Heavy-electron Compound Research Articles

Colloquium : Heavy-electron quantum criticality and single-particle spectroscopy

Angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM) have become indispensable tools in the study of correlated quantum materials. Both probe complementary aspects of the single-particle excitation spectrum. Taken together, ARPES and STM have the potential to explore properties of the electronic Green's function, a central object of many-body theory. This review explicates this potential with a focus on heavy-electron quantum criticality, especially the role of Kondo destruction. A discussion on how to probe the Kondo destruction effect across the quantum-critical point using ARPES and STM measurements is presented. Particular emphasis is placed on the question of how to distinguish between the signatures of the initial onset of hybridization-gap formation, which is the "high-energy" physics to be expected in all heavy-electron systems, and those of Kondo destruction, which characterizes the low-energy physics and, hence, the nature of quantum criticality. Recent progress and possible challenges in the experimental investigations are surveyed, the STM and ARPES spectra for several quantum-critical heavy-electron compounds are compared, and the prospects for further advances are outlined.

Emergent ferromagnetism andT-linear scattering inUSb2at high pressure

The material ${\mathrm{USb}}_{2}$ is a correlated, moderately heavy-electron compound within the uranium dipnictide (${\mathrm{UX}}_{2}$) series. It is antiferromagnetic with a relatively high transition temperature ${T}_{N}=204\phantom{\rule{4pt}{0ex}}\mathrm{K}$ and a large U-U separation. While the uranium atoms in the lighter dipnictides are considered to be localized, those of ${\mathrm{USb}}_{2}$ exhibit hybridization and itineracy, promoting uncertainty as to the continuity of the magnetic order within the ${\mathrm{UX}}_{2}$. We have explored the evolution of the magnetic order by employing magnetotransport measurements as a function of pressure and temperature. We find that the ${T}_{N}$ in ${\mathrm{USb}}_{2}$ is enhanced, moving towards that of its smaller sibling ${\mathrm{UAs}}_{2}$. But, long before reaching a ${T}_{N}$ as high as ${\mathrm{UAs}}_{2}$, the antiferromagnetism of ${\mathrm{USb}}_{2}$ is abruptly destroyed in favor of another magnetic ground state. We identify this pressure-induced ground state as being ferromagnetic based on the appearance of a strong anomalous Hall effect in the transverse resistance in magnetic field. With pressure, this emergent ferromagnetic state is suppressed and ultimately destroyed in favor of a non-Fermi-liquid ground state.

Emergence of superconductivity in the canonical heavy-electron metal YbRh₂Si₂.

The smooth disappearance of antiferromagnetic order in strongly correlated metals commonly furnishes the development of unconventional superconductivity. The canonical heavy-electron compound YbRh2Si2 seems to represent an apparent exception from this quantum critical paradigm in that it is not a superconductor at temperature T ≥ 10 millikelvin (mK). Here we report magnetic and calorimetric measurements on YbRh2Si2, down to temperatures as low as T ≈ 1 mK. The data reveal the development of nuclear antiferromagnetic order slightly above 2 mK and of heavy-electron superconductivity almost concomitantly with this order. Our results demonstrate that superconductivity in the vicinity of quantum criticality is a general phenomenon.

Extended s-wave pairing symmetry on the triangular lattice heavy fermion system

We investigate the pairing symmetry of the Kondo-Heisenberg model on triangular lattice, which is believed to capture the core competition of Kondo screening and local magnetic exchange interaction in heavy electron compounds. On the dominant background of the heavy fermion state, the introduction of the Heisenberg antiferromagnetic interaction (J H ) leads to superconducting pairing instability. Depending on the strength of the interactions, it is found that the pairing symmetry favours an extended s-wave for small J H and high conduction electron density but a chiral $$d_{x^2 - y^2 } + id_{xy}$$ -wave for large J H and low conduction electron density, which provides a phase diagram of pairing symmetry from the calculations of the ground-state energy. The transition between these two pairing symmetries is found to be first-order. Furthermore, we also analyze the phase diagram from the pairing strengths and find that the phase diagram obtained is qualitatively consistent with that based on the ground-state energy. In addition, we propose an effective single-band BCS Hamiltonian, which is able to describe the low-energy thermodynamic behaviors of the heavy fermion superconducting states. These results further deepen the understanding of the antiferromagnetic interaction which results in a geometric frustration for the model studied. Our work may provide a possible scenario to understand the pairing symmetry of the heavy fermion superconductivity, which is one of active issues in very recent years.

