Selection Rules for Two Channel Kondo Models of U and Ce ions in Metals

Symmetry based selection rules are developed providing minimal criteria for the existence of two-channel Kondo interactions between conduction electrons and the low energy degrees of freedom on U$^{4+}$ and Ce$^{3+}$ in a metal host, assuming that the underlying microscopics are regulated by the Anderson Hamiltonian. An additional dynamic selection rule is imposed on Ce$^{3+}$ ions. The selection rules restrict the two-channel quadrupolar Kondo effect to U$^{4+}$ ions in cubic, tetragonal, and hexagonal symmetry. For hexagonal and tetragonal symmetry, the Kondo effect for a U$^{4+}$ ion will always be quadrupolar. The selection rules for Ce$^{3+}$ ions restrict the two-channel magnetic Kondo effect to one of three possible doublet ionic ground states in hexagonal symmetry and the lone doublet ionic ground state in cubic symmetry. The dynamical selection rule apparently excludes two-channel Kondo behavior for Yb$^{3+}$ ions.Comment: (16 pages, 2 figures) [Figures in usable postscript shell now

Self-consistent Treatment of Crystal-Electric-Field-Levels in the Anderson Lattice

We consider an Anderson lattice model with a spin 1/2 degenerated conduction electron band and localized ionic CEF-levels, classified according to the irreducible representation of the point group of the lattice. We present the self-consistency equations for local approximations ("$d\rightarrow\infty"$ approximation) for the periodic Anderson model. It leads to a matrix formulation of the effective local density of states and the lattice $f$-Green's function. We derive the quasi-particle life-time which enters the Boltzmann transport equations. The impact of a $k$-dependent hybridization is discussed. We prove that vertex corrections will vanish, as long as all states of an irreducible representation couple to the conduction electron band with a hybridization matrix element of the same parity.Comment: 3 pages, REVTeX type, proceedings of SCES96 Z\"uric

Hidden non-Fermi liquid behavior due to crystal field quartet

We study a realistic Kondo model for crystal field quartet ground states having magnetic and non-magnetic (quadrupolar) exchange couplings with conduction electrons, using the numerical renormalization group method. We focus on a local effect dependent on singlet excited states coupled to the quartet, which reduces the non-magnetic coupling significantly and drives non-Fermi liquid behavior observed in the calculated quadrupolar susceptibility. A crossover from the non-Fermi liquid state to the Fermi liquid state is characterized by a small energy scale very sensitive to the non-magnetic coupling. On the other hand, the Kondo temperature observed in the magnetic susceptibility is less sensitive. The different crystal-field dependence of the two exchange couplings may be related to the different $x$ dependence of quadrupolar and magnetic ordering temperatures in Ce$_x$La$_{1-x}$B$_6$.Comment: 7 pages, 5 EPS figures, REVTe

Anderson-Yuval approach to the multichannel Kondo problem

We analyze the structure of the perturbation expansion of the general multichannel Kondo model with channel anisotropic exchange couplings and in the presence of an external magnetic field, generalizing to this case the Anderson-Yuval technique. For two channels, we are able to map the Kondo model onto a generalized resonant level model. Limiting cases in which the equivalent resonant level model is solvable are identified. The solution correctly captures the properties of the two channel Kondo model, and also allows an analytic description of the cross-over from the non Fermi liquid to the Fermi liquid behavior caused by the channel anisotropy.Comment: 23 pages, ReVTeX, 4 figures av. on reques

Multi-Channel Kondo Necklace

A multi--channel generalization of Doniach's Kondo necklace model is formulated, and its phase diagram studied in the mean--field approximation. Our intention is to introduce the possible simplest model which displays some of the features expected from the overscreened Kondo lattice. The $N$ conduction electron channels are represented by $N$ sets of pseudospins \vt_{j}, $j=1, ... , N$, which are all antiferromagnetically coupled to a periodic array of |\vs|=1/2 spins. Exploiting permutation symmetry in the channel index $j$ allows us to write down the self--consistency equation for general $N$. For $N>2$, we find that the critical temperature is rising with increasing Kondo interaction; we interpret this effect by pointing out that the Kondo coupling creates the composite pseudospin objects which undergo an ordering transition. The relevance of our findings to the underlying fermionic multi--channel problem is discussed.Comment: 29 pages (2 figures upon request from [email protected]), LATEX, submitted for publicatio

