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 crystal and magnetic structures of the n = 3 Ruddlesden−Popper phase with the ideal composition Ca4Mn3O10 have been studied using X-ray and neutron powder diffraction. The crystal structure at 293 K is relatively insensitive to the partial pressure of oxygen used in sample preparation. A sample prepared in air showed an orthorhombic distortion (space group Pbca, a = 5.26557(12), b = 5.26039(11), c = 26.8276(5) Å) from the ideal n = 3 RP structure, as did a sample prepared under 800 atm of O2 pressure (a = 5.26005(4), b = 5.25569(4), c = 26.83543(20) Å). Both samples showed a magnetic phase transition at 115 K from a paramagnetic phase with extensive short-range spin ordering to a weakly ferromagnetic (μferro = 2 × 10-3 μB per Mn) low-temperature phase. The antiferromagnetic components of the atomic magnetic moments (2.23(2) μB per Mn) order in a G-type manner within each perovskite block, and the interblock coupling reflects the orthorhombic symmetry of the structure.

Er2Ti2O7 is believed to be a realization of an XY antiferromagnet on a frustrated lattice of corner-sharing regular tetrahedra. It is presented as an example of the order-by-disorder mechanism in which fluctuations lift the degeneracy of the ground state, leading to an ordered state. Here we report detailed measurements of the low temperature magnetic properties of Er2Ti2O7, which displays a second-order phase transition at TN ≃ 1.2 K with coexisting short-and long-range orders. Magnetic-susceptibility studies show that there is no spin-glass-like irreversible effect. Heatcapacity measurements reveal that the paramagnetic critical exponent is typical of a 3-dimensional XY magnet while the low-temperature specific heat sets an upper limit on the possible spin-gap value and provides an estimate for the spin-wave velocity. Muon spin relaxation measurements show the presence of spin dynamics in the nanosecond time scale down to 21 mK. This time range is intermediate between the shorter time characterizing the spin dynamics in Tb2Sn2O7, which also displays long-and short-range magnetic order, and the time scale typical of conventional magnets. Hence the ground state is characterized by exotic spin dynamics. We determine the parameters of a symmetry-dictated Hamiltonian restricted to the spins in a tetrahedron, by fitting the paramagnetic diffuse neutron scattering intensity for two reciprocal lattice planes. These data are recorded in a temperature region where the assumption that the correlations are limited to nearest neighbors is fair.

We present a detailed muon spin relaxation (μ+SR) study of the spin-ice material Dy2Ti2O7. Polycrystalline samples of this material have been studied in the temperature range 0.02 K

Spin dynamics in Er2Ti2O7 and Er2Sn2O7 have been probed by means of muon-spin relaxation (μ+SR) in the temperature range  K. Both compounds are thought to constitute experimental realizations of the highly frustrated XY antiferromagnet on the pyrochlore lattice, for which theory predicts fluctuation-induced magnetic order. Our results for Er2Ti2O7 are consistent with a transition into an ordered state at  K, in agreement with previous neutron measurements. Below this temperature, the muon relaxation rate λ(T) remains large ( MHz) and temperature independent, in contrast to the behaviour in conventional magnets. The thermal evolution of λ(T) for Er2Sn2O7 is somewhat similar to that of the Ti material. However, the depolarization curves remain exponential over the entire temperature range, suggesting a dense distribution of rapidly fluctuating magnetic moments, and, thus, are compatible with the absence of long-range order at least for T>0.02 K.