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We study RKKY interaction in non-Fermi liquid metals. We find that the RKKYinteraction mediated by non-Fermi liquid metals can be of much longer rangethan for a Fermi liquid. The oscillatory nature of RKKY interaction thusbecomes more important in non-Fermi liquids, and gives rise to enhancedfrustration when the spins form a lattice. Frustration suppresses the magneticordering temperature of the lattice spin system. Furthermore, we find that thespin system with longer range RKKY interaction can be described by theBrazovskii model, where the ordering wavevector lies on a shell with constantradius. Strong fluctuations in such model lead to a first-order phasetransition and/or glassy phase. This may explain some recent experiments whereglassy behavior was observed in stoichiometric heavy fermion material close toa ferromagnetic quantum critical point.

RKKY Interaction and Intrinsic Frustration in Non-Fermi Liquid Metals