  We study RKKY interaction in non-Fermi liquid metals. We find that the RKKY
interaction mediated by non-Fermi liquid metals can be of much longer range
than for a Fermi liquid. The oscillatory nature of RKKY interaction thus
becomes more important in non-Fermi liquids, and gives rise to enhanced
frustration when the spins form a lattice. Frustration suppresses the magnetic
ordering temperature of the lattice spin system. Furthermore, we find that the
spin system with longer range RKKY interaction can be described by the
Brazovskii model, where the ordering wavevector lies on a shell with constant
radius. Strong fluctuations in such model lead to a first-order phase
transition and/or glassy phase. This may explain some recent experiments where
glassy behavior was observed in stoichiometric heavy fermion material close to
a ferromagnetic quantum critical point.
