Effect of a nonzero temperature on quantum critical points in itinerant fermion systems

Kondo breakdown and hybridization fluctuations in the kondo-heisenberg lattice

We study the deconfined quantum critical point of the Kondo-Heisenberg lattice in three dimensions using a fermionic representation for the localized spins. The mean-field phase diagram exhibits a zero temperature quantum critical point separating a spin liquid phase where the hybridization vanishes and a Kondo phase where it does not. Two solutions can be stabilized in the Kondo phase: namely, a uniform hybridization when the band masses of the conduction electrons and the spinons have the same sign, and a modulated one when they have opposite sign. For the uniform case, we show that above a very small temperature scale, the critical fluctuations associated with the vanishing hybridization have dynamical exponent z=3, giving rise to a resistivity that has a TlogT behavior. We also find that the specific heat coefficient diverges logarithmically in temperature, as observed in a number of heavy fermion metals.

Nonequilibrium quantum criticality in open electronic systems

A theory is presented of quantum criticality in open (coupled to reservoirs) itinerant-electron magnets, with nonequilibrium drive provided by current flow across the system. Both departures from equilibrium at conventional (equilibrium) quantum critical points and the physics of phase transitions induced by the nonequilibrium drive are treated. Nonequilibrium-induced phase transitions are found to have the same leading critical behavior as conventional thermal phase transitions.

Effect of fermi surface curvature on low-energy properties of fermions with singular interactions

We discuss the effect of Fermi surface curvature on long-distance or time asymptotic behaviors of two-dimensional fermions interacting via a gapless mode described by an effective gauge-field-like propagator. By comparing the predictions based on the idea of multidimensional bosonization with those of the strong-coupling Eliashberg approach, we demonstrate that an agreement between the two requires a further extension of the former technique.

Elementary excitations of quantum critical (2+1)-dimensional antiferromagnets

It has been proposed that there are degrees of freedom intrinsic to quantum critical points that can contribute to quantum critical physics. We point out that this conclusion is quite general below the upper critical dimension. We show that in (2+1)D antiferromagnets Skyrmion excitations are stable at criticality and identify them as the critical excitations. We find exact solutions composed of Skyrmion and anti-Skyrmion superpositions, which we call topolons. We include the topolons in the partition function and renormalize by integrating out small size topolons and short wavelength spin waves. We obtain a correlation length exponent nu=0.690 666 and anomalous dimension eta=0.0166.

Nonvanishing energy scales at the quantum critical point of CeCoIn5

Heat and charge transport were used to probe the magnetic field-tuned quantum critical point in the heavy-fermion metal CeCoIn5. A comparison of electrical and thermal resistivities reveals three characteristic energy scales. A Fermi-liquid regime is observed below T(FL), with both transport coefficients diverging in parallel and T(FL) -->0 as H --> Hc, the critical field. The characteristic temperature of antiferromagnetic spin fluctuations, T(SF), is tuned to a minimum but finite value at Hc, which coincides with the end of the T-linear regime in the electrical resistivity. A third temperature scale, T(QP), signals the formation of quasiparticles, as fermions of charge e obeying the Wiedemann-Franz law. Unlike T(FL), it remains finite at Hc, so that the integrity of quasiparticles is preserved, even though the standard signature of Fermi-liquid theory fails.

