Field-tuned Quantum Critical Point Research Articles

Quantum Critical Quasiparticle Scattering within the Superconducting State of CeCoIn_{5}.

The thermal conductivity κ of the heavy-fermion metal CeCoIn_{5} was measured in the normal and superconducting states as a function of temperature T and magnetic field H, for a current and field parallel to the [100] direction. Inside the superconducting state, when the field is lower than the upper critical field H_{c2}, κ/T is found to increase as T→0, just as in a metal and in contrast to the behavior of all known superconductors. This is due to unpaired electrons on part of the Fermi surface, which dominate the transport above a certain field. The evolution of κ/T with field reveals that the electron-electron scattering (or transport mass m^{⋆}) of those unpaired electrons diverges as H→H_{c2} from below, in the same way that it does in the normal state as H→H_{c2} from above. This shows that the unpaired electrons sense the proximity of the field-tuned quantum critical point of CeCoIn_{5} at H^{⋆}=H_{c2} even from inside the superconducting state. The fact that the quantum critical scattering of the unpaired electrons is much weaker than the average scattering of all electrons in the normal state reveals a k-space correlation between the strength of pairing and the strength of scattering, pointing to a common mechanism, presumably antiferromagnetic fluctuations.

Heat transport study of field-tuned quantum criticality inCeIrIn5

The in-plane electrical resistivity, rho, and thermal conductivity, kappa, of the heavy-fermion superconductor CeIrIn5 were measured down to 40mK in magnetic fields up to 11 T applied along the c axis. For all fields above Hc2=4T of filamentary superconductivity, we find that the ratio of heat and charge conductivities in the T to 0 limit obeys the Wiedemann-Franz law, kappa/T=L0/rho, where L0 = 2.45*10^-8 WOhmK^-2 is the Sommerfeld value of the Lorenz number. The temperature-dependent parts of both the electrical and thermal resistivity,w = T/L0 kappa, follow the functional dependence expected for the Fermi liquid theory of metals with rho - rho_0 = AT^2, w - w_0 = BT^2, with rho0 = w0 and B ~ 2A. The coefficient B does not show a significant field dependence even upon approaching Hc2 = 0.4 T of the bulk superconducting state. The weak response to the magnetic field is in stark contrast with the behavior found in the closely related CeCoIn5, in which the field-tuned quantum critical point coincides with Hc2. The value of the electron-electron mass enhancement, as judged by the A and B coefficients, is about one order of magnitude reduced in CeIrIn5 as compared to CeCoIn5 (in spite of the fact that the zero field gamma_0 in CeIrIn5 is twice as large as gamma_0 in CeCoIn5), which suggests that the material is significantly farther away from the magnetic quantum critical point at bulk Hc2 and at all of the studied fields. A suppressed Kadowaki-Woods ratio in CeIrIn5 compared to CeCoIn5 suggests a notably more localized nature of f electrons in the compound.

Spin-flip scattering of critical quasiparticles and the phase diagram ofYbRh2Si2

Several observed transport and thermodynamic properties of the heavy-fermion compound YbRh2Si2 in the quantum critical regime are unusual and suggest that the fermionic quasiparticles are critical, characterized by a scale-dependent diverging effective mass. A theory based on the concept of critical quasiparticles (CQP) scattering off antiferromagnetic spin fluctuations in a strong-coupling regime has been shown to successfully explain the unusual existing data and to predict a number of so far unobserved properties. In this paper, we point out a new feature of a magnetic field-tuned quantum critical point of a heavy-fermion metal: anomalies in the transport and thermodynamic properties caused by the freezing out of spin-flip scattering of critical quasiparticles and the scattering off collective spin excitations. We show that a step-like behavior as a function of magnetic field of e.g. the Hall coefficient and magnetoresistivity results, which accounts quantitatively for the observed behavior of these quantities. That behavior has been described as a crossover line T*(H) in the T - H phase diagram of YbRh2Si2. Whereas some authors have interpreted this observation as signaling the breakdown of Kondo screening and an associated abrupt change of the Fermi surface, our results suggest that the T* line may be quantitatively understood within the picture of robust critical quasiparticles.

