Session S16 - Non-Fermi Liquids II.
ORAL session, Wednesday afternoon, March 14
Room 303, Washington State Convention Center

[S16.001] ^27Al NMR Studies of Non-Fermi-Liquid Behavior in Y_0.8U_0.2Pd_2Al_3

^27Al NMR spectra have been taken on the Non-Fermi-Liquid (NFL) system Y_0.8U_0.2Pd_2Al_3 in order to characterize the role of disorder in the NFL behavior. Two peaks exhibiting Curie-Weiss-like temperature dependences in the Knight shifts and linewidths have been observed, as well as two additional peaks that have relatively little temperature dependence to the Knight shift. Plotting the Knight shifts K(T) of the respective peaks against the bulk susceptibility \chi(T) shows the minority peaks converging at \chi = 0 (high temperature) to meet one of the temperature-independent peaks (the bulk line) at K_0 = -0.10 \pm 0.04%. This is evidence that the temperature-dependent lines are impurity satellites due to ^27Al nuclei with various near-neighbor configurations of magnetic uranium atoms. The second temperature-independent peak has a Knight shift of 1.02 \pm 0.08% and does not merge with the other lines, and thus can be assumed to be an impurity phase. The linewidths of the impurity satellites increases at low temperatures, which is evidence for a disorder-driven mechanism for the NFL behavior.

Supported by the U.S. NSF.

[S16.002] NMR Studies of Fermi and non-Fermi liquid behavior in CePtSi_1-xGe_x, x=0 and x=0.1

Nuclear magnetic resonance (NMR) experiments have been carried out in the heavy-fermion compounds CePtSi_1-xGe_x, x=0 (Fermi-liquid like) and x=0.1 (non-Fermi-liquid (NFL) like). The ^29Si NMR linewidth in CePtSi_0.9Ge_0.1 increases rapidly with decreasing temperature and was found to be similar to that in CeRhRuSi_2, which is believed to agree well with disorder-driven NFL theories. CePtSi, in contrast, exhibits less line broadening than CePtSi_0.9Ge_0.1 at low temperatures. The difference between the linewidths for x=0 and x=0.1 alloys is \sim29 G at 24 K and \sim128 G at 4.2 K. This indicates that a wide distribution of local susceptibility induced by the crystallographic disorder could exist in this NFL material, and suggests that disorder effects play an important role in the NFL behavior.

Acknowledgment:

We gratefully thank Jungsoo Kim for measuring the susceptibility of our samples. The research has been supported by the U.S. NSF.

[S16.003] \boldmath \muSR and Non-Fermi-Liquid Behavior in UCu_5-xPd_x

Longitudinal-field muon spin-lat\-tice relaxation in the non-Fermi-liquid (NFL) heavy-fermion alloys UCu_5-xPd_x, x = 1.0 and 1.5, indicates strong inhomogeneity in the local f\/-electron spin dynamics. The relaxation function~G(t) is markedly sub-exponential, and at low fields exhibits the time/field scaling G(t,H) = G(t/H^\gamma) expected near a glassy transition [1]. At T = 0.05 K \gamma varies strongly with x: \gamma(x=1.0) = 0.3(1), but \gamma(x=1.5) = 0.7(1). This is in contrast to inelastic neutron scattering results (at much higher fre\-quencies), which yield \gamma = 0.33 for both concentrations [2]. From zero-field muon relaxation we find no evidence for static magnetism in UCu_4Pd above 0.05~K\@. The time/field scaling and lack of a finite-temperature phase transition seem to suggest quantum spin-glass behavior. [2pt] 1. A. Keren et al.\/, Phys. Rev. Lett. 77, 1386 (1996). 2. M. C. Aronson et al.\/, Phys. Rev. Lett. 75, 725 (1995).

[S16.004] Griffiths effects and quantum critical points in dirty superconductors without spin-rotation invariance: One-dimensional examples

We introduce a strong-disorder renormalization group (RG) approach suitable for investigating the quasiparticle excitations of disordered superconductors in which the quasiparticle spin is not conserved. We analyze one-dimensional models with this RG and with elementary transfer matrix methods. We find that such models with broken spin rotation invariance generically lie in one of two topologically distinct localized phases. Close enough to the critical point separating the two phases, the system has a power-law divergent low-energy density of states (with a non-universal continuously varying power-law) in either phase, due to quantum Griffiths singularities. This critical point belongs to the same infinite-disorder universality class as the one dimensional particle-hole symmetric Anderson localization problem, while the Griffiths phases in the vicinity of the transition are controlled by lines of strong (but not infinite) disorder fixed points terminating in the critical point.

[S16.005] Griffiths effects and delocalization transitions in two-dimensional bipartite random hopping

We study the random hopping problem on 2d bipartite lattices (e.g., 2d square lattice) using exact diagonalization methods and the strong-randomness RG approach. When all hopping elements are random and drawn from the same distribution, the system is in a `metallic' (delocalized) Griffiths phase: In this phase, the localization length diverges at the band center and the density of states exhibits a power-law behavior \rho(\epsilon) \sim \epsilon^-1+d/z; the dynamical exponent z is non-universal and depends on the strength of the disorder. Introducing staggered dimerization drives the system into a `band insulator' (localized) Griffiths phase for strong enough dimerization. At the critical point separating the two phases the density of states apparently exhibits a Gade singularity \rho(\epsilon) \sim \frac1\epsilon e^-c\sqrt|\ln \epsilon|. Our strong-randomness RG provides a physical picture of the Griffiths phases and tentatively identifies the critical point as a peculiar infinite-randomness fixed point.