Dimensional reduction at a quantum critical point

Competition between electronic ground states near a quantum critical point (QCP)--the location of a zero-temperature phase transition driven solely by quantum-mechanical fluctuations--is expected to lead to unconventional behaviour in low-dimensional systems. New electronic phases of matter have been predicted to occur in the vicinity of a QCP by two-dimensional theories, and explanations based on these ideas have been proposed for significant unsolved problems in condensed-matter physics, such as non-Fermi-liquid behaviour and high-temperature superconductivity. But the real materials to which these ideas have been applied are usually rendered three-dimensional by a finite electronic coupling between their component layers; a two-dimensional QCP has not been experimentally observed in any bulk three-dimensional system, and mechanisms for dimensional reduction have remained the subject of theoretical conjecture. Here we show evidence that the Bose-Einstein condensate of spin triplets in the three-dimensional Mott insulator BaCuSi2O6 (refs 12-16) provides an experimentally verifiable example of dimensional reduction at a QCP. The interplay of correlations on a geometrically frustrated lattice causes the individual two-dimensional layers of spin-(1/2) Cu2+ pairs (spin dimers) to become decoupled at the QCP, giving rise to a two-dimensional QCP characterized by linear power law scaling distinctly different from that of its three-dimensional counterpart. Thus the very notion of dimensionality can be said to acquire an 'emergent' nature: although the individual particles move on a three-dimensional lattice, their collective behaviour occurs in lower-dimensional space.

Quantum criticality in the cubic heavy-fermion system CeIn3-xSnx

We report a comprehensive study of CeIn3-xSnx (0.55<or=x< or=0.8) single crystals close to the antiferromagnetic quantum-critical point (QCP) at xc approximately 0.37 by means of the low-temperature thermal expansion and Grüneisen parameter. This system represents the first example for a cubic heavy fermion in which TN can be suppressed continuously down to T=0. A characteristic sign change of the Grüneisen parameter between the antiferromagnetic and paramagnetic states indicates the accumulation of entropy close to the QCP. The observed quantum-critical behavior is compatible with the predictions of the itinerant theory for three-dimensional critical spin fluctuations. This has important implications for the role of the dimensionality in heavy-fermion QCPs.

Nonlocal magnetic field-tuned quantum criticality in cubic CeIn(3-x)Sn(x) (x = 0.25)

We show that antiferromagnetism in lightly (approximately 8%) Sn-doped CeIn3 terminates at a critical field mu0H(c) = 42 +/- 2 T. Electrical transport and thermodynamic measurements reveal the effective mass m* not to diverge, suggesting that cubic CeIn3 is representative of a critical spin-density wave (SDW) scenario, unlike the local quantum critical points reported in anisotropic systems such as CeCu(6-x)Au(x) and YbRh2Si(2-x)Ge(x). The existence of a maximum in m* at a lower field mu0H(x) = 30 +/- 1 T may be interpreted as a field-induced crossover from local moment to SDW behavior as the Néel temperature falls below the Fermi temperature.

Field-dependent ordered phases and Kondo phenomena in the filled skutterudite compound PrOs4As12

Electrical resistivity, specific heat, and magnetization measurements to temperatures as low as 80 mK and magnetic fields up to 16 T were made on the filled skutterudite compound PrOs4As12. The measurements reveal the presence of two ordered phases at temperatures below approximately 2.3 K and in fields below approximately 3 T. Neutron-scattering experiments in zero field establish an antiferromagnetic ground state < 2.28 K. In the antiferromagnetically ordered state, the electronic-specific heat coefficient gamma approximately 1 J/mol x K2 below 1.6 K and 0 < or = H < or = 1.25 T. The temperature and magnetic-field dependence of the electrical resistivity and specific heat in the paramagnetic state are consistent with single-ion Kondo behavior with a low Kondo temperature on the order of 1 K. The electronic-specific heat in the paramagnetic state can be described by the resonance-level model with a large zero-temperature electronic-specific heat coefficient that decreases with increasing magnetic field from approximately 1 J/mol x K2 at 3 T to approximately 0.2 J/mol x K2 at 16 T.

Critical phenomena and the quantum critical point of ferromagnetic Zr(1-x)NbxZn2

We present a study of the magnetic properties of Zr(1-x)NbxZn2, using an Arrott plot analysis of the magnetization. The Curie temperature Tc is suppressed to zero temperature for Nb concentration xc = 0.083+/-0.002, while the spontaneous moment vanishes linearly with Tc as predicted by the Stoner theory. The initial susceptibility chi displays critical behavior for x <or= xc , with a critical exponent which smoothly crosses over from the mean field to the quantum critical value. For high temperatures and x <or= xc, and for low temperatures and x >or= xc we find that chi(-1) = chi0(-1) + aT(4/3), where chi0(-1) vanishes as x-->xc. The resulting magnetic phase diagram shows that the quantum critical behavior extends over the widest range of temperatures for x=xc, and demonstrates how a finite transition temperature ferromagnet is transformed into a paramagnet, via a quantum critical point.