Wiedemann-Franz law and nonvanishing temperature scale across the field-tuned quantum critical point ofYbRh2Si2

The in-plane thermal conductivity kappa(T) and electrical resistivity rho(T) of the heavy-fermion metal YbRh2Si2 were measured down to 50 mK for magnetic fields H parallel and perpendicular to the tetragonal c axis, through the field-tuned quantum critical point, Hc, at which antiferromagnetic order ends. The thermal and electrical resistivities, w(T) and rho(T), show a linear temperature dependence below 1 K, typical of the non-Fermi liquid behavior found near antiferromagnetic quantum critical points, but this dependence does not persist down to T = 0. Below a characteristic temperature T* ~ 0.35 K, which depends weakly on H, w(T) and rho(T) both deviate downward and converge in the T = 0 limit. We propose that T* marks the onset of short-range magnetic correlations, persisting beyond Hc. By comparing samples of different purity, we conclude that the Wiedemann-Franz law holds in YbRh2Si2, even at Hc, implying that no fundamental breakdown of quasiparticle behavior occurs in this material. The overall phenomenology of heat and charge transport in YbRh2Si2 is similar to that observed in the heavy-fermion metal CeCoIn5, near its own field-tuned quantum critical point.

Magnetic-field-tuned quantum criticality of the heavy-fermion system YbPtBi

In this paper, we present the systematic measurements of the temperature and magnetic field dependences of the thermodynamic and transport properties of the Yb-based heavy fermion YbPtBi for temperatures down to 0.02 K with magnetic fields up to 140 kOe to address the possible existence of a field-tuned quantum critical point. Measurements of magnetic field and temperature dependent resistivity, specific heat, thermal expansion, Hall effect, and thermoelectric power indicate that the AFM order can be suppressed by applied magnetic field of $H_{c}$ $\sim$ 4 kOe. In the $H-T$ phase diagram of YbPtBi, three regimes of its low temperature states emerges: (I) AFM state, characterized by spin density wave (SDW) like feature, which can be suppressed to $T$ = 0 by the relatively small magnetic field of $H_{c}$ $\sim$ 4\,kOe, (II) field induced anomalous state in which the electrical resistivity follows $\Delta\rho(T) \propto T^{1.5}$ between $H_{c}$ and $\sim$ 8 kOe, and (III) Fermi liquid (FL) state in which $\Delta\rho(T) \propto T^{2}$ for $H \geq$ 8 kOe. Regions I and II are separated at $T$ = 0 by what appears to be a quantum critical point. Whereas region III appears to be a FL associated with the hybridized 4$f$ states of Yb, region II may be a manifestation of a spin liquid state.

Low-temperature electrical resistivity of antiferromagnetic Ce4Pt12Sn25

The compound Ce4Pt12Sn25 has a rather complex cubic crystal structure in which the Ce atoms are encapsulated in cages of Pt and Sn resulting in a large Ce-Ce distance. Recently, specific heat and magnetic susceptibility measurements revealed a phase transition from a paramagnetic to an antiferromagnetic (AFM) ground state with a low Néel temperature of TN = 0.19K. Application of a magnetic field was shown to weaken the AFM phase and ultimately suppress it at a critical field of 0.7 T. Here we investigate the observed antiferromagnetic phase transition by electrical resistivity measurements in applied magnetic fields in the vicinity of this field-tuned quantum critical point.

Competition between valence and spin fluctuations in the vicinityof the quantum critical point of the heavy fermion compoundYbAuCu4

The quantum criticality of the Yb-based heavy fermion compoundYbAuCu4 with noninteger valence close to unity has been investigated through low-temperature resistivity,magnetization, and nuclear magnetic resonance measurements in several fixed magnetic fieldsH. We found that,with increasing H, YbAuCu4 is driven from the originally antiferromagnetically ordered ground state (Néel temperatureTN∼0.9 K) to a nonmagnetic Fermi liquid one through the field-tuned quantum critical point(QCP) at kOe. The experimental results also provide the first evidence that a crossover valencetransition near the magnetic QCP is stabilized with the application of external field, inmarked contrast to the destabilization of the first-order valence transition. TheT–H phasediagram of YbAuCu4 and the T–X phase diagramestablished for the YbXCu4 (X = Pd,Au, Cu, Ag) series indicate that the evolution of valence fluctuations near the magneticQCP quickly interacts with the critical spin fluctuations. We suggest that the competitionbetween the Kondo temperature and crossover valence transition temperature is central tothe long-standing puzzles of localized–itinerant duality and the extent of degeneracy in thecrystal electric field ground state.

