Ground state phase diagram of generic XY pyrochlore magnets with quantum fluctuations

Motivated by recent experimental and theoretical progress on the Er2Ti2O7 pyrochlore XY antiferromagnet, we study the general problem of quantum order-by-disorder in pyrochlore XY systems. We consider the nearest-neighbor pseudo-spin-1/2 Hamiltonian for such a system characterized by anisotropic spin-spin couplings J(e) equivalent to{J(+/-), J(+/-+/-), J(z +/-), 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(+/-)J(+/-+/-))/J(z perpendicular to)(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(+/-) a narrow psi(2) sliver sandwiched between two psi(3) regions in the J(zz)/J(+/-) vs J(zz)/J(+/-) phase diagram. From our results, one would be able to predict which state (psi(2) or psi(3)) may be realized in a real material given its set of J(e) couplings. Our results further illustrate the very large potential sensitivity of the ground state of XY pyrochlore systems to minute changes in their spin Hamiltonian. Finally, using the experimentally determined J(e) equivalent to{J(+/-), J(+/-+/-), J(z +/-), J(zz)} 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. As an avenue of research in XY pyrochlore materials distinct from the rare-earth pyrochlore oxides, we propose that the Cd2Dy2Se4 chalcogenide spinel, in which the Dy3+ ions form a pyrochlore lattice and may be XY-like, could be interesting to investigate.