A new non-Fermi liquid fixed point

We study a new exchange interaction in which the conduction electrons with pseudo spin $S_c=3/2$ interact with the impurity spin $S_I=1/2$. Due to the overscreening of the impurity spin by higher conduction electron spin, a new non-trivial intermediate coupling strength fixed point is realized. Using the numerical renormalization group (NRG), we show that the low-energy spectra are described by a non-Fermi liquid excitation spectrum. A conformal field theory analysis is compared with NRG results and excellent agreement is obtained. Using the double fusion rule to generate the operator spectrum with the conformal theory, we find that the specific heat coefficient and magnetic susceptibility will diverge as $T^{-2/3}$, that the scaling dimension of an applied magnetic field is $5/6$, and that exchange anisotropy is always relevant. We discuss the possible relevance of our work to two-level system Kondo materials and dilute cerium alloys, and we point out a paradox in understanding the Bethe-Ansatz solutions to the multichannel Kondo model.Comment: Revised. 20 page

Anomalous heavy-fermion and ordered states in the filled skutterudite PrFe4P12

Specific heat and magnetization measurements have been performed on high-quality single crystals of filled-skutterudite PrFe_4P_{12} in order to study the high-field heavy-fermion state (HFS) and low-field ordered state (ODS). From a broad hump observed in C/T vs T in HFS for magnetic fields applied along the direction, the Kondo temperature of ~ 9 K and the existence of ferromagnetic Pr-Pr interactions are deduced. The {141}-Pr nuclear Schottky contribution, which works as a highly-sensitive on-site probe for the Pr magnetic moment, sets an upper bound for the ordered moment as ~ 0.03 \mu_B/Pr-ion. This fact strongly indicates that the primary order parameter in the ODS is nonmagnetic and most probably of quadrupolar origin, combined with other experimental facts. Significantly suppressed heavy-fermion behavior in the ODS suggests a possibility that the quadrupolar degrees of freedom is essential for the heavy quasiparticle band formation in the HFS. Possible crystalline-electric-field level schemes estimated from the anisotropy in the magnetization are consistent with this conjecture.Comment: 7 pages and 7 figures. Accepted for publication in Phys. Rev.

The Ising-Kondo lattice with transverse field: an f-moment Hamiltonian for URu2Si2?

We study the phase diagram of the Ising-Kondo lattice with transverse magnetic field as a possible model for the weak-moment heavy-fermion compound URu2Si2, in terms of two low-lying f singlets in which the uranium moment is coupled by on-site exchange to the conduction electron spins. In the mean-field approximation for an extended range of parameters, we show that the conduction electron magnetization responds logarithmically to f-moment formation, that the ordered moment in the antiferromagnetic state is anomalously small, and that the Neel temperature is of the order observed. The model gives a qualitatively correct temperature-dependence, but not magnitude, of the specific heat. The majority of the specific heat jump at the Neel temperature arises from the formation of a spin gap in the conduction electron spectrum. We also discuss the single-impurity version of the model and speculate on ways to increase the specific heat coefficient. In the limits of small bandwidth and of small Ising-Kondo coupling, we find that the model corresponds to anisotropic Heisenberg and Hubbard models respectively.Comment: 20 pages RevTeX including 5 figures (1 in LaTeX, 4 in uuencoded EPS), Received by Phys. Rev. B 19 April 199

Multi-parameter scaling of the Kondo effect in quantum dots with an even number of electrons

We address a recent theoretical discrepancy concerning the Kondo effect in quantum dots with an even number of electrons where spin-singlet and -triplet states are nearly degenerate. We show that the discrepancy arises from the fact that the Kondo scaling involves many parameters, which makes the results depend on concrete microscopic models. We illustrate this by the scaling calculations of the Kondo temperature, $T_K$, as a function of the energy difference between the singlet and triplet states $\Delta$. $T_K(\Delta)$ decreases with increasing $\Delta$, showing a crossover from a power law with a universal exponent to that with a nonuniversal exponent. The crossover depends on the initial parameters of the model.Comment: 8 pages, 3 figure

Overshooting tipping point thresholds in a changing climate

Palaeorecords suggest that the climate system has tipping points, where small changes in forcing cause substantial and irreversible alteration to Earth system components called tipping elements. As atmospheric greenhouse gas concentrations continue to rise as a result of fossil fuel burning, human activity could also trigger tipping, and the impacts would be difficult to adapt to. Previous studies report low global warming thresholds above pre-industrial conditions for key tipping elements such as ice-sheet melt. If so, high contemporary rates of warming imply that exceeding these thresholds is almost inevitable, which is widely assumed to mean that we are now committed to suffering these tipping events. Here we show that this assumption may be flawed, especially for slow-onset tipping elements (such as the collapse of the Atlantic Meridional Overturning Circulation) in our rapidly changing climate. Recently developed theory indicates that a threshold may be temporarily exceeded without prompting a change of system state, if the overshoot time is short compared to the effective timescale of the tipping element. To demonstrate this, we consider transparently simple models of tipping elements with prescribed thresholds, driven by global warming trajectories that peak before returning to stabilize at a global warming level of 1.5 degrees Celsius above the pre-industrial level. These results highlight the importance of accounting for timescales when assessing risks associated with overshooting tipping point thresholds