Field-induced Quantum Critical Point Research Articles

Reentrant superconductivity driven by quantum tricritical fluctuations in URhGe: evidence from ^{59}Co NMR in URh_{0.9}Co_{0.1}Ge.

Our measurements of the ^{59}Co NMR spin-spin relaxation in URh_{0.9}Co_{0.1}Ge reveal a divergence of electronic spin fluctuations in the vicinity of the field-induced quantum critical point at H_{R}≈13 T, around which reentrant superconductivity (RSC) occurs in the ferromagnetic heavy fermion compound URhGe. We map out the strength of spin fluctuations in the (H_{b},H_{c}) plane of magnetic field components and show that critical fluctuations develop in the same limited region near the field H_{R} as that where RSC is observed. This strongly suggests these quantum fluctuations as the pairing glue responsible for the RSC. The fluctuations observed are characteristic of a tricritical point, followed by a phase bifurcation toward quantum critical end points.

Quantum criticality and superconducting pairing in Ce1-xYbxCoIn5 alloys

Charge transport measurements under magnetic field and pressure on Ce1-xYbxCoIn5 single crystalline alloys revealed that: (i) relatively small Yb substitution suppresses the field induced quantum critical point, with a complete suppression for Yb doping x > 0.07; (ii) the superconducting transition temperature (Tc) and Kondo lattice coherence temperature (Tcoh) decrease with x, yet they remain finite over the wide range of Yb concentrations; (iii) both Tc and Tcoh increase with pressure; (iv) there are two contributions to resistivity, which show different temperature and pressure dependences, implying that both heavy and light quasiparticles contribute to inelastic scattering. We also analyzed the pressure dependence of both Tcoh and Tc within the composite pairing theory. In the purely static limit, we find that the composite pairing mechanism necessarily causes opposite behaviors of Tcoh and Tc with pressure: if Tcoh grows with pressure, Tc must decrease with pressure and vice versa.

Evidence of a Kondo Destroying Quantum Critical Point in YbRh2Si2

The heavy-fermion metal YbRh$_{2}$Si$_{2}$ is a weak antiferromagnet below $T_{N} = 0.07$ K. Application of a low magnetic field $B_{c} = 0.06$ T ($\perp c$) is sufficient to continuously suppress the antiferromagnetic (AF) order. Below $T \approx 10$ K, the Sommerfeld coefficient of the electronic specific heat $\gamma(T)$ exhibits a logarithmic divergence. At $T < 0.3$ K, $\gamma(T) \sim T^{-\epsilon}$ ($\epsilon: 0.3 - 0.4$), while the electrical resistivity $\rho(T) = \rho_{0} + aT$ ($\rho_{0}$: residual resistivity). Upon extrapolating finite-$T$ data of transport and thermodynamic quantities to $T = 0$, one observes (i) a vanishing of the "Fermi surface crossover" scale $T^{*}(B)$, (ii) an abrupt jump of the initial Hall coefficient $R_{H}(B)$ and (iii) a violation of the Wiedemann Franz law at $B = B_{c}$, the field-induced quantum critical point (QCP). These observations are interpreted as evidence of a critical destruction of the heavy quasiparticles, i.e., propagating Kondo singlets, at the QCP of this material.

Routes to heavy-fermion superconductivity

Superconductivity in lanthanide- and actinide-based heavy-fermion (HF) metals can have different microscopic origins. Among others, Cooper pair formation based on fluctuations of the valence, of the quadrupole moment or of the spin of the localized 4f/5f shell have been proposed. Spin-fluctuation mediated superconductivity in CeCu2Si2 was demonstrated by inelastic neutron scattering to exist in the vicinity of a spin-density-wave (SDW) quantum critical point (QCP). The isostructural HF compound YbRh2Si2 which is prototypical for a Kondo-breakdown QCP has so far not shown any sign of superconductivity down to T ≈ 10 mK. In contrast, results of de-Haas-van-Alphen experiments by Shishido et al. (J. Phys. Soc. Jpn. 74, 1103 (2005)) suggest superconductivity in CeRhIn5 close to an antiferromagnetic QCP beyond the SDW type, at which the Kondo effect breaks down. For the related compound CeCoIn5 however, a field-induced QCP of SDW type is extrapolated to exist inside the superconducting phase.