Can Competition between the crystal field and the Kondo effect cause non-Fermi-liquid-like behavior?

The recently reported unusual behavior of the static and dynamical magnetic susceptibility as well as the specific heat in Ce(1-x)La(x)Ni9Ge4 has raised the question of a possible non-Fermi-liquid ground state in this material. We argue that for a consistent physical picture the crystal-field splitting of two low-lying magnetic doublets of the Ce 4f-shell must be taken into account. Furthermore, we show that for a splitting of the order of the low temperature scale T* of the system a crossover behavior between an SU(4) and an SU(2) Kondo effect is found. The screening of the two doublets occurs on different temperature scales leading to a different behavior of the magnetic susceptibility and the specific heat at low temperatures. The experimentally accessible temperature regime down to 50 mK still lies in the extended crossover regime into a strong-coupling Fermi-liquid fixed point.

Developments of the theory of spin fluctuations and spin fluctuation-induced superconductivity

Theory of spin fluctuations as developed in the past 30 years have played important roles in the theory of magnetism in metals, particularly in elucidating the properties around the magnetic instability or quantum critical points. Recently the theory has been extended to deal with the spin fluctuaion-mediated superconductivity with anisotropic order parameters in strongly correlated electron systems. These theoretical developments are briefly reviewed and the high temperature superconductivity of cuprates and organic and heavy electron superconductors are discussed in the light of these theories.

Non-Fermi liquid states in the pressurized CeCu2(Si1-xGex)2 system: two critical points

In the archetypal strongly correlated electron superconductor CeCu2Si2 and its Ge-substituted alloys CeCu2(Si1-xGex)2 two quantum phase transitions--one magnetic and one of so far unknown origin-can be crossed as a function of pressure. We examine the associated anomalous normal state by detailed measurements of the low temperature resistivity (rho) power-law exponent alpha. At the lower critical point (at pcl, 1<or=alpha<or=1.5) alpha depends strongly on Ge concentration x and thereby on disorder level, consistent with a Hlubina-Rice-Rosch scenario of critical scattering off antiferromagnetic fluctuations. By contrast, alpha is independent of x at the upper quantum phase transition (at pc2, alpha approximately equal to 1), suggesting critical scattering from local or q=0 modes, in agreement with a density- or valence-fluctuation approach.

Superfluid density of strongly underdoped cuprate superconductors from a four-dimensional XY model

A new phenomenology is proposed for the superfluid density rhos of strongly underdoped cuprate superconductors based on recent data for ultraclean single crystals of YBa2Cu3O7-x. We show that the puzzling departure from Uemura scaling and the decline of the slope as the Tc=0 quantum critical point is approached can be understood in terms of the renormalization of quasiparticle effective charge by quantum fluctuations of the superconducting phase. We then employ a (3+1)-dimensional XY model to calculate, within particular approximations, the renormalization of rhos and its slope, explain the new phenomenology, and predict its eventual demise close to the quantum critical point.

Quantum critical point of an itinerant antiferromagnet in a heavy fermion

A quantum critical point of the heavy fermion Ce(Ru(1-x)Rh(x))2Si2, (x = 0,0.03) has been studied by single-crystalline neutron scattering. By accurately measuring the dynamical susceptibility at the antiferromagnetic wave vector k3 = 0.35c*, we have shown that the inverse energy width gamma(k3), i.e., the inverse correlation time, depends on temperature as gamma(k3) = c1 + c2T((3/2)+/-0.1), where c1 and c2 are x dependent constants, in a low temperature range. This critical exponent 3/2 +/- 0.1 proves that the quantum critical point is controlled by that of the itinerant antiferromagnet.