Anomalous Flux Line Lattice in CeCoIn5

Flux line lattice (FLL) of a quasi-two-dimensional heavy fermion superconductor CeCoIn 5 in perpendicular field was investigated by small-angle neutron scattering technique. A square FLL was observed in magnetic fields up to 3 T and at 4 T a splitting of diffraction spots was observed, indicating reorganization of the FLL toward a triangular (rhombic) FLL. The FLL form factor is nearly field-independent up to 4 T. This is in sharp contrast to conventional superconductors, in which the form factor rapidly decays with increasing magnetic field. This behavior of the form factor, which indicates the anomalous field distribution around the vortex cores, can be attributed to strong Pauli paramagnetic effects and to field-tuned quantum critical point effects.

Effect of Pressure and Magnetic Field on the Superconducting State of a Heavy Fermion Superconductor NpPd5Al2

We have carried out the electrical resistivity measurements under high pressures and high magnetic fields in NpPd 5 Al 2 in order to investigate a quantum critical behavior and the stability of the superconducting phase. A T -linear dependence of the electrical resistivity is changed into the Fermi liquid relation of ρ∼ A T 2 under the magnetic fields, and A value indicates a divergent feature around the upper critical field H c2 , indicating the existence of a field-tuned quantum critical point (QCP) around H c2 . With increasing pressure, the superconducting transition temperature T sc decreases and becomes zero above 5.7 GPa, together with a decrease of the upper critical field, indicating that the electronic state of NpPd 5 Al 2 is located in the vicinity of QCP at ambient pressure and deviates from QCP with increasing pressure. Furthermore, we have constructed the superconducting phase diagram at 3.71 GPa.

New hints on the origin of quantum criticality in CeCoIn 5: A Hall effect study

We report Hall Effect measurements under pressure in the normal state of CeCoIn 5, from 60 to 355 mK and for fields exceeding the superconducting upper critical field H c 2 , with the field oriented parallel to [0 0 1]. At low pressures, the field dependence of the Hall coefficient exhibits a scaling consistent with the one reported in the normal state at higher temperatures, but at odds with the Δ H / T scaling expected near a field tuned quantum critical point. The breakdown of this scaling at higher pressures, concomitant with the suppression of spin fluctuations, suggests that it is a hallmark of the spin fluctuations.

Evolution of transport and low-energy spin fluctuations in [formula omitted] with the application of magnetic field

We have investigated evolution of transport and low-energy spin fluctuation properties of heavy Fermi liquid compounds YbAuCu 4 and YbPdCu 4 with the application of magnetic field. YbAuCu 4 is found to be driven from the originally antiferromagnetically (AFM) ordered ground state ( T N ∼ 0.8 K ) to a nonmagnetic Fermi liquid (FL) one through the field-tuned quantum critical point (QCP) at H cr ≃ 13 kOe ( T N → 0 ) . In the vicinity of H cr , the electrical resistivity measurement provides evidence for the increase in the inelastic scattering of heavy electrons, and the 63 Cu spin-lattice relaxation rate measurement exhibits the occurrence of AFM spin order instability. Whilst, YbPdCu 4 transforms from the originally ferromagnetically (FM) ordered ground state ( T C ∼ 0.6 K ) into the nonmagnetic FL state, without any intermediate NFL phenomena. This result indicates that the competition of the field-stabilized FM correlation and field-destabilized AFM correlation plays an important role on the field-driven quantum critical phenomena.

Unconventional quantum criticality in YbRh 2Si 2

YbRh 2Si 2 is a clean heavy fermion system which displays a magnetic field tuned quantum critical point. We present low-temperature electrical resistivity, magnetostriction and magnetization measurements on high-quality single crystals with a residual resistivity ratio of 150. The data provide evidence for a low-energy scale T ⋆ ( H ) which vanishes in addition to the boundaries of the magnetic ordering and Landau Fermi liquid regime at the quantum critical point, indicating unconventional quantum criticality.

Non-Fermi liquid phenomena and intermediate valence in Yb-based compounds located close to the quantum critical point

In this paper, we focus on the mechanism of non-Fermi liquid phenomena in the vicinity of the magnetic field-tuned quantum critical point in Yb-based heavy fermion compounds YbAuCu 4, YbRh 2Si 2 and YbFe 4P 12. A comparative study of YbAuCu 4 and YbPdCu 4 with differently magnetically ordered ground states of antiferromagnetic (AFM) and ferromagnetic (FM) indicates that the competition between the field-destabilized AFM and field-stabilized FM correlations plays an important role on the field-tuned quantum critical behavior. The non-integer valence of these compounds leads to a consideration that the experimental susceptibility is dominated by the weakly broadened 4f hole level above the Fermi sea that extends to the cf hybridized band located at the Fermi level. Whilst, the monotonic increase of T 0 (an estimate of Kondo temperature) with field, derived from the transport and spin-fluctuation measurements, is ascribed to the variation of conduction bands from a weakly cf hybridized band toward the originally underlying conduction bands. The important role of the crossover transition upon cooling from the mixed valence localized f hole state to an itinerant electron state with the intermediate valence is also suggested.