Non-Fermi liquid regimes with and without quantum criticality in Ce 1− x Yb x CoIn 5

One of the greatest challenges to Landau's Fermi liquid theory--the standard theory of metals--is presented by complex materials with strong electronic correlations. In these materials, non-Fermi liquid transport and thermodynamic properties are often explained by the presence of a continuous quantum phase transition that happens at a quantum critical point (QCP). A QCP can be revealed by applying pressure, magnetic field, or changing the chemical composition. In the heavy-fermion compound CeCoIn5, the QCP is assumed to play a decisive role in defining the microscopic structure of both normal and superconducting states. However, the question of whether a QCP must be present in the material's phase diagram to induce non-Fermi liquid behavior and trigger superconductivity remains open. Here, we show that the full suppression of the field-induced QCP in CeCoIn5 by doping with Yb has surprisingly little impact on both unconventional superconductivity and non-Fermi liquid behavior. This implies that the non-Fermi liquid metallic behavior could be a new state of matter in its own right rather than a consequence of the underlying quantum phase transition.

Magnetic cooling through quantum criticality

We report measurements and theoretical calculations of the magnetocaloric properties of low-dimensional spin-1/2 antiferromagnets close to their magnetic field-induced quantum critical points. We demonstrate that the accumulation of entropy around the quantum critical point, giving rise to a critically enhanced magnetocaloric effect ΓB, can be used for realizing a very efficient low-temperature magnetic cooling.

Hall effect in superconducting films

Near the superconducting phase transition, fluctuations significantly modify the electronic transport properties. Here we study the fluctuation corrections to the Hall conductivity in disordered films, extending previous derivations to a broader range of temperatures and magnetic fields, including the vicinity of the magnetic field induced quantum critical point. In the process, we found a new contribution to the Hall conductivity that was not considered before. Recently, our theory has been used to fit measurements of the Hall resistance in amorphous TaN films.

Low-temperature thermodynamic properties near the field-induced quantum critical point in NiCl2-4SC(NH2)2

We present a comprehensive experimental and theoretical investigation of the thermodynamic properties: specific heat, magnetization and thermal expansion in the vicinity of the field-induced quantum critical point (QCP) around the lower critical field $H_{c1} \approx 2$\,T in DTN . A $T^{3/2}$ behavior in the specific heat and magnetization is observed at very low temperatures at $H=H_{c1}$ that is consistent with the universality class of Bose-Einstein condensation of magnons. The temperature dependence of the thermal expansion coefficient at $H_{c1}$ shows minor deviations from the expected $T^{1/2}$ behavior. Our experimental study is complemented by analytical calculations and Quantum Monte Carlo simulations, which reproduce nicely the measured quantities. We analyze the thermal and the magnetic Gr\"{u}neisen parameters that are ideal quantities to identify QCPs. Both parameters diverge at $H_{c1}$ with the expected $T^{-1}$ power law. By using the Ehrenfest relations at the second order phase transition, we are able to estimate the pressure dependencies of the characteristic temperature and field scales.

Progress in Heavy-Fermion Superconductivity: Ce115 and Related Materials

Ce115 and related Ce compounds are particularly suited to detailed studies of the interplay of antiferromagnetic order, unconventional superconductivity and quantum criticality due to their availability as high quality single crystals and their tunability by chemistry, pressure and magnetic field. Neutron-scattering, NMR and angle-resolved thermodynamic measurements have deepened the understanding of this interplay. Very low temperature experiments in pure and lightly doped CeCoIn 5 have elaborated the FFLO-like magnetic state near the field-induced quantum-critical point. New, related superconducting materials have broadened the phase space for discovering underlying principles of heavy-fermion superconductivity and its relationship to nearby states. © 2012 The Physical Society of Japan.

Magnetocaloric effect and magnetic cooling near a field-induced quantum-critical point

The presence of a quantum-critical point (QCP) can significantly affect the thermodynamic properties of a material at finite temperatures T . This is reflected, e.g., in the entropy landscape S ( T , r ) in the vicinity of a QCP, yielding particularly strong variations for varying the tuning parameter r such as pressure or magnetic field B . Here we report on the determination of the critical enhancement of ∂ S /∂ B near a B -induced QCP via absolute measurements of the magnetocaloric effect (MCE), (∂ T /∂ B ) S and demonstrate that the accumulation of entropy around the QCP can be used for efficient low-temperature magnetic cooling. Our proof of principle is based on measurements and theoretical calculations of the MCE and the cooling performance for a Cu 2+ -containing coordination polymer, which is a very good realization of a spin-½ antiferromagnetic Heisenberg chain—one of the simplest quantum-critical systems.

