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Thermal fluctuations lift the high ground state degeneracy of the classical nearest neighbour pyrochlore antiferromagnet, with easy plane anisotropy, giving a first order phase transition to a long range ordered state. We show, from spin wave analysis and numerical simulation, that even below this transition a continuous manifold of states, of dimension N^{2/3} exist (N is the number of degrees of freedom). As the temperature goes to zero a further `order by disorder' selection is made from this manifold. The pyrochlore antiferromagnet Er_2Ti_2O_7, is believed to have an easy plane anisotropy and is reported to have the same magnetic structure. The latter is perhaps surprising, given that the dipole interaction lifts the degeneracy of the classical model in favour of a different structure. We interpret our results in the light of these facts., Comment: 7 pages, 9 figures, to appear in JPCM - HFM2003 conference proceeding

We introduce a Hubbard model on a particular class of geometries, and consider the effect of doping the highly spin-degenerate Mott-insulating state with a microscopic number of holes in the extreme strong-coupling limit. The geometry is quite general, with pairs of atomic sites at each superlattice vertex, and a highly frustrated inter-atomic connectivity: the one dimensional realization is a chain of edge-sharing tetrahedra. The sole model parameter is the ratio of intra-pair to inter-pair hopping matrix elements. If the intra-pair hopping is negligible then introducing a microscopic number of holes results in a ferromagnetic Nagaoka groundstate. Conversely, if the intra-pair hopping is comparable with the inter-pair hopping then the groundstate is low spin with short-ranged spin correlations. We exactly solve the correlated motion of a pair of holes in such a state and find that, in 1-d and 2-d, they form a bound pair on a length scale that increases with diminishing binding energy. This result is pertinent to the long-standing problem of hole motion in the copper-oxide planes of the high-temperature superconductors: we have rigorously shown that, on our frustrated geometry, the holes pair up and a short-ranged low-spin state is generated by hole motion alone., Comment: 11 pages, presented at the international workshop on Strongly Correlated Electrons in New Materials (SCENM02), Loughborough, UK (15-17 December 2002). Submitted to Journal of Physics A: Mathematical and General for a special issue

Er_2Ti_2O_7 has been suggested to be a realization of the frustrated < 111 > XY pyrochlore lattice antiferromagnet, for which theory predicts fluctuation-induced symmetry breaking in a highly degenerate ground state manifold. We present a theoretical analysis of the classical model compared to neutron scattering experiments on the real material, both below and above T_N = 1.173(2) K. The model correctly predicts the ordered magnetic structure, suggesting that the real system has order stabilised by zero-point quantum fluctuations that can be modelled by classical spin wave theory. However, the model fails to describe the excitations of the system, which show unusual features., Comment: 4 pages, 3 figures, resubmitted to PRL 11/02

Neutron scattering has been used to investigate the magnetic correlations in the the spin ice material dysprosium titanate, Dy2Ti2O7. An isotopically enriched sample was used to minimise neutron absorption. In zero field no magnetic order was observed down to 50 mK but the magnetic diffuse scattering was in qualitative agreement with that expected for the disordered low temperature state of dipolar spin ice. Application of a field of ~ 0.8 T in the [100] direction led to long range order. With the field applied in the [1-10] direction a coexistence of long range ferromagnetic and short range antiferromagnetic order was observed. This is attributed to the pinning of only half the spins by the field. The hysteresis loops in both field orientations displayed unusual steps and plateaus., Comment: 3 pages, 4 figures

The rare earth pyrochlore material Gd2Ti2O7 is considered to be an ideal model frustrated Heisenberg antiferromagnet with additional dipolar interactions. For this system there are several untested theoretical predictions of the ground state ordering pattern. Here we establish the magnetic structure of isotopically enriched (160)Gd2Ti2O7, using powder neutron diffraction at a temperature of 50 mK. The magnetic structure at this temperature is a partially ordered, non-collinear antiferromagnetic structure, with propagation vector k= 1/2 1/2 1/2. It can be described as a set of "q=0" ordered kagome planes separated by zero interstitial moments. This magnetic structure agrees with theory only in part, leaving an interesting problem for future research., Comment: 4 pages, 2 figures

The Ising-like spin ice model, with a macroscopically degenerate ground state, has been shown to be approximated by several real materials. Here we investigate a model related to spin ice, in which the Ising spins are replaced by classical Heisenberg spins. These populate a cubic pyrochlore lattice and are coupled to nearest neighbours by a ferromagnetic exchange term J and to the local <1,1,1> axes by a single-ion anisotropy term D. The near neighbour spin ice model corresponds to the case D/J infinite. For finite D/J we find that the macroscopic degeneracy of spin ice is broken and the ground state is magnetically ordered into a four-sublattice structure. The transition to this state is first-order for D/J > 5 and second-order for D/J < 5 with the two regions separated by a tricritical point. We investigate the magnetic phase diagram with an applied field along [1,0,0] and show that it can be considered analogous to that of a ferroelectric., Comment: 7 pages, 4 figures

The pyrochlore material $\rm Ho_{2}Ti_{2}O_{7}$ has been suggested to show ``spin ice'' behaviour. We present neutron scattering and specific heat results that establish unambiguously that Ho$_2$Ti$_2$O$_7$ exhibits spin ice correlations at low temperature. Diffuse magnetic neutron scattering from Ho$_2$Ti$_2$O$_7$ is found to be quite well described by a near neighbour spin ice model and very accurately described by a dipolar spin ice model. The heat capacity is well accounted for by the sum of a dipolar spin ice contribution and an expected nuclear spin contribution, known to exist in other Ho$^{3+}$ salts. These results settle the question of the nature of the low temperature spin correlations in $\rm Ho_{2}Ti_{2}O_{7}$ for which contradictory claims have been made., Comment: 1 Color POSTSCRIPT figures included. 1 BW POSTSCRIPT figure included Submitted to Physical Review Letters Contact: gingras@gandalf.uwaterloo.ca This version corrects for an incomplete version accidentally submitted the first time