Geometric frustration in the mixed layer pnictide oxides

We present results from a Monte Carlo investigation of a simple bilayer model with geometrically frustrated interactions similar to those found in the mixed layer pnictide oxides $(Sr_{2}Mn_{3}Pn_{2}O_{2}, Pn=As,Sb).$ Our model is composed of two inequivalent square lattices with nearest neighbor intra- and interlayer interactions. We find a ground state composed of two independent N\'{e}el ordered layers when the interlayer exchange is an order of magnitude weaker than the intralayer exchange, as suggested by experiment. We observe this result independent of the number of layers in our model. We find evidence for local orthogonal order between the layers, but it occurs in regions of parameter space that are not experimentally realized. We conclude that frustration caused by nearest neighbor interactions in the mixed layer pnictide oxides is not sufficient to explain the long--range orthogonal order that is observed experimentally, and that it is likely that other terms (e.g., local anisotropies) in the Hamiltonian are required to explain the magnetic behavior.Comment: Revetex, 4 pages, 3 figures, to appear in the proceedings of "HFM 2000" (Waterloo, June 2000); submitted to Can. J. Phy

Geometric frustration in the mixed layer pnictide oxides

We present results from a Monte Carlo investigation of a simple bilayer model with geometrically frustrated interactions similar to those found in the mixed layer pnictide oxides $(Sr_{2}Mn_{3}Pn_{2}O_{2}, Pn=As,Sb).$ Our model is composed of two inequivalent square lattices with nearest neighbor intra- and interlayer interactions. We find a ground state composed of two independent N\'{e}el ordered layers when the interlayer exchange is an order of magnitude weaker than the intralayer exchange, as suggested by experiment. We observe this result independent of the number of layers in our model. We find evidence for local orthogonal order between the layers, but it occurs in regions of parameter space that are not experimentally realized. We conclude that frustration caused by nearest neighbor interactions in the mixed layer pnictide oxides is not sufficient to explain the long--range orthogonal order that is observed experimentally, and that it is likely that other terms (e.g., local anisotropies) in the Hamiltonian are required to explain the magnetic behavior.Comment: Revetex, 4 pages, 3 figures, to appear in the proceedings of "HFM 2000" (Waterloo, June 2000); submitted to Can. J. Phy

Ill-Behaved Convergence of a Model of the Gd3Ga5O12 Garnet Antiferromagnet with Truncated Magnetic Dipole-Dipole Interactions

Previous studies have found that calculations which consider long-range magnetic dipolar interactions truncated at a finite cut-off distance Rc predict spurious (unphysical) long-range ordered phases for Ising and Heisenberg systems on the pyrochlore lattice. In this paper we show that, similar to these two cases, calculations that use truncated dipolar interactions to model the Gd3Ga5O12 garnet antiferromagnet also predict unphysical phases with incommensurate ordering wave vector q_ord that is very sensitive to the dipolar cut-off distance Rc.Comment: 7 pages, 2 color figures; Proceedings of the HFM2006 conference, to appear in a special issue of J. Phys.: Condens. Matte

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

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 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 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+.Comment: Revtex4, 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 publicatio

Understanding Paramagnetic Spin Correlations in the Spin-Liquid Pyrochlore Tb2Ti2O7

Recent elastic and inelastic neutron scattering studies of the highly frustrated pyrochlore antiferromagnet Tb2Ti2O7 have shown some very intriguing features that cannot be modeled by the local classical Ising model, naively expected to describe this system at low temperatures. Using the random phase approximation to take into account fluctuations between the ground state doublet and the first excited doublet, we successfully describe the elastic neutron scattering pattern and dispersion relations in Tb2Ti2O7, semi-quantitatively consistent with experimental observations.Comment: revtex4, 4 pages, 1 Color+ 2 BW figure

Sign change of the extended s-wave pairing vertex in the dynamic Hubbard model : a quantum Monte Carlo study

8 pagesInternational audienceThe “dynamic” Hubbard Hamiltonian describes interacting fermions on a lattice whose on-site repulsion is modulated by a coupling to a fluctuating bosonic field. We investigate one such model, introduced by Hirsch, using the determinant quantum Monte Carlo method. Our key result is that the extended s-wave pairing vertex, repulsive in the usual static Hubbard model, becomes attractive as the coupling to the fluctuating Bose field increases. The sign problem prevents us from exploring a low enough temperature to see if a superconducting transition occurs. We also observe a stabilization of antiferromagnetic correlations and the Mott gap near half-filling, and a near linear behavior of the energy as a function of particle density which indicates a tendency toward phase separation