Behavior of the Quantum Critical Point and the Fermi-Liquid Domain in the Heavy Fermion Superconductor CeCoIn5 Studied by Resistivity

We report detailed very low temperature resistivity measurements on the heavy fermion compounds Ce_{1-x}La_{x}CoIn5 (x=0 and x=0.01), with current applied in two crystallographic directions [100] (basal plane) and [001] (perpendicular to the basal plane) under magnetic field applied in the [001] or [011] direction. We found a Fermi liquid (\rho \propto T^{2}) ground state, in all cases, for fields above the superconducting upper critical field. We discuss the possible location of a field induced quantum critical point with respect to Hc2(0), and compare our measurements with the previous reports in order to give a clear picture of the experimental status on this long debated issue.

Thermoelectric power investigations of YbAgGe across the quantum critical point

The magnetic field and temperature dependences of the thermoelectric power (TEP) of the antiferromagnetically ordered heavy fermion compound YbAgGe are measured across the field-induced quantum critical point. These TEP measurements reproduce the earlier $H\text{\ensuremath{-}}T$ phase diagram and identify an additional domelike phase between $\ensuremath{\sim}45$ and $\ensuremath{\sim}70\text{ }\text{kOe}$. On the low-field side of this region, $Hg{H}_{c}\ensuremath{\sim}45\text{ }\text{kOe}$, the sign of the TEP changes from negative to positive; on the high-field side of this region, $H\ensuremath{\approx}70\text{ }\text{kOe}$, a non-Fermi-liquid state is evidenced as the logarithmic temperature dependence of $S(T)/T$, in agreement with previous specific heat results $C(T)/T\ensuremath{\propto}\ensuremath{-}\text{log}(T)$. For higher fields, $Hg70\text{ }\text{kOe}$, the observed large value of $\ensuremath{\alpha}$, $S(T)=\ensuremath{\alpha}T$, is indicative of the heavy fermion state and shows a correlation with $C(T)/T$.

Field-induced quantum critical point in planar Heisenberg ferromagnets with long-range interactions: Two-time Green’s function framework

The two-time Green's function method is used to study the critical properties and crossover phenomena near the field-induced quantum critical point (QCP) of a $d$-dimensional spin-$S$ planar Heisenberg ferromagnet with long-range interactions decaying as ${r}^{\ensuremath{-}\ensuremath{\alpha}}$ (with $\ensuremath{\alpha}gd$) with the distance $r$ between spins. We adopt the Callen scheme for spin $S$ and the Tyablikov decoupling procedure which is expected to provide suitable results at low temperatures. Different quantum critical regimes are found in the $(\ensuremath{\alpha},d)$ plane and the global structure of the phase diagram is determined showing the typical V-shaped region close to the QCP. Depending on the values of $\ensuremath{\alpha}$, we find that also for dimensionalities $d\ensuremath{\leqslant}2$ a finite-temperature critical line, ending in the QCP, exists with asymptotic behaviors and crossovers which can be employed as a useful guide for experimental studies. Moreover, these crossovers are shown to be suitably described in terms of $(\ensuremath{\alpha},d)$-dependent scaling functions and effective critical exponents.

Comment on “Quantum Criticality and Nodal Superconductivity in the FeAs-Based SuperconductorKFe2As2”

In a recent Letter [J. K. Dong et al., Phys. Rev. Lett. 104, 087005 (2010)], Dong \textit{et al}. have observed a $T^{1.5}$ dependence of resistivity $\rho$ in KFe$_2$As$_2$ at the upper critical field $B_{c2}$ = 5 T parallel to the c axis and have suggested the existence of a field-induced quantum critical point (QCP) at $B_{c2}$. In this comment, we argue that observation of a $T^{1.5}$ dependence of $\rho$ in a sample showing broad resistive transitions does not constitute evidence for a QCP and that recent dHvA results do not support the proposed QCP.

Thermopower Evidence for an Abrupt Fermi Surface Change at the Quantum Critical Point ofYbRh2Si2

We present low-temperature thermopower results, S(T), on the heavy-fermion compound YbRh2Si2 in the vicinity of its field-induced quantum critical point (QCP). At B=0, a logarithmic increase of -S(T)/T between 1 and 0.1 K reveals strong non-Fermi-liquid behavior. A pronounced downturn of -S(T)/T below T{max}=0.1 K and a sign change from negative to positive S(T) values at T{0} approximately 30 mK are observed on the low-field side of the Kondo breakdown crossover line T{*}(B). In the field-induced, heavy Landau-Fermi-liquid regime, S(T)/T assumes constant, negative values below T{LFL}. A pronounced crossover in the -S(B)/T isotherms at T{*}(B) sharpens with decreasing T and seems to evolve toward a steplike function for T-->0. This is attributed to an abrupt change of the Fermi volume upon crossing the unconventional QCP of YbRh2Si2.

