Heat transport as a probe of electron scattering by spin fluctuations: the case of antiferromagnetic CeRhIn(5)

A criterion for strange metallicity in the Lorenz ratio

The Wiedemann-Franz (WF) law, stating that the Lorenz ratio L = κ/(Tσ) between the thermal and electrical conductivities in a metal approaches a universal constant L 0 = π 2 k B 2 / ( 3 e 2 ) at low temperatures, is often interpreted as a signature of fermionic Landau quasi-particles. In contrast, we show that various models of weakly disordered non-Fermi liquids also obey the WF law at T → 0. Instead, we propose using the leading low-temperature correction to the WF law, L(T) - L0 (proportional to the inelastic scattering rate), to distinguish different types of strange metals. As an example, we demonstrate that in a solvable model of a marginal Fermi-liquid, L(T) - L0 ∝ - T. Using the quantum Boltzmann equation (QBE) approach, we find analogous behavior in a class of marginal- and non-Fermi liquids with a weakly momentum-dependent inelastic scattering. In contrast, in a Fermi-liquid, L(T) - L0 is proportional to - T2. This holds even when the resistivity grows linearly with T, due to T - linear quasi-elastic scattering (as in the case of electron-phonon scattering at temperatures above the Debye frequency). Finally, by exploiting the QBE approach, we demonstrate that the transverse Lorenz ratio, Lxy = κxy/(Tσxy), exhibits the same behavior.

T-Square Dependence of the Electronic Thermal Resistivity of Metallic Strontium Titanate

The temperature dependence of the phase space for electron-electron (e-e) collisions leads to a T-square contribution to electrical resistivity of metals. Umklapp scattering is identified as the origin of momentum loss due to e-e scattering in dense metals. However, in dilute metals like lightly doped strontium titanate, the origin of T-square electrical resistivity in the absence of umklapp events is yet to be pinned down. Here, by separating electron and phonon contributions to heat transport, we extract the electronic thermal resistivity in niobium-doped strontium titanate and show that it also displays a T-square temperature dependence. Its amplitude correlates with the T-square electrical resistivity. The Wiedemann-Franz law strictly holds in the zero-temperature limit, but not at finite temperature, because the two T-square prefactors are different by a factor of ≈3, like in other Fermi liquids. Recalling the case of ^{3}He, we argue that T-square thermal resistivity does not require umklapp events. The approximate recovery of the Wiedemann-Franz law in the presence of disorder would account for a T-square electrical resistivity without umklapp.

Anisotropic Melting of Frustrated Ising Antiferromagnets

Magnetic frustrations and dimensionality play an important role in determining the nature of the magnetic long-range order and how it melts at temperatures above the ordering transition T_{N}. In this Letter, we use large-scale Monte Carlo simulations to study these phenomena in a class of frustrated Ising spin models in two spatial dimensions. We find that the melting of the magnetic long-range order into an isotropic gaslike paramagnet proceeds via an intermediate stage where the classical spins remain anisotropically correlated. This correlated paramagnet exists in a temperature range T_{N}<T<T^{*}, whose width increases as magnetic frustrations grow. This intermediate phase is typically characterized by short-range correlations; however, the two-dimensional nature of the model allows for an additional exotic feature-formation of an incommensurate liquidlike phase with algebraically decaying spin correlations. The two-stage melting of magnetic order is generic and pertinent to many frustrated quasi-2D magnets with large (essentially classical) spins.

Thermal resistivity and hydrodynamics of the degenerate electron fluid in antimony

Detecting hydrodynamic fingerprints in the flow of electrons in solids constitutes a dynamic field of investigation in contemporary condensed matter physics. Most attention has been focused on the regime near the degeneracy temperature when the thermal velocity can present a spatially modulated profile. Here, we report on the observation of a hydrodynamic feature in the flow of quasi-ballistic degenerate electrons in bulk antimony. By scrutinizing the temperature dependence of thermal and electric resistivities, we detect a size-dependent departure from the Wiedemann-Franz law, unexpected in the momentum-relaxing picture of transport. This observation finds a natural explanation in the hydrodynamic picture, where upon warming, momentum-conserving collisions reduce quadratically in temperature both viscosity and thermal diffusivity. This effect has been established theoretically and experimentally in normal-state liquid ³He. The comparison of electrons in antimony and fermions in ³He paves the way to a quantification of momentum-conserving fermion-fermion collision rate in different Fermi liquids.

