On the heavy fermion behaviour of CeCu3Ga2

The hexagonal compound CeCu₃Ga₂ has been identified as another example of a Ce based heavy fermion system. The electronic contribution to the specific heat amounts at 1.45 K to about 730 mJ/mole K². A negative temperature coefficient of the electrical resistivity was observed between 1.7 and 300 K. The thermopower of CeCu₃Ga₂ exhibits at 20 K a huge maximum of about 36 μV/K. Magnetization and susceptibility measurements down to 1.5 K do not show any sign of a transition into a magnetic ordered ground state.     

Valence fluctuation and heavy fermion behaviour in rare earth and actinide based compounds

A brief historical review of some of the experimental work reported on the mixed valent (MV) or valence fluctuating (VF) and heavy fermion (HF) systems is given. The characteristic physical properties of MV and HF systems are discussed. The salient features of the theoretical models are outlined. Results on some systems are presented.     

Coexistence of heavy fermion and intermediate valence behaviour in Ce24Co11

Low temperature specific heat, magnetic susceptibility andL _III-XAS measurements on Ce₂₄Co₁₁ are reported. The electronic specific heat can be decomposed into two contributions: a low temperature one (arising atT<5 K), with a maximum of 2.2 J/Kmole at 0.9 K, and another one becoming dominant atT>5 K, characterized by a _HT = 1.8 J/K² mole coefficient. The ·T product changes continuously with temperature, from 0.48 emu K/mole at 2 K to 7.85 emu K/mole at 200 K. TheL _III-mean valence is =3.15.As the 24 Ce atoms are distributed in ten unequivalent crystalline sites, we interpret the experimental results as due to: one atom which behaves as a Heavy Fermion and the rest as Kondo and Intermediate Valent, with a distribution of characteristic energies governed by nine different environments. Qualitatively, the specific heat behaviour under applied field and the =3.15 value are in agreement with this interpretation.     

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.     

Signatures of spin-glass freezing in Co/CoO nanospheres and nanodiscs

We present a study of the magnetic properties of Co nanoparticles having a combination of both spherical and disk shapes. The hcp Co nanospheres with an average diameter of 11 nm and nanodiscs of dimensions ∼2.5×15 nm² were prepared by thermal decomposition of di-cobalt octacarbonyl in the presence of an amine surfactant. The as-synthesized nanoparticles were oxidized to grow an antiferromagnetic layer. High resolution transmission electron microscopy showed the presence of a ferromagnet/antiferromagnet (Co/CoO) interface with a 2.2-nm thick CoO shell on the spherical nanoparticles and 0.5 nm thick on nanodiscs. We report the temperature and field dependent DC magnetization, frequency, field, and temperature dependent AC susceptibility, and the radio frequency transverse susceptibility. A low temperature paramagnetic behavior was observed in the DC magnetization at high fields and is assigned to defects in the CoO shell that are not coupled to the antiferromagnetic lattice. Our results support the existence of a low temperature frozen, disordered magnetic state, characterized by a strong exchange coupling between the structurally disordered, spin-glass CoO shell and Co core.     

YbNi2: A heavy fermion ferromagnet

Measurements of the magnetization and specific heat of YbNi₂ binary alloy are reported. The DC magnetic susceptibility displays a ferromagnetic behavior with a Curie temperature T_C=10.5 K, one of the highest found in Yb compounds. Moreover, the temperature dependence of the specific heat exhibits a lambda anomaly with a peak of 5.12 J/mol K at 9.4 K. The analysis also shows an additional magnetic contribution around 32 K stemming from the crystalline electric field of a quartet at ${\Delta }_1=72\mathrm{K}$ and a doublet at ${\Delta }_2=126\mathrm{K}$, according to the splitting of the Yb³⁺ ion in cubic symmetry. From the magnetic contribution to the specific heat, a relatively high Kondo temperature $T_K=27\mathrm{K}$ is estimated. Below the magnetic transition, the specific heat shows a huge value of the electronic coefficient ${\gamma }_{\mathit{LT}}=573\mathrm{mJ}/\mathrm{mol}\mathrm{K}$, which is a signature of a heavy fermion behavior. Therefore, this alloy is a fine example of enhanced ferromagnetism and heavy fermion behavior among Yb compounds.     