Collective spin resonance excitation in the gapped itinerant multipole hidden order phase ofURu2Si2

An attractive proposal for the hidden order (HO) in the heavy electron compound URu2Si2 is an itinerant multipole order of high rank. It is due to the pairing of electrons and holes centered on zone center and boundary, respectively in states that have maximally different total angular momentum components. Due to the pairing with commensurate zone boundary ordering vector the translational symmetry is broken and a HO quasiparticle gap opens below the transition temperature T_HO. Inelastic neutron scattering (INS) has demonstrated that for T<T_HO the collective magnetic response is dominated by a sharp spin exciton resonance at the ordering vector Q that is reminiscent of spin exciton modes found inside the gap of unconventional superconductors and Kondo insulators. We use an effective two-orbital tight binding model incorporating the crystalline electric field effect to derive closed expressions for quasiparticle bands reconstructed by the multipolar pairing terms. We show that the magnetic response calculated within that model exhibits the salient features of the resonance found in INS. We also use the calculated dynamical susceptibility to explain the low temperature NMR relaxation rate.

High-field ultrasound measurements inUPt3and the single-energy-scale model of metamagnetism

We report longitudinal ultrasound velocity measurements for magnetic fields up to 33 T applied parallel to the a-axis of the heavy electron compound UPt$_{3}$. A characteristic dip in the sound velocity at the metamagnetic critical field, $H_{c}=20$ T, reported in earlier work is reproduced and shown to be independent of temperature at very low temperatures. We show that the single energy scale model (B.S. Shivaram et al., Phys. Rev. B89, 241107(R), 2014) captures the observed key features of the field dependence in the sound velocity shift, $\delta v_{s}$. The shift $\delta v_{s}$ at $H_{c}$ is found to be inversely dependent on temperature above 3\thinspace K and assumes a fixed value at low T. This saturation in $\delta v_{s}$ below 3 K is accounted for by level broadening of the Uranium spin states.

Properties near magnetic instability of heavy-electron compounds Ce3M4Sn13 and La3M4Sn13, with M=Co, Rh and Ru

In this review, we report the thermodynamic, magnetic and electronic transport properties of the skutterudite-related Ce3M4Sn13 and La3M4Sn13 intermetallic compounds with M = Co, Rh and Ru, which display a variety of behaviours. Ce3M4Sn13 exhibit a large increase in C/T with a maximum value of about 4 JK-2mol-1Ce due to strong electron and short-range magnetic correlations. These compounds show a crossover from a magnetically correlated heavy-fermion state to a single impurity state in applied magnetic fields. In order to study the proximity of Ce3Co4Sn13 to the possible magnetic quantum critical point (QCP), we investigated the system of Ce3-xLaxCo4Sn13 alloys. We found the critical concentration , which separates the magnetically correlated state () from a single impurity state (), however the low-T C(T)/T and the magnetic susceptibility behaviours are not characteristic of the QCP. With increasing of the magnetic field, resistivity follows power law behaviour for the samples , with n strongly field dependent. The -anomaly is discussed on the base of spin-fluctuation theory of Moriya and Takimoto. Specific heat data show that La3M4Sn13 are typical BCS superconductors, however, La3Rh4Sn13 and La3Ru4Sn13 exhibit a second superconducting phase, characteristic of inhomogeneous superconductors.