Viscous fermionic flow appears in liquid helium but rarely appears in metallic solid. Here, Jaoui et al. report a T-square thermal resistivity due to momentum conserving electronic scattering in semi-metallic antimony, which is in agreement with the hydrodynamic scenario.

Thermoelectric properties of heavy fermion CeRhIn5 using density functional theory combined with semiclassical Boltzmann theory

Experimental evidences show that Ce-based compounds can be good candidates for thermoelectric applications due to their high thermoelectric efficiencies at low temperatures. However, thermoelectric properties have been studied less than the other properties for CeRhIn₅, a technologically and fundamentally important compound. Thus, we comprehensively investigate the thermoelectric properties, including the Seebeck coefficient, electrical conductivity, electronic part of thermal conductivity, power factor and electronic figure of merit, by a combination of quantum mechanical density functional and semiclassical Boltzmann theories, including relativistic spin–orbit interactions using different exchange–correlation functionals at temperatures T ≤ 300 K for CeRhIn₅ along its a and c crystalline axes. The temperature dependences of the thermoelectric quantities are investigated. Our results reveal a better Seebeck coefficient, electrical conductivity, power factor and thermoelectric efficiency at T ≪ 300, in agreement with various other Ce-based compounds, when a high degree of localization is considered for the 4f-Ce electrons. The Seebeck coefficient, power factor and thermoelectric efficiency are made more efficient near room temperature by decreasing the degree of localization for 4f-Ce electrons. Our results also show that the thermoelectric efficiency along the a crystalline axis is slightly better than that of the c axis. We also investigate the effects of hydrostatic pressure on the thermoelectric properties of the compound at low and high temperatures. The results show that the effects of imposing pressure strongly depend on the degree of localization considered for 4f-Ce electrons.

Consistent with experimental data, theoretical thermoelectric results calculated by our developed strategy show that CeRhIn₅ is a good candidate for thermoelectric cooling applications due to its high thermoelectric efficiency at low temperatures.

Reduction of the Lorenz Number in Copper at Room Temperature due to Strong Inelastic Electron Scattering Brought about by High-Density Dislocations

In this work, heat and charge transport were measured in a series of deformed bulk Cu samples where dislocation density was tuned but dislocation character generally remained unchanged. We observed a notable violation of the Wiedemann-Franz law at room temperature for such a conventional metal. We show that high-density dislocations introduce strong inelastic electron scattering, which relax heat and charge currents to different extents. A reduction of Lorenz number by 15% was observed. We reveal that the contribution from elastic scattering to the incremental thermal resistivity scarcely varies with dislocation density, but the contribution due to inelastic scattering monotonically increases and becomes overwhelmingly dominant for dislocation density above 1.0 × 10¹⁵ m^-2.

Modular portable unit for thermal conductivity measurements in multiple cryogenic/magnetic field environments

A modular design for a miniature thermal conductivity cell suitable for a dilution refrigerator and other sample-in-vacuum cryogenic environments with different magnet options is described. The sample is mounted once and the contacts remain in place when the unit is repositioned or transported between different magnets and cryostats. This mobility enables comprehensive measurements with access to specific options, such as vector magnet in one lab and ultra-high field in another. This design enables significant expansion of the temperature range by using not only dilution refrigerators but also ³He, ⁴He cryostats and even ubiquitous Quantum Design Physical Property Measurement System.

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.

Thermal Conductivity through the Quantum Critical Point in YbRh_{2}Si_{2} at Very Low Temperature

The thermal conductivity of YbRh_{2}Si_{2} has been measured down to very low temperatures under field in the basal plane. An additional channel for heat transport appears below 30 mK, both in the antiferromagnetic and paramagnetic states, respectively, below and above the critical field suppressing the magnetic order. This excludes antiferromagnetic magnons as the origin of this additional contribution to thermal conductivity. Moreover, this low temperature contribution prevails a definite conclusion on the validity or violation of the Wiedemann-Franz law at the field-induced quantum critical point.

