  We show that the recent string theory embedding of a spacetime with
nonrelativistic Schrodinger symmetry can be generalised to a twenty one
dimensional family of solutions with that symmetry. Our solutions include IIB
backgrounds with no three form flux turned on, and arise as near horizon limits
of branewave spacetimes. We show that there is a hypersurface in the space of
these theories where an instability appears in the gravitational description,
indicating a phase transition in the nonrelativistic field theory dual. We also
present simple embeddings of duals for nonrelativistic critical points where
the dynamical critical exponent can take many values z \neq 2.