Schwinger boson approach to the fully screened Kondo model

We apply the Schwinger boson scheme to the fully screened Kondo model and generalize the method to include antiferromagnetic interactions between ions. Our approach captures the Kondo crossover from local moment behavior to a Fermi liquid with a nontrivial Wilson ratio. When applied to the two-impurity model, the mean-field theory describes the "Varma-Jones" quantum phase transition between a valence bond state and a heavy Fermi liquid.

Breakdown of weak-field magnetotransport at a metallic quantum critical point

We show how the collapse of an energy scale in a quantum critical metal can lead to physics beyond the weak-field limit usually used to compute transport quantities. For a density-wave transition we show that the presence of a finite magnetic field at the critical point leads to discontinuities in the transport coefficients as temperature tends to zero. The origin of these discontinuities lies in the breakdown of the weak-field Jones-Zener expansion which has previously been used to argue that magnetotransport coefficients are continuous at simple quantum critical points. The presence of potential scattering and magnetic breakdown rounds the discontinuities over a window determined by tauDelta < 1 where Delta is the order parameter and tau is the quasiparticle elastic lifetime.

Universal scaling of the conductivity at the superfluid-insulator phase transition

The scaling of the conductivity at the superfluid-insulator quantum phase transition in two dimensions is studied by numerical simulations of the Bose-Hubbard model. In contrast to previous studies, we focus on properties of this model in the experimentally relevant thermodynamic limit at finite temperature T. We find clear evidence for deviations from omega k scaling of the conductivity towards omega k/T scaling at low Matsubara frequencies omega k. By careful analytic continuation using Padé approximants we show that this behavior carries over to the real frequency axis where the conductivity scales with omega/T at small frequencies and low temperatures. We estimate the universal dc conductivity to be sigma* = 0.45(5)Q2/h, distinct from previous estimates in the T = 0, omega/T >> 1 limit.

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 re-examining 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 ω/T scaling and non-trivial exponents describe the temperature and frequency dependences of various physical quantities. These properties are to be contrasted with the conventional spin density wave 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 ϵ-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 Ruderman-Kittel-Kasuya-Yosida interactions is avoided in EDMFT.

Thermodynamic properties in the approach to the quantum critical point of the spin-ladder material Na2Co2(C2O4)3(H2O)2

Magnetic susceptibility and heat capacity measurements as a function of temperature on a single-crystal sample of a spin-ladder material, Na2Co2(C2O4)3(H2O)2, are reported. Principal susceptibilities, parallel and perpendicular to the ladder direction, respectively, show broad maxima around 22 and 17 K. Both susceptibilities decay exponentially down to about 5 K and thereafter they are essentially independent of temperature. These findings amount to a signature of a quantum phase transition from a spin-liquid to Néel ordered state previously predicted theoretically. No anomaly is found in the heat capacity around the transition temperature.

Phase bifurcation and quantum fluctuations in Sr3Ru2O7

The bilayer ruthenate Sr3Ru2O7 has been cited as a textbook example of itinerant metamagnetic quantum criticality. However, recent studies of the ultrapure system have revealed striking anomalies in magnetism and transport in the vicinity of the quantum critical point. Drawing on fresh experimental data, we show that the complex phase behavior reported here can be fully accommodated within the framework of a simple Landau theory. We discuss the potential physical mechanisms that underpin the phenomenology, and assess the capacity of the ruthenate system to realize quantum tricritial behavior.

Quantum correction to conductivity close to a ferromagnetic quantum critical point in two dimensions

We study the temperature dependence of the conductivity due to quantum interference processes for a two-dimensional disordered itinerant electron system close to a ferromagnetic quantum critical point. Near the quantum critical point, the crossover between diffusive and ballistic regimes of quantum interference effects occurs at a temperature T*=1/taugamma(E(F)tau)2, where gamma is the parameter associated with the Landau damping of the spin fluctuations, tau is the impurity scattering time, and E(F) is the Fermi energy. For a generic choice of parameters, T* is smaller than the nominal crossover scale 1/tau. In the ballistic quantum critical regime, the conductivity behaves as T1/3.