Short-range magnetic correlations in the highly correlated electron compoundCeCu4Ga

We present experimental results for the heavy-electron compound CeCu$_{4}$Ga which show that it possesses short-range magnetic correlations down to a temperature of $T = 0.1$ K. Our neutron scattering data show no evidence of long-range magnetic order occurring despite a peak in the specific heat at $T^{*} =1.2$ K. Rather, magnetic diffuse scattering occurs which corresponds to short-range magnetic correlations occurring across two unit cells. The specific heat remains large as $T\sim0$ K resulting in a Sommerfeld coefficient of $\gamma_{0} = 1.44(2)$ J/mol-K$^{2}$, and, below $T^{*}$, the resistivity follows $T^{2}$ behavior and the ac magnetic susceptibility becomes temperature independent. A magnetic peak centered at an energy transfer of $E_{\rm{c}}=0.24(1)$ meV is seen in inelastic neutron scattering data which shifts to higher energies and broadens under a magnetic field. We discuss the coexistence of large specific heat, magnetic fluctuations, and short-range magnetic correlations at low temperatures and compare our results to those for materials possessing spin-liquid behavior.

Plasma wave mediated attractive potentials: a prerequisite for electron compound formation

Abstract. Coagulation of electrons to form macro-electrons or compounds in high temperature plasma is not generally expected to occur. Here we investigate, based on earlier work, the possibility for such electron compound formation (non-quantum "pairing") mediated in the presence of various kinds of plasma waves via the generation of attractive electrostatic potentials, the necessary condition for coagulation. We confirm the possibility of production of attractive potential forces in ion- and electron-acoustic waves, pointing out the importance of the former and expected consequences. While electron-acoustic waves presumably do not play any role, ion-acoustic waves may potentially contribute to formation of heavy electron compounds. Lower-hybrid waves also mediate compound formation but under different conditions. Buneman modes which evolve from strong currents may also potentially cause non-quantum "pairing" among cavity-/hole-trapped electrons constituting a heavy electron component that populates electron holes. The number densities are, however, expected to be very small and thus not viable for justification of macro-particles. All these processes are found to potentially generate cold compound populations. If such electron compounds are produced by the attractive forces, the forces provide a mechanism of cooling a small group of resonant electrons, loosely spoken, corresponding to classical condensation.

Thermoelectric Power Anomaly of PrTi2Al20and PrV2Al20with Non-Kramers Γ3Ground State

We investigated thermoelectric properties for PrTi2Al20 and PrV2Al20 below room temperature down to 0.13 K. A clear positive peak has been observed at 75 K in the thermoelectric power \(S\) for PrTi2Al20. Also for PrV2Al20, the similar \(S\) peak has been detected at 40 K. These peaks arise from the Kondo effect in the magnetic excited levels of the \(4f\)-electronic state under a cubic crystalline electric field (CEF). In addition, for PrTi2Al20, \(S\) takes a minimum with a negative sign at 10 K owing to the CEF effect, and shows an additional tiny negative hump below 2 K as a signature of quadrupole ordering. On the other hand, \(S\) for PrV2Al20 manifests a large negative peak at 3 K with the magnitude of 3 μV/K. This gives a large enhancement in absolute \(S\) divided by temperature \(T\), \(|S|/T\), approximately below 10 K on cooling. \(|S|/T\) reaches 4 μV/K2 at 0.2 K, which is larger than that in the zero-\(T\) limit for a heavy-electron compound CeRu2Si2. This observation strongly indicates that the heavy-electron state brought by the quadrupolar Kondo effect is realized in the non-Kramers Γ3 ground state of PrV2Al20.

Anomalous Hall effect in heavy electron materials

We propose a new empirical formula for the anomalous Hall effect in heavy electron materials based on a phenomenological two-fluid description of the f-electron states. The new formula incorporates two previous theories proposed by Fert and Levy in 1987 and Kontani et al. in the early 1990s and takes into account both incoherent and coherent skew scatterings from local and itinerant f-electrons. We perform experimental analysis in several heavy electron compounds and show that the new formula provides a consistent description of the evolution of the Hall coefficient in the whole temperature range down to only a few Kelvin.

