Rare earth titanate pyrochlore magnets with the chemical composition A2B2O7 have been a playground for the physics of geometrical frustration.  Many magnetic trivalent rare earth ions can reside on the A site of this structure, and such compounds give rise to physical realizations of magnetic moments decorating a network of corner-sharing tetrahedra.  Such networks can be combined with antiferromagnetism and ferromagnetism along with different spin anisotropies to produce materials with varied and exotic, sometimes disordered, ground states.

I will discuss new neutron scattering work on two magnetic pyrochlores Er2Ti2O7 and Yb2Ti2O7, which can be thought of in terms of XY moments decorating a network of corner sharing tetrahedra.  The ferromagnet, Yb2Ti2O7 displays an unexpected disordered ground state which can be brought to order in an applied magnetic field.  The antiferromagnet, Er2Ti2O7, displays a long range ordered state at low temperatures which can be driven into a disordered state by application of a magnetic field.