Understanding the heavy fermion phenomenology from a microscopic model

We solve the 3D periodic Anderson model using a two impurity cluster dynamical mean field theory. We obtain the temperature versus hybridization phase diagram. Approaching the quantum critical point (QCP) both the Néel and lattice Kondo temperatures decrease and they do not cross at the lowest temperature we reached. While strong ferromagnetic spin fluctuation on the Kondo side is observed, our result suggests the critical static spin susceptibility is local in space at the QCP. We observe in the crossover region a logarithmic temperature dependence in the specific heat coefficient and spin susceptibility.

Fractionalization and Fermi-surface volume in heavy-fermion compounds: the case of YbRh2Si2

We establish an effective theory for heavy-fermion compounds close to a zero temperature antiferromagnetic (AFM) transition. Coming from the heavy Fermi liquid phase across to the AFM phase, the heavy electron fractionalizes into a light electron, a bosonic spinon, and a new excitation: a spinless fermionic field. Assuming this field acquires dynamics and dispersion when one integrates out the high energy degrees of freedom, we give a scenario for the volume of its Fermi surface through the phase diagram. We apply our theory to the special case of YbRh2(Si1-xGex)2 where we recover, within experimental resolution, several low temperature exponents for transport and thermodynamics.

Superconductivity in CeCoIn5-xSnx: veil over an ordered state or novel quantum critical point?

Measurements of specific heat and electrical resistivity in magnetic fields up to 9 T along [001] and temperatures down to 50 mK of Sn-substituted CeCoIn5 are reported. The maximal -ln(T) divergence of the specific heat at the upper critical field Hc2 down to the lowest temperature characteristic of non-Fermi-liquid systems at the quantum critical point (QCP), the universal scaling of the Sommerfeld coefficient, and agreement of the data with spin-fluctuation theory provide strong evidence for quantum criticality at Hc2 for all x< or =0.12 in CeCoIn5-xSnx. These results indicate the "accidental" coincidence of the QCP located near Hc2 in pure CeCoIn5, in actuality, constitute a novel quantum critical point associated with unconventional superconductivity.

Non-Fermi-liquid behavior within the ferromagnetic phase in URu2-xRexSi2

The URu2-xRexSi2 system exhibits ferromagnetic order for Re concentrations 0.3 < x < or =1.0. Non-Fermi-liquid (NFL) behavior is observed in the specific heat for 0.15< or = x< or =0.6 [C/T proportional to, -lnT (or T(-0.1))], and also in the power-law T dependence of the electrical resistivity [rhoT proportional to, Tn] with n<2 for 0.15< or = x <0.8, at low T, providing strong evidence that the NFL behavior persists within the ferromagnetic phase. Furthermore, the deviation of the physical properties of URu2-xRexSi2 from Fermi-liquid behavior is most pronounced at the ferromagnetic quantum critical point, and the NFL behavior found in the ferromagnetic phase may be consistent with the Griffiths-McCoy phase model.

Local Quantum Critical Point in the Pseudogap Anderson Model: Finite-T Dynamics and ω/T Scaling

The pseudogap Anderson impurity model is a paradigm for locally critical quantum phase transitions. Within the framework of the local moment approach we study its finite-T dynamics, as embodied in the single-particle spectrum, in the vicinity of the symmetric quantum critical point (QCP) separating generalized Fermi liquid (Kondo screened) and local moment phases. The scaling spectra in both phases, and at the QCP itself, are obtained analytically. A key result is that pure omega/T scaling obtains at the QCP, where the Kondo resonance has just collapsed. The connection between the scaling spectra in either phase and that at the QCP is explored in detail.

Quantum criticality

As we mark the centenary of Albert Einstein's seminal contribution to both quantum mechanics and special relativity, we approach another anniversary--that of Einstein's foundation of the quantum theory of solids. But 100 years on, the same experimental measurement that puzzled Einstein and his contemporaries is forcing us to question our understanding of how quantum matter transforms at ultra-low temperatures.