Field-induced collective spin-exciton condensation in a quasi-2D dx2–y2-wave heavy electron superconductor

The origin of the spin resonance observed in CeCoIn5 with Inelastic Neutron Scattering is subject to debate. It has been shown recently that in this heavy electron compound at low temperature an instability to a ground state with coexisting dx2-y2-wave superconductivity and Spin Density Wave (SDW) order in a magnetic field is a corollary of the consideration of a collective spin excitation mode in a quasi-2D dx2-y2-wave Pauli-limited superconductor. This provides a natural scenario for the occurence of the puzzling high-field-low-temperature phase highlighted in CeCoIn5. We present perspectives on this ground state transition and propose directions for future experiment.

Textured superconductivity in the presence of a coexisting order: Ce115s and other heavy-fermion compounds

Superconductivity in strongly correlated electron systems frequently emerges in proximity to another broken symmetry. In heavy-electron superconductors, the nearby ordered state most commonly is magnetism, and the so-called Ce115 heavy-electron compounds have been particularly instructive for revealing new relationships between magnetism and superconductivity. From measurements of the resistive and bulk transitions to superconductivity in these materials, we find that the resistive transition appears at a temperature considerably higher than the bulk transition when superconductivity and magnetic order coexist, but this temperature difference disappears in the absence of long-range magnetic order. Further, in the pressure–temperature region of coexistence in CeRhIn5, a new anisotropy in the resistive transition develops even though the tetragonal crystal structure apparently remains unchanged, implying a form of textured superconductivity. We suggest that this texture may be a generic response to coexisting order in these and other heavy-fermion superconductors.

Field-induced spin-exciton condensation in thedx2−y2-wave superconductor CeCoIn5

The implications of the spin exciton mechanism are exposed in the context of a spin density wave (SDW) instability occurring inside the superconducting phase of a layered heavy electron compound. In this model a magnetic field serves as a tuning parameter bringing the system to the point where the transverse spin correlations are enhanced due to ${d}_{{x}^{2}\text{\ensuremath{-}}{y}^{2}}$-wave superconductivity and inducing an instability to a phase with coexisting superconductivity and SDW order. The model considers electrons in a crystal with antiferromagnetic interactions and provides restrictions on the Fermi surface characteristics and on the ordering wave vector (which can be commensurate or incommensurate close to commensuration). The applications of the model are addressed to the low-temperature--high-magnetic-field phase of CeCoIn${}_{5}$ [M. Kenzelmann et al., Science 321, 1652 (2008); M. Kenzelmann et al., Phys. Rev. Lett. 104, 127001 (2010)].

Field Tuning and Quantum Criticality in Ytterbium Based Heavy Electron Compounds

We review here the results of magnetization, specific heat, and inelastic neutron scattering measurements conducted on Yb3Pt4, Yb2Pt2Pb, Yb5Pt9, and YbRh2Pb, which indicate that the Yb moments in these heavy electron compounds are appreciably localized, at least in their paramagnetic states. The magnetic ground states in each are isolated magnetic doublets, and we show that magnetic fields suppress long ranged magnetic order and lead to a characteristic magnetic field-temperature phase diagram where order vanishes suddenly above a critical value for the field. We argue that the stability of magnetic order in these compounds arises from the competition between the Zeeman splitting gμBH of the ground state doublet, which favors a spin polarized state with minimal entropy and without long range order, and the exchange splitting Δ of the doublet, which enables long ranged magnetic order.

