Magnetic Quantum Phase Transitions in Kondo Lattices

The identification of magnetic quantum critical points in heavy fermion metals has provided an ideal setting for experimentally studying quantum criticality. Motivated by these experiments, considerable theoretical efforts have recently been devoted to reexamine the interplay between Kondo screening and magnetic interactions in Kondo lattice systems. A local quantum critical picture has emerged, in which magnetic interactions suppress Kondo screening precisely at the magnetic quantum critical point (QCP). The Fermi surface undergoes a large reconstruction across the QCP and the coherence scale of the Kondo lattice vanishes at the QCP. The dynamical spin susceptibility exhibits $\omega/T$ scaling and non-trivial exponents describe the temperature and frequency dependence of various physical quantities. These properties are to be contrasted with the conventional spin-density-wave (SDW) picture, in which the Kondo screening is not suppressed at the QCP and the Fermi surface evolves smoothly across the phase transition. In this article we discuss recent microscopic studies of Kondo lattices within an extended dynamical mean field theory (EDMFT). We summarize the earlier work based on an analytical $\epsilon$-expansion renormalization group method, and expand on the more recent numerical results. We also discuss the issues that have been raised concerning the magnetic phase diagram. We show that the zero-temperature magnetic transition is second order when double counting of the RKKY interactions is avoided in EDMFT.Comment: 10 pages, 4 figures; references added; as published in JPCM in early September, except for the correction to the legend for Figure

Susceptibility Inhomogeneity and Non-Fermi-Liquid Behavior in Ce(Ru_{0.5}Rh_{0.5})_2Si_2

Magnetic susceptibility and muon spin rotation (\muSR) experiments have been carried out to study the effect of structural disorder on the non-Fermi-liquid (NFL) behavior of the heavy-fermion alloy Ce(Ru_{0.5}Rh_{0.5})_2Si_2. Analysis of the bulk susceptibility in the framework of disorder-driven Griffiths-phase and Kondo-disorder models for NFL behavior yields relatively narrow distributions of characteristic spin fluctuation energies, in agreement with \muSR linewidths that give the inhomogeneous spread in susceptibility. \muSR and NMR data both indicate that disorder explains the "nearly NFL" behavior observed above \sim2 K, but does not dominate the NFL physics found at low temperatures and low magnetic fields.Comment: 6 pages, 4 figures, REVTeX, submitted to Phys. Rev.

Non-Fermi-Liquid Scaling in Ce(Ru_{0.5}Rh_{0.5})_2Si_2

We study the temperature and field dependence of the magnetic and transport properties of the non-Fermi-liquid compound Ce(Ru_{1-x}Rh_x)_2Si_2 at x=0.5. For fields $\lesssim$0.1T the experimental results show signatures of the presence of Kondo-disorder, expected to be large at this concentration. For larger fields, however, magnetic and transport properties are controlled by the coupling of the conduction electrons to critical spin-fluctuations. The temperature dependence of the susceptibility as well as the scaling properties of the magnetoresistance are in very good agreement with the predictions of recent dynamical mean-field theories of Kondo alloys close to a spin-glass quantum critical point.Comment: 4 pages, 4 figures. Improved discussion. To appear in Phys. Rev. Let

Neutron Scattering Study on Competition between Hidden Order and Antiferromagnetism in U(Ru_{1-x}Rh_x)_2Si_2 (x <= 0.05)