Specific heat of Gd₄Co₃

The specific heat (C(T)) of Gd₄Co₃ was measured in the temperature range 2-300 K and its magnetic contribution (C(m)(T)) was determined using a new method that fits the electronic specific heat coefficient (γ) and the Debye temperature (θ(D)) by constraining the resulting magnetic entropy (S(m)(T)) to saturate at temperatures far above the Curie temperature (T(C)). C(m)(T) exhibits a low-temperature bump originating from thermal excitation of gapped spin waves, which is responsible for pronounced peaks, at ≈35 K, in both C(m)/T and the temperature derivative of the magnetic contribution to electrical resistivity (dρ(m)/dT). Apart from in the vicinity of T(C), an excellent global correlation was found between C(m)/T and dρ(m)/dT. Our results provide strong support for the consistency of the new method proposed for the determination of C(m)(T) and rule out any major role of short-range order on Gd moments or d-electron spin fluctuation effects in the paramagnetic phase. A comparative analysis with other methods used in similar compounds points to the need for a better evaluation of C(m)(T) in such compounds, especially in the magnetically ordered phase, where a deficient evaluation of C(m)/T has a larger impact on the S(m)(T) curve.

Violation of the Wiedemann-Franz law at the Kondo breakdown quantum critical point

We study the electrical and thermal transport near the heavy-fermion quantum critical point, identified with the breakdown of the Kondo effect. We show that the electrical conductivity comes mainly from conduction electrons while the thermal conductivity is given by both conduction electrons and localized fermions (spinons), scattered with hybridization fluctuations of dynamical exponent z = 3. As a result, we reveal that not only electrical but also thermal resistivity displays quasilinear temperature dependence in the intermediate temperature range, the main prediction of our transport study. An important feature turns out to be emergence of additional entropy carriers, that is, spinon excitations. We find that the Wiedemann-Franz ratio should be larger than the standard value, differentiating the Kondo breakdown scenario from the Hertz-Moriya-Millis framework.

Anisotropic Violation of the Wiedemann-Franz Law at a Quantum Critical Point

A quantum critical point transforms the behavior of electrons so strongly that new phases of matter can emerge. The interactions at play are known to fall outside the scope of the standard model of metals, but a fundamental question remains: Is the basic concept of a quasiparticle-a fermion with renormalized mass-still valid in such systems? The Wiedemann-Franz law, which states that the ratio of heat and charge conductivities in a metal is a universal constant in the limit of zero temperature, is a robust consequence of Fermi-Dirac statistics. We report a violation of this law in the heavy-fermion metal CeCoIn5 when tuned to its quantum critical point, depending on the direction of electron motion relative to the crystal lattice, which points to an anisotropic destruction of the Fermi surface.

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.

Thermal conductivity in the vicinity of the quantum critical end point in Sr3Ru2O7

Thermal conductivity of Sr3Ru2O7 was measured down to 40 mK and at magnetic fields through the quantum critical end point at Hc=7.85 T. A peak in the electrical resistivity as a function of the field was mimicked by the thermal resistivity. In the limit as T-->0 K, we find that the Wiedemann-Franz law is satisfied to within 5% at all fields, implying that there is no breakdown of the electron despite the destruction of the Fermi liquid state at quantum criticality. A significant change in disorder [from rho0(H=0 T)=2.1 to 0.5 microOmega cm] does not influence our conclusions. At finite temperatures, the temperature dependence of the Lorenz number is consistent with ferromagnetic fluctuations causing the non-Fermi liquid behavior as one would expect at a metamagnetic quantum critical end point.

Drastic change in transport of entropy with quadrupolar ordering in

The antiferroquadrupolar ordering of is explored by probing thermal and thermoelectric transport. The lattice thermal conductivity drastically increases with the ordering, as a consequence of a large drop in carrier concentration and a strong electron-phonon coupling. The low level of carrier density in the ordered state is confirmed by the anomalously large values of the Seebeck and Nernst coefficients. The results are reminiscent of and suggest that both belong to the same class of partial metal-insulator transitions. The magnitude of the Nernst coefficient, larger than in any other metal, indicates a new route for Ettingshausen cooling at Kelvin temperatures.

Ballistic magnon transport and phonon scattering in the antiferromagnet Nd2CuO4

The thermal conductivity of the antiferromagnet Nd2CuO4 was measured down to 50 mK. Using the spin-flop transition to switch on and off the acoustic Nd magnons, we can reliably separate the magnon and phonon contributions to heat transport. We find that magnons travel ballistically below 0.5 K, with a thermal conductivity growing as T3, from which we extract their velocity. We show that the rate of scattering of acoustic magnons by phonons grows as T3, and the scattering of phonons by magnons peaks at twice the average Nd magnon frequency.