Fermi surface properties of YbCu2Si2

AbstractWe succeeded in growing high‐quality single crystals of a heavy electron compound YbCu2Si2. The electronic specific heat coefficient γ is determined to be 150 mJ/K2·mol, which is consistent with the A value of the electrical resistivity from Kadowaki–Woods relation. We succeeded in observing the de Haas‐van Alphen (dHvA) oscillations. The dHvA frequencies and large cyclotron effective masses in YbCu2Si2 are highly different from those in a non‐4f reference compound YCu2Si2. From these dHvA results, the heavy electron state of YbCu2Si2 is characterized by the large contribution of 4f‐electrons to the topology of the Fermi surface and also to the strong enhancement of effective mass caused by the spin fluctuations.

Specific Heat-Coefficient of YbAl3 Studied by Combined Nearly Free Electron Conduction Band Hybridized with Localized f Electrons with Correlation Effect

Based on the recently proposed band model, the electronic specific heat of moderately heavy electron compound YbAl$_3$ are investigated. The band term of the Hamiltonian consists of three parts; conduction electrons described by the nearly free electron method, localized 4f electrons of Yb ions and the hybridization term between these electrons. Extracting several bands near the Fermi level, we reconstruct the low-energy effective Hamiltonian in order to consider the correlation effect, which is studied by using the self-consistent second order perturbation theory combined with local approximation. The temperature dependence of the specific heat $c_{\rm v}(T)$ is calculated as a function of temperature $T$ from the numerical derivative of the internal energy. Sommerfeld coefficient $\gamma$ is also calculated from the direct formula. The overall structure of $c_{\rm v}(T)/T$ is in quantitative agreement with the experimental results, which have the characteristic two-peak structures. They originate from the correlation effect and the structure of the non-interacting density of states, respectively. We show that our effective Hamiltonian yielding the realistic band structure may describe quantitatively heavy electron compounds with conduction bands composed of s- or p- electrons.

Pressure-induced variation of the ground state ofCeAl3

Pressure-induced variations of $^{27}\mathrm{Al}$ NMR spectra of $\mathrm{Ce}{\mathrm{Al}}_{3}$ indicate significant changes in the ground-state characteristics of this prototypical heavy-electron compound. Previously reported magnetic and electronic inhomogeneities at ambient pressure and very low temperatures are removed with external pressures exceeding $1.2\phantom{\rule{0.3em}{0ex}}\mathrm{kbars}$. The spectra and results of corresponding measurements of the NMR spin-lattice relaxation rates indicate a pressure-induced emergence of a simple paramagnetic state involving electrons with moderately enhanced masses and no magnetic order above $65\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$.

Low temperature NMR study of CeAl 3 under hydrostatic pressure

Results of 27Al-NMR measurements on the heavy-electron compound CeAl 3, recorded in low magnetic fields (of the order of 1 kG), very low temperatures ( T < 1.5 K ) , and at hydrostatic pressures up to 5.6 kbar are presented. We observe drastic changes of the NMR spectra and of the spin-lattice relaxation rates T 1 - 1 with increasing pressure. For p < 1.2 kbar , the 27Al spectrum is rather broad and complicated, but the situation changes significantly at higher pressures. The spectra narrow rapidly and can be reproduced by simulation calculations using reasonable parameters. The spin-lattice relaxation rate drops by almost two orders of magnitude upon increasing the pressure up to 5.6 kbar, indicating a substantial decrease of the density of electronic states at the Fermi energy. The data suggest a simple paramagnetic ground state for p > 1.2 kbar , without any evidence of magnetic order above 65 mK.

Magnetovolume effects of quasi-one-dimensional itinerant electron magnets [formula omitted

Magnetovolume effects of 3d heavy-electron compounds with linear spin chains, ( La 1 - x Y x ) Mn 4 Al 8 with x ⩽ 0.15 and = 1 , have been investigated to get information on the ground state of LaMn 4 Al 8 and the nature of spin fluctuations in this system. The negative thermal expansion observed for LaMn 4 Al 8 is suppressed by the substitution of a small amount of Y for La. Together with the field-cooled effect in the susceptibility, the magnetovolume effect suggests the development of short-range magnetic correlation in LaMn 4 Al 8 at low temperatures.