We have performed elastic and inelastic neutron scattering experiments on the solid solutions U(Ru_{1-x}Rh_x)_2Si_2 for the Ru rich concentrations: x=0, 0.01, 0.02, 0.025, 0.03, 0.04 and 0.05. Hidden order is suppressed with increasing x, and correspondingly the onset temperature T_m (~ 17.5 K at x=0) of weak antiferromagnetic (AF) Bragg reflection decreases. For x=0.04 and 0.05, no magnetic order is detected in the investigated temperature range down to 1.4 K. In the middle range, 0.02 <= x <= 0.03, we found that the AF Bragg reflection is strongly enhanced. At x=0.02, this takes place at ~ 7.7 K (=T_M), which is significantly lower than T_m (~ 13.7 K). T_M increases with increasing x, and seems to merge with T_m at x=0.03. If the AF state is assumed to be homogeneous, the staggered moment \mu_o estimated at 1.4 K increases from 0.02(2) \mu_B/U (x=0) to 0.24(1) \mu_B/U (x=0.02). The behavior is similar to that observed under hydrostatic pressure (\mu_o increases to ~ 0.25 \mu_B/U at 1.0 GPa), suggesting that the AF evolution induced by Rh doping is due to an increase in the AF volume fraction. We also found that the magnetic excitation observed at Q=(1,0,0) below T_m disappears as T is lowered below T_M.Comment: 4 pages, 4 figures, submitted to J. Phys. Soc. Jp

Effect of Pressure on Tiny Antiferromagnetic Moment in the Heavy-Electron Compound URu_2Si_2

We have performed elastic neutron-scattering experiments on the heavy-electron compound URu_2Si_2 for pressure P up to 2.8 GPa. We have found that the antiferrmagnetic (100) Bragg reflection below T_m ~ 17.5 K is strongly enhanced by applying pressure. For P < 1.1 GPa, the staggered moment mu_o at 1.4 K increases linearly from ~ 0.017(3) mu_B to ~ 0.25(2) mu_B, while T_m increases slightly at a rate ~ 1 K/GPa, roughly following the transition temperature T_o determined from macroscopic anomalies. We have also observed a sharp phase transition at P_c ~ 1.5 GPa, above which a 3D-Ising type of antiferromagnetic phase (mu_o ~ 0.4 mu_B) appears with a slightly reduced lattice constant.Comment: RevTeX, 4 pages, 4 eps figures, accepted for publication in Phys. Rev. Let

Fermi-liquid instabilities at magnetic quantum phase transitions

This review discusses instabilities of the Fermi-liquid state of conduction electrons in metals with particular emphasis on magnetic quantum critical points. Both the existing theoretical concepts and experimental data on selected materials are presented; with the aim of assessing the validity of presently available theory. After briefly recalling the fundamentals of Fermi-liquid theory, the local Fermi-liquid state in quantum impurity models and their lattice versions is described. Next, the scaling concepts applicable to quantum phase transitions are presented. The Hertz-Millis-Moriya theory of quantum phase transitions is described in detail. The breakdown of the latter is analyzed in several examples. In the final part experimental data on heavy-fermion materials and transition-metal alloys are reviewed and confronted with existing theory.Comment: 62 pages, 29 figs, review article for Rev. Mod. Phys; (v2) discussion extended, refs added; (v3) shortened; final version as publishe

Superconductivity in Ce- and U-based "122" heavy-fermion compounds

This review discusses the heavy-fermion superconductivity in Ce- and U-based compounds crystallizing in the body-centered tetragonal ThCr2Si2 structure. Special attention will be paid to the theoretical background of these systems which are located close to a magnetic instability.Comment: 12 pages, 9 figures. Invited topical review (special issue on "Recent Developments in Superconductivity") Metadata and references update

Decoupling between Field-instabilities of Antiferromagnetism and Pseudo-metamagnetism in Rh-doped CeRu2Si2 Kondo Lattice

Doping Kondo lattice system CeRu2Si2 with Rh-8% (Ce(Ru0.92Rh0.08)2Si2) leads to drastic consequences due to the mismatch of the lattice parameters between CeRu2Si2 and CeRh2Si2. A large variety of experiments clarifies the unusual properties of the ground state induced by the magnetic field from longitudinal antiferromagnetic (AF) mode at H = 0 to polarized paramagnetic phase in very high magnetic field. The separation between AF phase, paramagnetic phase and polarized paramagnetic phase varying with temperature, magnetic field and pressure is discussed on the basis of the experiments down to very low temperature. Similarities and differences between Rh and La substituted alloys are discussed with emphasis on the competition between transverse and longitudinal AF modes, and ferromagnetic fluctuations.Comment: 10 pages, 21 figures, accepted for publication in J. Phys. Soc. Jp