Induced Magnetic Order in Yb$_2$Ti$_2$O$_7$

Yb$_2$Ti$_2$O$_7$ is part of family of pyrochlore materials with a magnetic rare-earth and a non-magnetic transition metal. In similar compounds containing holmium, erbium, or terbium the geometric frustration results in several exotic ground states including spin-ice, spin-liquid, field-induced ordering, and low-dimensional behavior. The ytterbium-based compound has a strong anomaly in the specific heat at 240~mK [Hodges {\em et al.}, J Phys Cond Mat {\bf 13}, 9301 (2001)] but without accompanying long range order. We have made measurements of the elastic and inelastic neutron scattering on a large single crystal of Yb$_2$Ti$_2$O$_7$ over a broad range of the $(hhl)$ scattering plane using the DCS spectrometer at the NIST Center for Neutron Research. Our studies have confirmed the presence of diffuse ``rods'' of scattering along the (111) directions that persist below 100~mK. However, when the sample is field-cooled in fields as low as 0.5~T the rods of scattering are replaced by well-defined magnetic excitations. We will present the results of our studies at a variety of temperatures and fields.