paper

Ground State Phase Diagram of Generic XY Pyrochlore Magnets with Quantum Fluctuations

arXiv:1311.3299 · doi:10.1103/PhysRevB.88.144402

Abstract

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_{\pm\pm}, J_{z\pm}, 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 Γ_5 irreducible representation, the ψ_2 and ψ_3 (basis) states, are rather accurately determined by a cubic equation in J_{\pm}J_{\pm\pm})/J_{z\pm}^2. Depending on the value of J_{zz}, there can be one or three phase boundaries that separate alternating regions of ψ_2 and ψ_3 states. In particular, we find for sufficiently small J_{zz}/J_{\pm} a narrow ψ_2 sliver sandwiched between two ψ_3 regions in the J_{\pm\pm}/J_\pm vs J_{z\pm}/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 ψ_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.

8 pages, 3 figures. Version is the same as the published one, within epsilon

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