Superconductivity in heavy fermion systems

The heavy fermion state in the f-electron systems is due to competition between the RKKY interaction and the Kondo effect. The typical compound is CeCu₆. To understand the electronic state, we studied the Fermi surface properties via the de Haas–van Alphen (dHvA) experiment and energy band calculation for CeSn₃,CeRu₂Si₂,UPt₃, and nowadays, transuranium compounds. Pressure is also an important technique to control the electronic state. The Néel temperature T_N decreases with increasing pressure P and becomes zero at the critical pressure for . The typical compound is an antiferromagnet CeRhIn₅, which we studied from the dHvA experiment under pressure. A change of the 4f-electronic state from localized to itinerant is realized at , revealing the first-order phase transition, together with a divergent tendency of the cyclotron mass at P_c. It is stressed that appearance of superconductivity in CeRhIn₅ is closely related to the heavy fermion state. It is also noted that the parity-mixed novel superconducting state might be realized in a pressure-induced superconductor CeIrSi₃ without inversion symmetry in the crystal structure.     

Antiferromagnetic correlations in the cubic heavy fermion compound CeInCu2

CeInCu₂ is a heavy fermion compound close to magnetic instability. The electrical resistivity has aT ² behaviour between 1 and 2.5 K. and the AC field susceptibility has a faint maximum at 0.9 K, indicating the onset of coherence near 1 K for this compound. The magnetoresistance keeps a negative sign down to 0.3 K. Neutron inelastic scattering give a crystal field splitting of 90 K, with a doublet ground state, and a residual quasielastic linewidth of 0.3 meV.We have studied the resistivity, susceptibility and specific heat of some dilute solutions La_1–xCe_xInCu₂ and Y_1–xCe_xInCu₂. The spin-dependent part of the resistivity may be decomposed into a single impurity term plus a pair interaction term, the magnitude of which folows a Curie-Weiss law, as in classical spin glassesCuMn orAuFe.The magnetisation and susceptibility at low temperatures may be represented within the resonant level model, taking into account antiferromagnetic interactions. Finally, the specific heat of CeInCu₂ shows a bump near 2.3 K, absent for dilute solutions, which may also be interpreted by introducing a magnetic interaction term.     

Asymmetries in heavy fermion production and decay

We calculate the forward-backward asymmetries of heavy fermions and of leptons from their semileptonic decay in e⁺e⁻ annihilation. In particular we study the corrections to the lowest-order prediction resulting from intial-state radiation, kinematic effects in heavy quark decay and the role of quark polarization.     

Electronic structure evolution accompanying heavy fermion formation in CeCu_2Si_2

The cooper pairs in the heavy-fermion superconductor CeCu_2Si_2 are formed of heavy fermions. Therefore, the heavy fermions are fundamental to the emergence of unconventional superconductivity and associated non-Fermi-liquid behavior in the normal state. The interplay between localization and itinerancy manifested on the electronic structure is key for understanding the heavyfermion behavior. Here, via the first-principle density functional theory(DFT) combined with single-site dynamical mean-field theory(DMFT), we investigate the temperature(T) evolution of the electronic structure of CeCu_2Si_2 in the normal state, focusing on the role of the 4f states in the low energy regime. Two characteristic temperature scales of this evolution, which accompanied the heavy-fermion formation, are established. The coherence onset temperature is around 130K, whereas the heavy-fermion band formation temperature is between 40 and 80K; both characteristic temperature scales are higher than the transport coherence temperature. Furthermore, the heavy-fermion formation is confirmed by calculating its effective mass variation with the temperature. Based on the calculated T-dependent evolution of the 4 f orbital occupancy and electronic structure, an explanation on the behavior of the temperature evolution of the correlation strength of CeCu_2Si_2 is provided. Our results offer a comprehensive microscopic picture of the heavy-fermion formation in CeCu_2Si_2, which is essential for further understanding the emergent superconducting pairing mechanism.     

