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Register a new userTheory of multiple--phase competition in pyrochlore magnets with anisotropic exchange, with application to Yb2Ti2O7, Er2Ti2O7 and Er2Sn2O7
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The family of magnetic rare-earth pyrochlore oxides R2M2O7 plays host to a diverse array of exotic phenomena, driven by the interplay between geometrical frustration and spin-orbit interaction, which leads to anisotropy in both magnetic moments and their interactions. In this article we establish a general, symmetry--based theory of pyrochlore magnets with anisotropic exchange interactions. Starting from a very general model of nearest-neighbour exchange between Kramers ions, we find four distinct classical ordered states, all with q=0, competing with a variety of spin-liquids and unconventional forms of magnetic order. The finite-temperature phase diagram of this model is determined by Monte Carlo simulation, supported by classical spin-wave calculations. We pay particular attention to the region of parameter space relevant to the widely studied materials Er2Ti2O7, Yb2Ti2O7, and Er2Sn2O7. We find that many of the most interesting properties of these materials can be traced back to the accidental degeneracies where phases with different symmetries meet. These include the ordered ground state selection by fluctuations in Er2Ti2O7, the dimensional-reduction observed in Yb2Ti2O7, and the lack of reported magnetic order in Er2Sn2O7. We also discuss the application of this theory to other pyrochlore oxides.
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We investigate thermodynamic properties like specific heat $c_{V}$ and susceptibility $chi$ in anisotropic $J_1$-$J_2$ triangular quantum spin systems ($S=1/2$). As a universal tool we apply the finite temperature Lanczos method (FTLM) based on exact diagonalization of finite clusters with periodic boundary conditions. We use clusters up to $N=28$ sites where the thermodynamic limit behavior is already stably reproduced. As a reference we also present the full diagonalization of a small eight-site cluster. After introducing model and method we discuss our main results on $c_V(T)$ and $chi(T)$. We show the variation of peak position and peak height of these quantities as function of control parameter $J_2/J_1$. We demonstrate that maximum peak positions and heights in Neel phase and spiral phases are strongly asymmetric, much more than in the square lattice $J_1$-$J_2$ model. Our results also suggest a tendency to a second side maximum or shoulder formation at lower temperature for certain ranges of the control parameter. We finally explicitly determine the exchange model of the prominent triangular magnets Cs$_2$CuCl$_4$ and Cs$_{2}$CuBr$_{4}$ from our FTLM results.
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.
Motivated by recent experimental and theoretical progress on the Er2Ti2O7 pyrochlore XY antiferromagnet, we study the problem of quantum order-by-disorder in pyrochlore XY systems. We consider the most general nearest-neighbor pseudo spin-1/2 Hamiltonian for such a system characterized by anisotropic spin-spin couplings J_e = [J_pm, J_{pmpm}, J_{zpm}, J_{zz}] and construct zero-temperature phase diagrams. Combining symmetry arguments and spin-wave calculations, we show that the ground state phase boundaries between the two candidate ground states of the Gamma_5 irreducible representation, the psi_2 and psi_3 (basis) states, are rather accurately determined by a cubic equation in J_{pm}J_{pmpm})/J_{zpm}^2. Depending on the value of J_{zz}, there can be one or three phase boundaries that separate alternating regions of psi_2 and psi_3 states. In particular, we find for sufficiently small J_{zz}/J_{pm} a narrow psi_2 sliver sandwiched between two psi_3 regions in the J_{pmpm}/J_pm vs J_{zpm}/J_pm phase diagram. Our results further illustrate the very large potential sensitivity of the ground state of XY pyrochlore systems to minute changes in their spin Hamiltonian. Using the experimentally determined J_3 and g-tensor values for Er2Ti2O7, we show that the heretofore neglected long-range 1/r^3 magnetostatic dipole-dipole interactions do not change the conclusion that Er2Ti2O7 has a psi_2 ground state induced via a quantum order-by-disorder mechanism. We propose that the CdDy2Se4 chalcogenide spinel, in which the Dy^{3+} ions form a pyrochlore lattice and may be XY-like, could prove interesting to investigate.
ersn, is considered, together with erti, as a realization of the XY antiferromagnet on the pyrochlore lattice. We present magnetization measurements confirming that ersn, does not order down to 100 mK but exhibits a freezing below 200 mK. Our neutron scattering experiments evidence the strong XY character of the er moment and point out the existence of short range correlations in which the magnetic moments are in peculiar configurations, the Palmer-Chalker states, predicted theoretically for an XY pyrochlore antiferromagnet with dipolar interactions. Our estimation of the ersn, parameters confirm the role of the latter interactions on top of relatively weak and isotropic exchange couplings.
We report the exact dimer phase, in which the ground states are described by product of singlet dimer, in the extended XYZ model by generalizing the isotropic Majumdar-Ghosh model to the fully anisotropic region. We demonstrate that this phase can be realized even in models when antiferromagnetic interaction along one of the three directions. This model also supports three different ferromagnetic (FM) phases, denoted as $x$-FM, $y$-FM and $z$-FM, polarized along the three directions. The boundaries between the exact dimer phase and FM phases are infinite-fold degenerate. The breaking of this infinite-fold degeneracy by either translational symmetry breaking or $mathbb{Z}_2$ symmetry breaking leads to exact dimer phase and FM phases, respectively. Moreover, the boundaries between the three FM phases are critical with central charge $c=1$ for free fermions. We characterize the properties of these boundaries using entanglement entropy, excitation gap, and long-range spin-spin correlation functions. These results are relevant to a large number of one dimensional magnets, in which anisotropy is necessary to isolate a single chain out from the bulk material. We discuss the possible experimental signatures in realistic materials with magnetic field along different directions and show that the anisotropy may resolve the disagreement between theory and experiments based on isotropic spin-spin interactions.
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