Localization of 4 f State in YbRh2Si2 under Magnetic Field and High Pressure: Comparison with CeRh2Si2

We present detailed measurements of the electrical resistivity and microcalorimetry under magnetic field and high pressure which confirm the proximity of YbRh 2 Si 2 to a quantum critical point at ambient pressure. Our data seems to rule out the divergence of the heavy quasiparticle mass at the magnetic field tuned quantum critical point. Further Mössbauer spectroscopy gives evidence that the observed ESR resonance cannot be assigned directly to the trivalent Yb local spin dynamics. We report for the first time on quantum oscillations in YbRh 2 Si 2 . The obtained angular dependence is compared with band-structure calculation. A significant change of the resistivity and specific heat under high pressure and magnetic field is observed. Above 5 GPa ferromagnetic coupling plays the dominant role. The unusual high pressure phase diagram of YbRh 2 Si 2 cannot be explained in term of the Doniach phase diagram. In Yb heavy fermion case, slow valence fluctuations may occur due to an occupation number of the trivalent state which differs notably from unity. The differences between the Ce and Yb heavy fermion systems are discussed. In particular a comparison is made between CeRh 2 Si 2 and YbRh 2 Si 2 . The observed field and pressure variations of the Hall voltage in CeRh 2 Si 2 are not straightforwardly linked to the change in the Fermi surface topology. A tiny change in the 4 f electron occupation number will have a huge effect on the effective mass of different orbits of the complex band structure and thus on the Hall effect in this multiband electronic structure. A similar scenario must be certainly considered for YbRh 2 Si 2 .

Nonvanishing Energy Scales at the Quantum Critical Point ofCeCoIn5

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.

Pressure study of quantum criticality inCeCoIn5

We report resistivity measurements in the normal state of CeCoIn5 down to 40 mK and simultaneously in magnetic fields up to 9 T in the [001] crystallographic direction and under pressures up to 1.3 GPa. At ambient pressure the data are consistent with a field tuned quantum critical point coincident with the superconducting upper critical field H_{c2}, as observed previously. We find that with increasing pressure the quantum critical point moves inside the superconducting dome to lower fields. Thus, we can rule out that superconductivity is directly responsible for the non-Fermi liquid behavior in CeCoIn5. Instead, the data point toward an antiferromagnetic quantum critical point scenario.

Hall number inYbRh2Si2

Recent experimental studies have revealed an abrupt change in the Hall number at a field tuned quantum critical point in the heavy fermion magnet ${\mathrm{YbRh}}_{2}{\mathrm{Si}}_{2}$. We investigate this by calculating the local density band structure for this metal and the appropriate transport integrals. We find the Fermi surface to be multisheeted with the two largest sheets having opposite sign contributions to the Hall number. Small changes in the $f$ electron occupation are sufficient to reproduce the observed large change in the Hall number. This suggests that ${\mathrm{YbRh}}_{2}{\mathrm{Si}}_{2}$ may be an example of a quantum critical valence fluctuator.

Investigation of the field-tuned quantum critical point in CeCoIn5

The main properties and the type of the field-tuned quantum critical point in the heavy-fermion metal CeCoIn$_5$ arisen upon applying magnetic fields $B$ are considered within the scenario based on the fermion condensation quantum phase transition. We analyze the behavior of the effective mass, resistivity, specific heat, charge and heat transport as functions of applied magnetic fields $B$ and show that in the Landau Fermi liquid regime these quantities demonstrate the critical behavior which is scaled by the critical behavior of the effective mass. We show that in the high-field non-Fermi liquid regime, the effective mass exhibits very specific behavior, $M^*\sim T^{-2/3}$, and the resistivity demonstrates the $T^{2/3}$ dependence. Finally, at elevated temperatures, it changes to $M^*\sim T^{-1/2}$, while the resistivity becomes linear in $T$. In zero magnetic field, the effective mass is controlled by temperature $T$, and the resistivity is also linear in $T$. The obtained results are in good agreement with recent experimental facts.