Quantum Criticality and Nodal Superconductivity in the FeAs-Based SuperconductorKFe2As2

The in-plane resistivity rho and thermal conductivity kappa of the FeAs-based superconductor KFe2As2 single crystal were measured down to 50 mK. We observe non-Fermi-liquid behavior rho(T) approximately T{1.5} at H{c{2}}=5 T, and the development of a Fermi liquid state with rho(T) approximately T{2} when further increasing the field. This suggests a field-induced quantum critical point, occurring at the superconducting upper critical field H{c{2}}. In zero field, there is a large residual linear term kappa{0}/T, and the field dependence of kappa_{0}/T mimics that in d-wave cuprate superconductors. This indicates that the superconducting gaps in KFe2As2 have nodes, likely d-wave symmetry. Such a nodal superconductivity is attributed to the antiferromagnetic spin fluctuations near the quantum critical point.

Magnetization study on the field-induced quantum critical point in YbRh2Si2

We study the field-induced quantum critical point (QCP) in YbRh2Si2 by low-temperature magnetization, M(T), and magnetic Grüneisen ratio, Γmag, measurements and compare the results with previous thermal expansion, β(T), and critical Gr̈neisen ratio, Γcr (T), data on YbRh2(Si0.95Ge0.05)2. In the latter case, a slightly negative chemical pressure has been used to tune the system towards its zero-field QCP. The magnetization derivative –dM/dT is far more singular than thermal expansion, reflecting a strongly temperature dependent pressure derivative of the field at constant entropy, (dH/dP)s = Vmβ/(dM/dT) (Vm: molar volume), which saturates at (0.15±0.04) T/GPa for T → 0. The line T*(H), previously observed in Hall-and thermodynamic measurements, separates regimes in T-H phase space of stronger (ε > 1) and weaker (ε < 1) divergent Γmag(T) ∝ T−ε.

Valence Fluctuations Revealed by Magnetic Field and Pressure Scans: Comparison with Experiments in YbXCu4(X=In, Ag, Cd) and CeYIn5(Y=Ir, Rh)

The mechanism of how critical end points of the first-order valence transition (FOVT) are controlled by a magnetic field is discussed. We demonstrate that critical temperature is suppressed to be a quantum critical point (QCP) by a magnetic field. This results explain the field dependence of the isostructural FOVT observed in Ce metal and YbInCu 4 . Magnetic field scan can make the system reenter in a critical valence fluctuation region. Even in intermediate-valence materials, the QCP is induced by applying a magnetic field, at which magnetic susceptibility also diverges. The driving force of the field-induced QCP is shown to be a cooperative phenomenon of the Zeeman effect and the Kondo effect, which creates a distinct energy scale from the Kondo temperature. The key concept is that the closeness to the QCP of the FOVT is vital in understanding Ce- and Yb-based heavy-fermions. This explains the peculiar magnetic and transport responses in CeYIn 5 (Y=Ir, Rh) and metamagnetic transition in YbXCu 4 for X=In...

Quantum criticality and the suppression of the heavy fermion state in UBe13 by high magnetic fields

We have measured the electrical resistivity of a single crystal of UBe13 below 1 K and in high magnetic fields to 33 T. The resistivity exhibits the T 2 dependence characteristic of a Fermi liquid at low temperatures. The field dependence of the coefficient of the T 2 term in the resistivity suggests that the heavy fermion state is suppressed by high magnetic fields. We discuss these results in light of a proposed field-induced quantum critical point immersed in the novel superconducting state of this compound.

Low-temperature thermopower study of YbRh2Si2

The heavy-fermion compound YbRh2Si2 exhibits an antiferromagnetic (AFM) phase transition at an extremely low temperature of Tn = 70 mK. Upon applying a tiny magnetic field of Bc = 60 mT the AFM ordering is suppressed and the system is driven toward a field-induced quantum critical point (QCP). Here, we present low-temperature thermopower S(T) measurements of high-quality YbRh2Si2 single crystals down to 30 mK. S(T) is found negative with comparably large values in the paramagnetic state. In zero field no Landau-Fermi-liquid (LFL) like behavior is observed within the magnetically ordered phase. However, a sign change from negative to positive appears at lowest temperatures on the magnetic side of the QCP. For higher fields B > Bc a linear extrapolation of S to zero clearly evidences the recovery of LFL regime. The crossover temperature TlFl is sharply determined and coincides perfectly with the one derived from resistivity ρ(T) and specific heat cp(T) investigations.