[S16.006] Numerical study of disordered quantum magnets.

We study the behavior of the fully connected quantum spin glasses by exact diagonalization techniques. For the disordered Ising model in a transverse field \Gamma at T=0, we obtain the behavior of static and dynamical quantities in the disordered and in the spin glass ordered phase. We find that the order parameter grows linearly with \Gamma_c - \Gamma below the quantum critical point \Gamma_c. While the spectral function \chi''(ømega) is gaped in the disordered phase, we find a dramatic change in the glassy phase, where it splits into a delta function contribution plus a regular part.

[S16.007] Onset of magnetic order in the doped semimetal Ce(Ni,Cu)Sn

Several single crystals of the doped semimetal CeNi_1-xCu_xSn were investigated by magnetization (M) and specific heat (C) measurements at low temperatures (T) and high magnetic fields (B \parallel a) close to the onset of magnetic order. While M and C/T are steadily increasing towards low T for x=0.05 and x=0.067 , they show a small maximum at the same T_M=0.4K for x=0.078, hinting at the onset of antiferromagnetic order, which is destroyed in a small field B<1T. At higher T (T \approx 4K) a pronounced shoulder in M(T) is still visible, which is suppressed in high magnetic fields (B \approx 9T). This feature is reminiscent of the maximum in pure CeNiSn hinting at a pseudogap. Through chemical doping with Cu, magnetic order evolves before the pseudogap has completely vanished, leading to two energy scales in the low energy excitation spectrum.

[S16.008] La4Ru6O19 and La3Ru3O11: quantum critical behavior resulting from metal-metal bonding

Even though La_4Ru_6O_19 has direct Ru-Ru bonding and La_3Ru_3O_11 does not, these two compounds are otherwise very similar. Both compounds have a virtually identical Ru_12O_36 conduction networks and identical Ru oxidation states of +4.33. However, La_3Ru_3O_11 has transport and magnetic behavior typical to metals while La_4Ru_6O_19 has a number of unusual properties, including T-linear resistivity, a large electronic contribution to the specific heat, and a possible spin gap observable in the magnetic susceptibility data. Taken together, these data suggest that La_4Ru_6O_19 is experiencing quantum critical fluctuations and is therefore at the boundary of a quantum phase transition. Thus metal-metal bonding is believed to a major factor in determining the unique properties of La_4Ru_6O_19.

[S16.009] Spectroscopy of Matter Near Criticality

We predict a new spectroscopic effect that should occur very generaly at quantum phase transitions described by O(n) sigma models, between any fully gapped quantum disordered insulator and a state with continuous broken symmetry such as an antiferromagnet or a superconductor. The effect we predict is a sequence of resonances in the susceptibility when the system is slightly detuned from criticality. On the insulating side these resonances might be understood physically as bound states of excitons, while on the ordered side they may be thought of as bound states of Goldstones. Since this spectrum is formally similar to a meson spectrum in particle physics, this prediction is relevant to the larger issue of whether the empty vacuum of space might occur as an emergent phenomenon is ordinary matter. Our prediction rests on an analogy between 1D antiferromagnets and 2D systems at a phase transition. The shape of the susceptibility in 1D antiferromagnets not at a phase transition, known from exact solution to be given by the fractionalization of the spin-wave in 2 spinons, is very similar to the shape of the susceptibility of 2D systems at a quantum phase transition. We propose that the exciton, the elementary excitation of an insulator, fractionalizes at the quantum phase transition in two 'spinons', in our case, the electron and the hole. We find a solid state realization of our transition by a tight-binding model of electrons on a lattice which undergoes an insulator to antiferromagnet transition.

[S16.010] Thermoelectric Behaviour Near Magnetic Quantum Critical Point

We use a coupled spin-fermion model to study the thermoelectric behaviour of a heavy fermion compound when it is close to an antiferromagnetic quantum critical point. When the low energy spin fluctuations are quasi two dimensional, as has been observed in magnetic susceptibility of YbRh_2Si_2 and CeCu_6-xAu_x , most of the Fermi surfaceis ``hot''. Due to enhanced scattering with the nearly critical spin fluctuations, the electrons in the hot region are strongly renormalized. We argue that there is an intermediate energy scale in which the qualitative aspects of the renormalized hot electrons are captured by a weak-coupling perturbative calculation. Our examination of the electron self energy shows that the entropy carried by the hot electrons is larger than usual. This accounts for the anomalous logarithmic temperature dependence of specific heat observed in the materials mentioned above. We show that the same mechanism produces logarithmic temperature dependence in thermopower. This has been observed in CeCu_6-xAu_x . We expect to see the same behaviour from future experiments on YbRh_2Si_2.