Hall coefficient in heavy fermion metals

Experimental studies of the antiferromagnetic (AF) heavy fermion metal YbRh₂Si₂ in a magnetic field B indicate the presence of a jump in the Hall coefficient at a magnetic-field tuned quantum state in the zero temperature limit. This quantum state occurs at B ≥ B_c0 and induces the jump even though the change of the magnetic field at B = B_c0 is infinitesimal. We investigated this by using the model of heavy electron liquid with the fermion condensate. Within this model, the jump takes place when the magnetic field reaches the critical value B_c0 at which the ordering temperature T_N(B = B_c0) of the AF transition vanishes. We show that at B → B_c0, this second order AF phase transition becomes the first order one, making the corresponding quantum and thermal critical fluctuations vanish at the jump. At T → 0 and B = B_c0 the Grüneisen ratio as a function of the temperature T diverges. We demonstrate that both the divergence and the jump are determined by the specific low temperature behavior of the entropy \(S(T) \propto S_0 + a\sqrt T + bT\) with S₀; a and b are temperature independent constants.     

Density fluctuations in heavy fermion systems

We show explicitly that the hydrodynamic density modes of a heavy fermion system in the presence of long range Coulomb interactions can be reduced to those of an effective Hamiltonian used previously. Outside the hydrodynamic regime one finds acoustic plasmon (or zero sound) excitations as well as high energy plasmons. When the Fermi level intersects more than one heavy quasiparticle band, a situation which is expected to occur in most cases, then also a low-energy optical plasmon excitation should exist. The latter can be overdamped under special conditions.     

Hybridization gap in heavy fermion compounds

We report the results of optical studies of new heavy fermion compounds YbFe(4)Sb(12) and CeRu(4)Sb(12). We show that these compounds, as well as several other heavy fermion materials with a nonmagnetic ground state, obey a universal scaling relationship between the quasiparticle effective mass m(*) and the magnitude of the energy gap Delta in the excitation spectrum. This result is in accord with the picture of hybridization of localized f-electron and free carrier states.     

Current issues in heavy fermion superconductivity

An attempt is made to summarize our current understanding of the superconductivity occuring in heavy fermion systems. The last three years have seen the discovery of two new superconductors (UNi₂Al₃ and UPd₂Al₃), much more use of directional probes to investigate the anisotropy of the gap structure, further experimental and theoretical inquiry into a possible coupling of magnetic and superconducting order parameters, wider application of pressure and uniaxial stress to examine the onset of ordering and some new indications of unconventional superconductivity. These topics will be reviewed along with others of current interest.     

Hydrodynamic fluctuations in heavy fermion systems

A theory of hydrodynamic fluctuations in heavy fermion systems is presented. It is used to compute the attenuation and velocity of longitudinal ultrasound. The attenuation is dominated by the coupling of phonons to electronic density fluctuations. A discrepancy is resolved between theory and experiments on UPt₃, which has been existing with respect to the absolute magnitude of the temperature dependent attenuation. The latter provides direct proof for a large Fermi liquid parameterF ₀ ^s . The phonon Green's function is found to have a four-pole structure, resulting in two diffusive modes. One is the conventional one due to heat diffusion while the other is due to electron density diffusion and is a characteristic feature of heavy fermion systems. The two modes are coupled at finite temperatures. With the help of a model Hamiltonian (slave boson mean-field formulation of the Anderson lattice Hamiltonian) the ultrasound attenuation is calculated for low temperatures.     

