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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 Tb2Ti2O7, 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 Tb2Ti2O7 system. Modeling Tb 2Ti2O7 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 Tb 2Ti2O7 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+.
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Despite the availability of a spin Hamiltonian for the Gd3Ga5O12 garnet (GGG) for over 25 years, there has so far been little theoretical insight regarding the many unusual low temperature properties of GGG. Here we investigate GGG in zero magnetic field using mean-field theory. We reproduce the spin liquid-like correlations and, most importantly, explain the positions of the sharp peaks seen in powder neutron diffraction experiments. We show that it is crucial to treat accurately the long-range nature of the magnetic dipolar interactions to allow for a determination of the small exchange energy scales involved in the selection of the experimental ordering wave vector. Our results show that the incommensurate order in GGG is classical in nature, intrinsic to the microscopic spin Hamiltonian and not caused by weak disorder. © 2006 The American Physical Society.
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Dynamic Hubbard models describe relaxation of atomic orbitals when electrons are added to already occupied orbitals, a phenomenon that is not present in the conventional Hubbard model and that may play a role in superconductivity. We use the determinant algorithm to study the properties of a particular dynamic Hubbard model on a two-dimensional square lattice. We report preliminary results for a set of correlation functions, and our data are compared to results from the standard Hubbard model. We find that a dynamic interaction enhances the pair-field susceptibility, signaling the possible on-set of a superconducting phase. © 2006 American Institute of Physics.
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Reentrance, the return of a system from an ordered phase to a previously encountered less-ordered one as a controlled parameter is continuously varied, is a recurring theme found in disparate physical systems, yet its microscopic cause is often not investigated thoroughly. Here, through detailed characterization and theoretical modeling, we uncover the microscopic mechanism behind reentrance in the strongly frustrated pyrochlore antiferromagnet Er2Sn2O7. We use single crystal heat capacity measurements to expose that Er2Sn2O7 exhibits multiple instances of reentrance in its magnetic field B vs temperature T phase diagram for magnetic fields along three cubic high symmetry directions. Through classical Monte Carlo simulations, mean field theory, and classical linear spin-wave expansions, we argue that the origins of the multiple occurrences of reentrance observed in Er2Sn2O7 are linked to soft modes. These soft modes arise from phase competition and enhance thermal fluctuations that entropically stabilize a specific ordered phase, resulting in an increased transition temperature for certain field values and thus the reentrant behavior. Our work represents a detailed examination into the mechanisms responsible for reentrance in a frustrated magnet and may serve as a template for the interpretation of reentrant phenomena in other physical systems. © 2021 American Physical Society.
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Dy2Ti2O7 has been advanced as an ideal spin ice material. We present a neutron scattering investigation of a single-crystal sample of 162Dy2Ti2O 7. The scattering intensity has been mapped in zero applied field in the h,h,l and h,k,0 planes of reciprocal space at temperatures between 0.05 and 20 K. The measured diffuse scattering has been compared with that predicted by the dipolar spin ice model. The comparison is good, except at the Brillouin-zone boundaries where extra scattering appears in the experimental data. It is concluded that the dipolar spin ice model provides a successful basis for understanding Dy2Ti2O7, but that there are issues which remain to be clarified.
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