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

In this paper we provide a theoretical basis for the problem of Griffiths-M cCoy singularities close to the quantum critical point for magnetic orderin g in U and Ce intermetallics. We show that the competition between the Kond o effect and Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction can be expres sed in Hamiltonian form, and that the dilution effect due to alloying leads to a quantum percolation problem driven by the number of magnetically comp ensated moments. We argue that the exhaustion paradox proposed by Nozieres is explained when the RKKY interaction is taken into account. We revisit th e one- and two-impurity Kondo problem, and show that in the presence of par ticle-hole symmetry-breaking operators the system Rows to a line of fixed p oints characterized by coherent (clusterlike) motion of the spins. Moreover , close to the quantum critical point, clusters of magnetic atoms can quant um mechanically tunnel between different states either via the anisotropy o f the RKKY interaction or by what we call the cluster Kondo effect. We calc ulate explicitly from the microscopic Hamiltonian the parameters which appe ar in all the response functions. We show that there is a maximum number N- c of spins in the clusters such that, above this number, tunneling ceases t o 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 mode l wt-rich describes the critical behavior of metallic magnetic systems. Thi s model predicts that in the paramagnetic phase there is a crossover temper ature T*, above which Griffiths-McCoy-like singularities with magnetic susc eptibility chi (T)proportional to T-1+lambda and specific heat C-V(T)propor tional toT(lambda), with lambda <1, appear. Below T*, however, a regime dom inated by dissipation occurs, with divergences stronger than power law: <ch i>(T)proportional to1/[Tln(1/T)] and C-V(T)proportional to 1/ln(2)(1/T). We estimate that T* is exponentially small with N-c. Our results should he ap plicable to a broad class of metallic magnetic systems which are described by the Kondo lattice Hamiltonian.