RKKY Interaction and Intrinsic Frustration in Non-Fermi-Liquid Metals

We study the RKKY interaction in non-Fermi-liquid metals. We find that the RKKY interaction mediated by some non-Fermi-liquid metals can be of much longer range than for a Fermi liquid. The oscillatory nature of the RKKY interaction thus becomes more important in such 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 a longer range RKKY interaction can be described by the Brazovskii model, where the ordering wave vector lies on a higher dimensional manifold. Strong fluctuations in such a 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.

Figure 1

Schematic electronic (a) and magnetic (b) phase diagrams for a Kondo lattice model with strongly interacting conduction electrons coupled to localized spins. (a): Crossover from FL to NFL behavior. $x$ represents non-thermal tuning parameter, e.g., pressure, magnetic field, doping. Distance dependence of RKKY interaction is shown in the insets. (b): Magnetic transition temperature decreases with increasing frustration resulting from NFL-mediated longer-range RKKY interaction. New phases (shaded region), e.g., a glass phase, emerge near the putative QCP.

Figure 2

(a) The static spin susceptibility $\chi (q)$ as a function of momentum for a FL (dashed, black) and the gauge-fermion model with $\sigma <1/3$ (dotted, blue) and $\sigma >1/3$ (solid, red). (b) $F(q)$ as a function of momentum for angles $\theta =0$, $\pi /6$, $\pi /4$. The curves for different angles are almost identical. Here the spins form a square lattice, and $\sigma =1/2$, $k_{F}a=0.2$.

Figure 3

Ferromagmetic transition temperature as function of range of random exchange interaction.