• Quantum spin fluctuations in the dipolar Heisenberg-like rare earth pyrochlores
• The Spin Liquid State of the Tb2Ti2O7 Pyrochlore Antiferromagnet: A Puzzling State of Affairs
• Neutron Scattering Study of the Spin Correlation in the Spin Ice System Ho2Ti2O7
• Field-Driven Transitions in the Dipolar Pyrochlore Antiferromagnet Gd${}_2$Ti${}_2$O${}_7$
• Spin Liquid Phase in the Pyrochlore Antiferromagnet
• Origin of Spin Ice Behavior in Ising Pyrochlore Magnets with Long Range Dipole Interactions: an Insight from Mean-Field Theory
• Spin-Ice and Other Frustrated Magnets on the Pyrochlore Lattice

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