# Non-fermi-liquid behavior in U and Ce alloys: Criticality, disorder, dissipation, and Griffiths-McCoy singularities

## Abstract

In this paper we provide a theoretical basis for the problem of Griffiths-McCoy singularities close to the quantum critical point for magnetic ordering in U and Ce intermetallics. We show that the competition between the Kondo effect and Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction can be expressed in Hamiltonian form, and that the dilution effect due to alloying leads to a quantum percolation problem driven by the number of magnetically compensated moments. We argue that the exhaustion paradox proposed by Nozières is explained when the RKKY interaction is taken into account. We revisit the one- and two-impurity Kondo problem, and show that in the presence of particle-hole symmetry-breaking operators the system flows to a line of fixed points characterized by coherent (clusterlike) motion of the spins. Moreover, close to the quantum critical point, clusters of magnetic atoms can quantum mechanically tunnel between different states either via the anisotropy of the RKKY interaction or by what we call the cluster Kondo effect. We calculate explicitly from the microscopic Hamiltonian the parameters which appear in all the response functions. We show that there is a maximum number Nc of spins in the clusters such that, above this number, tunneling ceases to occur. These effects lead to a distribution of cluster Kondo temperatures which vanishes for finite clusters, and therefore leads to strong magnetic response. From these results we propose a dissipative quantum droplet model which describes the critical behavior of metallic magnetic systems. This model predicts that in the paramagnetic phase there is a crossover temperature T*, above which Griffiths-McCoy-like singularities with magnetic susceptibility χ(T)∝T-1+λ and specific heat C v(T)∝Tλ, with λ <1, appear. Below T*, however, a regime dominated by dissipation occurs, with divergences stronger than power law: χ(T)∝1/[Tln(1/T)] and Cv(T)∝1/ln2(1/T). We estimate that T* is exponentially small with Nc. Our results should be applicable to a broad class of metallic magnetic systems which are described by the Kondo lattice Hamiltonian.