[S16.011] The Kondo Lattice model from local viewpoint.

We study the phase diagram and the spectrum of excitations of the two-dimensional S=1/2 Kondo lattice model at finite doping. The starting point of our calculation is the paramagnetic phase where we use the bond-operator representation to take into account the local singlet correlations between the f and d electrons. An attractive feature of this representation is that it naturally leads to the existence of a bosonic S=1 (spin gap) mode. We present results for the evolution of the magnetic mode as a function of doping far from as well as close to the quantum phase transition point separating the paramagnetic and antiferromagnetically ordered phases. The relationship between our work and previous approaches and recent experiments on CeCu_6-xAu_x is discussed.

[S16.012] Local criticality in heavy fermion metals: a dynamical mean field analysis of Kondo lattice models

Recently, we have introduced the notion of a locally critical quantum phase transition for strongly correlated metals[1]. Here we present a microscopic analysis of Kondo lattices using an extended dynamical mean-field theory. The Kondo lattice is mapped to a self-consistent impurity problem describing a local moment coupled to two dissipative baths. A fermionic bath accounts for temporal fluctuations arising from hopping of electrons between the local site and the rest of the lattice; a bosonic bath represents a fluctuating magnetic field generated by the moments at all other sites. We find two types of quantum critical point. The first corresponds to the traditional picture encoded in the Doniach phase diagram, with critical behavior given by the Hertz theory. The second type is locally critical; two kinds of critical degrees of freedom co-exist: long-wavelength fluctuations of the order parameter, and local fluctuations originating from the local moments. The lattice susceptibility has an anomalous frequency dependence throughout the Brillouin zone, and at the ordering wavevector exhibits ømega/T scaling. The uniform susceptibility has a modified Curie-Weiss form: \chi^-1\!\sim\!\Theta\!+\!B T^\alpha. Comparison will be made with experiments in heavy fermion metals.

[1]Q. Si, S. Rabello, K. Ingersent, and J. L. Smith, cond-mat/0011477

[S16.013] Locally critical quantum phase transitions in strongly correlated metals

When a metal undergoes a continuous quantum phase transition, non-Fermi liquid behavior arises near the critical point. It is standard to assume that all low-energy degrees of freedom induced by quantum criticality are spatially extended, corresponding to long-wavelength fluctuations of the order parameter. However, this picture has been contradicted by recent experiments on a prototype system: heavy fermion metals at a zero-temperature magnetic transition. Examples include CePd_2Si_2, CeCu_6-xAu_x, CeNi_2Ge_2, and Yb Rh_2Si_2. In particular, neutron scattering from CeCu_6-xAu_x has revealed anomalous dynamics at atomic length scales. Here we give some general arguments for the existence of a locally critical quantum phase transition in a model of heavy fermions[1]. The dynamics at the critical point are in agreement with the neutron scattering and magnetization experiments in the heavy fermion systems. We also argue that local criticality is a phenomenon of general relevance to strongly correlated metals, including doped Mott insulators.

[1]Q. Si, S. Rabello, K. Ingersent, and J. L. Smith, cond-mat/0011477.

[S16.014] Thermal expansion in heavy fermion metals close to quantum criticality

We give general scaling arguments about thermal expansion of metals close to a quantum critical point. The thermal expansion coefficient is in general more singular than the specific heat and can hence serve as an important probe of non-Fermi liquid behavior. We present calculations of the thermal expansion in specific microscopic models of quantum critical points and compare our results with experiments[1] in CeCu2Si2 and YbRh2Si2.

[1] P. Gegenwart, private communications.

[S16.015] Thermopower in Cobalt Oxides

Recently, Terasaki et al., [PRB\bf56, R12685 (1997).] have discovered large thermopower in the layered compound NaCo_2O_4, and proposed that the compound is of importance in view of potential application in thermoelectric devices which convert heat into energy. Some other cobalt oxides also show large thermopower. It is, therefore, of importance to examine the origin of the large thermopower.

We have examined the thermopower in the cobalt oxides theoretically using Heikes formula. The formula indicates that the thermopower is governed by the change of degeneracy per added carrier. In the cobalt oxides, carriers have characteristic degeneracy due to spin and orbital degrees of freedom caused by strong correlation. The motion of carriers causes the motion of the degeneracy, which depends on the difference of degeneracy between local electronic states of Co^3+ and Co^4+ ions. Then, we find the thermopower (Q) in the cobalt oxides to be Q=-k_Bøver e\ln \left(g_3øver g_4xøver 1-x\right) , where g_3 and g_4 denote the degeneracies of Co^3+ and Co^4+ ions, respectively, and x is the concentration of Co^4+ ions. When we apply the theory to NaCo_2O_4, the large positive thermopower is obtained assuming low-spin(LS) state of Co^3+ and LS (and/or high-spin) state of Co^4+ ions. These ionic states have been observed by the magnetic susceptibility and NMR measurements [R.Ray et al., PRB 59, 9454 (1999).] in NaCo_2O_4. The ionic states and the observed large thermopower are consistent with our theory.

Part S of program listing