Hall-effect evolution across a heavy-fermion quantum critical point

A quantum critical point (QCP) develops in a material at absolute zero when a new form of order smoothly emerges in its ground state. QCPs are of great current interest because of their singular ability to influence the finite temperature properties of materials. Recently, heavy-fermion metals have played a key role in the study of antiferromagnetic QCPs. To accommodate the heavy electrons, the Fermi surface of the heavy-fermion paramagnet is larger than that of an antiferromagnet. An important unsolved question is whether the Fermi surface transformation at the QCP develops gradually, as expected if the magnetism is of spin-density-wave (SDW) type, or suddenly, as expected if the heavy electrons are abruptly localized by magnetism. Here we report measurements of the low-temperature Hall coefficient (R(H))--a measure of the Fermi surface volume--in the heavy-fermion metal YbRh2Si2 upon field-tuning it from an antiferromagnetic to a paramagnetic state. R(H) undergoes an increasingly rapid change near the QCP as the temperature is lowered, extrapolating to a sudden jump in the zero temperature limit. We interpret these results in terms of a collapse of the large Fermi surface and of the heavy-fermion state itself precisely at the QCP.

Anomalous scaling at the quantum critical point in itinerant antiferromagnets

We show that the Hertz phi(4) theory of quantum criticality is incomplete as it misses anomalous nonlocal contributions to the interaction vertices. For antiferromagnetic quantum transitions, we found that the theory is renormalizable only if the dynamical exponent z=2. The upper critical dimension is still d=4 - z=2; however, the number of marginal vertices at d=2 is infinite. As a result, the theory has a finite anomalous exponent already at the upper critical dimension. We show that for d<2 the Gaussian fixed point splits into two non-Gaussian fixed points. For both fixed points, the dynamical exponent remains z=2.

Emergent fluctuation hot spots on the fermi surface of CeIn(3) in strong magnetic fields

de Haas-van Alphen measurements on CeIn3 in pulsed magnetic fields of up to 65 T reveal an increase in the quasiparticle effective mass with the field concentrated at "hot spots" on the Fermi surface as the Néel phase is suppressed. As well as revealing the existence of fluctuations deep within the antiferromagnetic phase, these data suggest that a possible new type of quantum critical point may exist in strong magnetic fields that involves only parts of the Fermi surface.

4f-electron localization in CexLa 1-xM In5 with M=Co, Rh, or Ir

de Haas-van Alphen measurements on Ce(x)La(1-x)MIn(5) yield contrasting types of behavior that depend on whether M=Co and Ir or M=Rh. A stronger x-dependent scattering in the case of M=Co and Ir is suggestive of a stronger relative coupling, J/W, of the conduction electrons to the 4f electrons, which would then account for the development of a heavy composite Fermi-liquid state as x-->1. The failure of a composite Fermi-liquid state to form for any x in the case of M= Rh is shown to be inconsistent with theoretical models that propose antiferromagnetism to result from spin-density-wave formation.

Breakdown of the perturbative renormalization group at certain quantum critical points

It is shown that the presence of multiple time scales at a quantum critical point can lead to a breakdown of the loop expansion for critical exponents, since coefficients in the expansion diverge. Consequently, results obtained from finite-order perturbative renormalization-group treatments may not be an approximation in any sense to the true asymptotic critical behavior. This problem manifests itself as a nonrenormalizable field theory, or, equivalently, as the presence of a dangerous irrelevant variable. The quantum ferromagnetic transition in disordered metals provides an example.

Grüneisen ratio divergence at the quantum critical point in CeCu(6-x)Agx

The heavy-fermion system CeCu6-xAgx is studied at its antiferromagnetic quantum critical point, xc=0.2, by low-temperature (T> or =50 mK) specific heat, C(T), and volume thermal expansion, beta(T), measurements. Whereas C/T proportional to log((T0/T) would be compatible with the predictions of the itinerant spin-density-wave (SDW) theory for two-dimensional critical spin fluctuations, beta(T)/T and the Grüneisen ratio, Gamma(T) proportional to beta/C, diverge much weaker than expected, in strong contrast to this model. Both C and beta, plotted as a function of the reduced temperature t=T/T0 with T0=4.6 K, are similar to what was observed for YbRh2(Si(0.95)Ge(0.05))2 (T0=23.3 K), indicating a striking discrepancy to the SDW prediction in both systems.

