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Magnetic susceptibility, NMR, muon spin relaxation, and inelastic neutron scattering measurements show that kapellasite, Cu3Zn(OH)6Cl2, a geometrically frustrated spin-1/2 kagome antiferromagnet polymorphic with herbertsmithite, is a gapless spin liquid showing unusual dynamic short-range correlations of noncoplanar cuboc2 type which persist down to 20 mK. The Hamiltonian is determined from a fit of a high-temperature series expansion to bulk susceptibility data and possesses competing exchange interactions. The magnetic specific heat calculated from these exchange couplings is in good agreement with experiment. The temperature dependence of the magnetic structure factor and the muon relaxation rate are calculated in a Schwinger-boson approach and compared to experimental results.

Er2Ti2O7 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 TN =1.173(2) K. The model correctly predicts the ordered magnetic structure, suggesting that the real system has order stabilized 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.PACS numbers: 28.20. Cz, 75.25.+z An important aspect of condensed matter is the separation of energy scales, such that the minimization of one set of interactions may result in the frustration of another. A paradigm is the frustrated antiferromagnet, in which the local magnetic couplings between ions are frustrated by the crystal symmetry that the ions adopt. However, a systematic study of the rare earth pyrochlore titanates R 2 Ti 2 O 7 has shown that local antiferromagnetic bond frustration is neither a necessary, nor a sufficient condition for magnetic frustration 1,2,3,4,5 . Rather, it arises from the interplay, in the context of the crystal symmetry, of the principal terms in the spin Hamiltonian. In the case of R 2 Ti 2 O 7 , the main terms are single-ion anisotropy, exchange and dipolar coupling. Depending on the balance of these factors, one observes spin ice behavior (R = Ho, Dy) 1,2,3 , spin liquid behavior (R = Tb) 4 , and dipole induced partial order (R = Gd)5 . Such behavior is best classified in terms of the dominant 111 single-ion anisotropy that arises from the trigonal crystal electric field (CEF) at the rare earth site. For example, whereas the Heisenberg antiferromagnet has a spin liquid ground state 6 , the 111 Ising (dipolar) ferromagnet has a spin ice ground state 1,3,7 . There is thus a clear motivation to study models based on other simple anisotropies and their realization in the titanate series. In this Letter we study one such model -the 111 XY model antiferromagnet 8 -and its realization Er 2 Ti 2 O 7 9,10,11,12 . We consider the Hamiltonian:where the classical spins, S i , populate a face centered cubic array of corner sharing tetrahedra: the pyrochlore lattice. The spins are confined to easy XY planes by a local d i = 111 anisotropy, D < 0, and are coupled antiferromagnetically by exchange J < 0. This model was first studied in Ref.8 , where a discrete, but macroscopically degenerate, set of ground states was identified. At finite temperature thermal fluctuations were found to select an ordered state by the mechanism that Villain called "order by disorder"13 and a first order phase transition was observed in numerical simulations. The propagation vector of the ordered state was found to be k = 0, 0, 0 (henceforth "k = 0"), but the basis vectors of the magnetic structure were not determined. We have recently discovere...

The geometrically frustrated antiferromagnet Gd2Ti2O7 exhibits magnetic behaviour of such complexity that it poses a challenge to both experiment and theory. Magnetic ordering commences at TN = 1.1 K and there is a further magnetic phase transition at  K. Here we use neutron diffraction to definitively establish the nature of the phase transition at and the magnetic structure adopted below this temperature. Between and TN the structure is partly ordered, as previously reported. Below the remaining spins order, but only weakly. The magnetic structure in this temperature range is shown to be a 4-k structure, closely related to the 1-k structure previously suggested. The 4-k and 1-k variants of the structure are distinguished by analysis of the diffuse scattering, which we believe represents a new method of solving the ‘multi-k’ problem of magnetic structure determination.

Er2Ti2O7 has been proposed as a realization of the pyrochlore antiferromagnet with dipolar interactions, where the spins of Er3+ lie perpendicular to the local axes. Below a Néel temperature of TN = 1.173 K magnetic order with the propagation vector occurs. Previous powder neutron diffraction studies were not able to determine details of the magnetic ordering beyond its symmetry due to powder averaging. In an attempt to resolve the questions as regards the ordering in this model magnet we performed a spherical neutron polarimetry experiment using CRYOPAD. The analysis of these data and a proposed magnetic order are presented.