Order Induced by Dilution in Pyrochlore XY Antiferromagnets

XY pyrochlore antiferromagnets are well-known to exhibit order-by-disorder through both quantum and thermal selection. In this paper we consider the effect of substituting non-magnetic ions onto the magnetic sites in a pyrochlore XY model with generally anisotropic exchange tuned by a single parameter $J^{\pm\pm}/J^\pm$. The physics is controlled by two points in this space of parameters $J^{\pm\pm}/J^\pm=\pm 2$ at which there are line modes in the ground state and hence an $O(L^2)$ ground state degeneracy intermediate between that of a conventional magnet and a Coulomb phase. At each of these points, single vacancies seed pairs of line defects. Two line defects carrying incompatible spin configurations from different vacancies can cross leading to an effective one-dimensional description of the resulting spin texture. In the thermodynamic limit at finite density, we find that dilution selects a state "opposite" to the state selected by thermal and quantum disorder which is understood from the single vacancy limit. The latter finding hints at the possibility that Er$_{2-x}$Y$_x$Ti$_2$O$_7$ for small $x$ exhibits a second phase transition within the thermally selected $\psi_2$ state into a $\psi_3$ state selected by the quenched disorder.Comment: 14 pages, 12 figure

Possible Quantum Diffusion of Polaronic Muons in Dy2_2Ti2_2O7_7 Spin Ice

We interpret recent measurements of the zero field muon relaxation rate in the frustrated magnetic pyrochlore Dy$_2$Ti$_2$O$_7$ as resulting from the quantum diffusion of muons in the substance. In this scenario, the plateau observed at low temperature ($<7$ K) in the relaxation rate is due to coherent tunneling of the muons through a spatially disordered spin state and not to any magnetic fluctuations persisting at low temperature. Two further regimes either side of a maximum relaxation rate at $T^* = 50$ K correspond to a crossover between tunnelling and incoherent activated hopping motion of the muon. Our fit of the experimental data is compared with the case of muonium diffusion in KCl.Comment: 15 pages, 2 figure

Order-by-Disorder in the XY Pyrochlore Antiferromagnet Revisited

We investigate the properties of the XY pyrochlore antiferromagnet with local planar anisotropy. We find the ground states and show that the configurational ground state entropy is subextensive. By computing the free energy due to harmonic fluctuations and by carrying out Monte Carlo simulations, we confirm earlier work indicating that the model exhibits thermal order-by-disorder leading to low temperature long-range order consisting of discrete magnetic domains. We compute the spin wave spectrum and show that thermal and quantum fluctuations select the same magnetic structure. Using Monte Carlo simulations, we find that the state selected by thermal fluctuations in this XY pyrochlore antiferromagnet can survive the addition of sufficiently weak nearest-neighbor pseudo-dipolar interactions to the spin Hamiltonian. We discuss our results in relation to the Er2Ti2O7 pyrochlore antiferromagnet.Comment: 13 pages, 6 figure

Local Susceptibility of the Yb2Ti2O7 Rare Earth Pyrochlore Computed from a Hamiltonian with Anisotropic Exchange

The rare earth pyrochlore magnet Yb2Ti2O7 is among a handful of materials that apparently exhibit no long range order down to the lowest explored temperatures and well below the Curie-Weiss temperature. Paramagnetic neutron scattering on a single crystal sample has revealed the presence of anisotropic correlations and recent work has led to the proposal of a detailed microscopic Hamiltonian for this material involving significantly anisotropic exchange. In this article, we compute the local sublattice susceptibility of Yb2Ti2O7 from the proposed model and compare with the measurements of Cao and coworkers [Physical Review Letters, {103}, 056402 (2009)], finding quite good agreement. In contrast, a model with only isotropic exchange and long range magnetostatic dipoles gives rise to a local susceptiblity that is inconsistent with the data.Comment: 11 pages, 2 figures. Accepted for publication in J. Phys.:Condensed Matter, in a special issue dedicated on frustrated magnetis

Spin-Space Groups and Magnon Band Topology

Band topology is both constrained and enriched by the presence of symmetry. The importance of anti-unitary symmetries such as time reversal was recognized early on leading to the classification of topological band structures based on the ten-fold way. Since then, lattice point group and non-symmorphic symmetries have been seen to lead to a vast range of possible topologically nontrivial band structures many of which are realized in materials. In this paper we show that band topology is further enriched in many physically realizable instances where magnetic and lattice degrees of freedom are wholly or partially decoupled. The appropriate symmetry groups to describe general magnetic systems are the spin-space groups. Here we describe cases where spin-space groups are essential to understand the band topology in magnetic materials. We then focus on magnon band topology where the theory of spin-space groups has its simplest realization. We consider magnetic Hamiltonians with various types of coupling including Heisenberg and Kitaev couplings revealing a hierarchy of enhanced magnetic symmetry groups depending on the nature of the lattice and the couplings. We describe, in detail, the associated representation theory and compatibility relations thus characterizing symmetry-enforced constraints on the magnon bands revealing a proliferation of nodal points, lines, planes and volumes.Comment: 30 pages, 7 figure