Ferromagnetic transition in one-dimensional itinerant electron systems

We use bosonization to derive the effective field theory that properly describes ferromagnetic transition in one-dimensional itinerant electron systems. The resultant theory is shown to have dynamical exponent z = 2 at tree level and upper critical dimension dc = 2. Thus one dimension is below the upper critical dimension of the theory, and the critical behavior of the transition is controlled by an interacting fixed point, which we study via epsilon expansion. Comparisons will be made with the Hertz-Millis theory, which describes the ferromagnetic transition in higher dimensions.

Quantum phase transitions of magnetic rotons

Because of weak spin-orbit coupling and broken inversion symmetry the paramagnons of an itinerant, almost ferromagnetic system become magnetic rotons. Using self-consistent Hartree and renormalization group calculations, we study weak fluctuation-driven first-order quantum phase transitions, a quantum tricritical point controlled by anisotropy, and non-Fermi liquid behavior associated with the large phase volume of magnetic rotons. We propose that magnetic rotons are essential for the description of the anomalous high-pressure behavior of the itinerant helical ferromagnet MnSi.

Unusual oscillation in tunneling magnetoresistance near a quantum critical point in Sr3Ru2O7

We performed single-electron tunneling measurements on bilayer ruthenate Sr3Ru2O7. We observe an unusual oscillation in tunneling magnetoresistance near the metamagnetic quantum phase transition. The characteristic features of this oscillation suggest that it is unrelated to traditional quantum oscillations caused by orbit quantization. In addition, tunneling spectra are found to change sharply in the low bias voltage range of V<2 mV near the transition field. These observations reveal that the Fermi surface of Sr3Ru2O7 changes in a surprising way as the system undergoes strong critical fluctuations.

High resolution study of magnetic ordering at absolute zero

High resolution pressure measurements in the zero-temperature limit provide a unique opportunity to study the behavior of strongly interacting, itinerant electrons with coupled spin and charge degrees of freedom. Approaching the precision that has become the hallmark of experiments on classical critical phenomena, we characterize the quantum critical behavior of the model, elemental antiferromagnet chromium, lightly doped with vanadium. We resolve the sharp doubling of the Hall coefficient at the quantum critical point and trace the dominating effects of quantum fluctuations up to surprisingly high temperatures.

Instability of the quantum-critical point of itinerant ferromagnets

We study the stability of the quantum-critical point for itinerant ferromagnets commonly described by the Hertz-Millis-Moriya (HMM) theory. We argue that in D</=3 long-range spatial correlations associated with the Landau damping of the order parameter field generate a universal negative, nonanalytic |q|((D+1)/2) contribution to the static magnetic susceptibility chi(s)(q,0), which makes HMM theory unstable. We argue that the actual transition is either towards incommensurate ordering, or first order. We also show that singular corrections are specific to the spin problem, while charge susceptibility remains analytic at criticality.

Spin fluctuation in heavy fermion CeRu2Si2

Spin fluctuations of the archetypal heavy fermion compound CeRu2Si2 have been investigated by neutron scattering in an entire irreducible Brillouin zone. The dynamical susceptibility is remarkably well described by the self-consistent renormalization (SCR) theory of the spin fluctuation in a phenomenological way, proving the effectiveness of the theory. The present analysis using the SCR phenomenology has allowed us to determine 14 exchange constants, which show the long-range nature of the Ruderman-Kittel-Kasuya-Yosida interaction.

