  Paramagnetic correlations in the magnetic material Yb2Ti2O7 have been
investigated via neutron scattering, revealing a [111] rod of scattering
intensity. Assuming interactions between the Yb^{3+} ions composed of all
symmetry-allowed nearest neighbor exchange interactions and long-range dipolar
interactions, we construct a model Hamiltonian that allows for an excellent
description of the neutron scattering data. Our results provide compelling
evidence for significant anisotropic exchange interactions in an insulating
magnetic pyrochlore oxide. We also compute the real space correlations leading
to the [111] rod of scattering.