Phase inhomogeneity of the itinerant ferromagnet MnSi at high pressures

The pressure induced quantum phase transition of the weakly ferromagnetic metal MnSi is studied using zero-field 29Si NMR spectroscopy and relaxation. Below P(*) approximately 1.2 GPa, the intensity of the signal and the nuclear spin-lattice relaxation are independent of pressure, even though the amplitude of the magnetization drops by 20% from the ambient-pressure amplitude. For P>P(*), the decreasing intensity within the experimentally detectable bandwidth signals the onset of an inhomogeneous phase that persists to the highest pressure measured, P>/=1.75 GPa, which is well beyond the known critical pressure P(c)=1.46 GPa. Implications for the non-Fermi liquid behavior observed for P>P(c) are discussed.

Magnetic-field-induced quantum critical point and competing order parameters in URu2Si2

A comprehensive transport study, as a function of temperature and continuous magnetic fields of up to 45 T, reveals that URu2Si2 possesses all the essential hallmarks of quantum criticality at fields around 37+/-1 T. The formation of multiple phases at low temperatures at and around the quantum critical point suggests the existence of competing order parameters.

Low temperature electron spin resonance of the Kondo ion in a heavy fermion metal: YbRh2Si2

We report an electron spin resonance (ESR) study on single crystals of the heavy fermion metal YbRh2Si2 which shows pronounced non-Fermi liquid behavior related to a close antiferromagnetic quantum critical point. It is shown that the observed ESR spectra can be ascribed to a bulk Yb3+ resonance. This is the first observation of ESR of the Kondo ion itself in a dense Kondo lattice system. The ESR signal occurs below the Kondo temperature (T(K)) which thus indicates the existence of large unscreened Yb3+ moments below T(K). We observe the spin dynamics as well as the static magnetic properties of the Yb3+ spins to be consistent with the results of nuclear magnetic resonance and magnetic susceptibility.

Fermi-liquid breakdown in the paramagnetic phase of a pure metal

Fermi-liquid theory (the standard model of metals) has been challenged by the discovery of anomalous properties in an increasingly large number of metals. The anomalies often occur near a quantum critical point--a continuous phase transition in the limit of absolute zero, typically between magnetically ordered and paramagnetic phases. Although not understood in detail, unusual behaviour in the vicinity of such quantum critical points was anticipated nearly three decades ago by theories going beyond the standard model. Here we report electrical resistivity measurements of the 3d metal MnSi, indicating an unexpected breakdown of the Fermi-liquid model--not in a narrow crossover region close to a quantum critical point where it is normally expected to fail, but over a wide region of the phase diagram near a first-order magnetic transition. In this regime, corrections to the Fermi-liquid model are expected to be small. The range in pressure, temperature and applied magnetic field over which we observe an anomalous temperature dependence of the electrical resistivity in MnSi is not consistent with the crossover behaviour widely seen in quantum critical systems. This may suggest the emergence of a well defined but enigmatic quantum phase of matter.

Extended versus local fluctuations in quantum critical Ce(Ru1-xFex)2Ge2 (x=xc=0.76)

We present inelastic neutron scattering experiments, performed near the antiferromagnetic quantum critical point in Ce(Ru0.24Fe0.76)2Ge2. Both local and long-range fluctuations of the local moments are observed, but due to the Kondo effect only the latter are critical. We propose a phenomenological expression which fits the energy E, temperature T, and wave vector q dependences of the dynamic susceptibility, describing the non-Fermi liquid E/T scaling found at every q.

Universally diverging Grüneisen parameter and the magnetocaloric effect close to quantum critical points

At a generic quantum critical point, the thermal expansion alpha is more singular than the specific heat c(p). Consequently, the "Grüneisen ratio," Gamma=alpha/c(p), diverges. When scaling applies, Gamma approximately T(-1/(nu z)) at the critical pressure p=p(c), providing a means to measure the scaling dimension of the most relevant operator that pressure couples to; in the alternative limit T-->0 and p not equal p(c), Gamma approximately 1/(p-p(c)) with a prefactor that is, up to the molar volume, a simple universal combination of critical exponents. For a magnetic-field driven transition, similar relations hold for the magnetocaloric effect (1/T) partial differential T/ partial differential H|(S). Finally, we determine the corrections to scaling in a class of metallic quantum critical points.