Superfluid response in heavy fermion superconductors

Motivated by a recent London penetration depth measurement [H. Kim, et al., Phys. Rev. Lett. 114, 027003 (2015)] and novel composite pairing scenario [O. Erten, R. Flint, and P. Coleman, Phys. Rev. Lett. 114, 027002 (2015)] of the Yb-doped heavy fermion superconductor CeCoIn₅, we revisit the issue of superfluid response in the microscopic heavy fermion lattice model. However, from the literature, an explicit expression for the superfluid response function in heavy fermion superconductors is rare. In this paper, we investigate the superfluid density response function in the celebrated Kondo–Heisenberg model. To be specific, we derive the corresponding formalism from an effective fermionic large-N mean-field pairing Hamiltonian whose pairing interaction is assumed to originate from the effective local antiferromagnetic exchange interaction. Interestingly, we find that the physically correct, temperature-dependent superfluid density formula can only be obtained if the external electromagnetic field is directly coupled to the heavy fermion quasi-particle rather than the bare conduction electron or local moment. Such a unique feature emphasizes the key role of the Kondo-screening-renormalized heavy quasi-particle for low-temperature/energy thermodynamics and transport behaviors. As an important application, the theoretical result is compared to an experimental measurement in heavy fermion superconductors CeCoIn5 and Yb-doped Ce_1?xYb_xCoIn₅ with fairly good agreement and the transition of the pairing symmetry in the latter material is explained as a simple doping effect. In addition, the requisite formalism for the commonly encountered nonmagnetic impurity and non-local electrodynamic effect are developed. Inspired by the success in explaining classic 115-series heavy fermion superconductors, we expect the present theory will be applied to understand other heavy fermion superconductors such as CeCu₂Si₂ and more generic multi-band superconductors.     

μSR study of intermediate heavy fermion system CeRuSi2

We have studied the magnetic spinel (Zn)[Fe₂]O₄ (T_ N\approx10.5\ K) and the non‐magnetic spinels (Zn)[Al₂]O₄, (Zn)[Ga₂]O₄, (Zn)[ZnTi]O₄ and (Zn)[ZnSn]O₄ , both with surface and decay channel muons. In (Zn)[Fe₂]O₄ the relaxation rate increases monotonically from room temperature down, typical for a paramagnet. Around 30 K, an additional, stronger damped signal appears which is the signature of short‐range ordered (SRO) regions. Their total volume fraction increases drastically towards T_ N (reaching 75%) and astonishingly, continues to be present also below T_ N where the rest of the material has become long‐range ordered. Longitudinal field μSR proves the SRO to be dynamic. In (Zn)[Al₂]O₄ and (Zn)[Ga₂]O₄ muon depolarization is caused solely by ²⁷Al or ^69,71Ga nuclear dipoles. In the inverse spinel (Zn)[ZnTi]O₄, half of the implanted muons depolarize rapidly (\lambda\approx 3μs^-1 at room temperature). This, together with repolarization behavior in longitudinal fields indicates that the muon in (Zn)[ZnTi]O₄ undergoes a chemical reaction after implantation forming muonium. The fact that no such muonium formation occurred in another inverse spinel ( (Zn)[ZnSn]O₄) means that the presence of muonium is not connected to the inverse structure but rather due to the presence of Ti which offers two d‐electrons to participate in the chemical bonding. Additional evidence for d‐electron participation is provided by ⁶⁷Zn‐Mössbauer data which indicate unusual electron densities at the ⁶⁷Zn nuclei only in (Zn)[ZnTi]O₄.     

Spin fluctuations and magnetic order in the heavy fermion compound CePt2Sn2

We present zero and longitudinal field μ SR measurements of single crystal and polycrystalline specimens of the heavy fermion compound CePt₂Sn₂. Above 1 K the behaviour of the two samples is indistinguishable; the muon 1/T_1 increases with decreasing temperature until 25 K when it plateaus. The 1/T_1 relaxation rate differs strongly for the two cases below \sim\,0.8\ K. At 0.1 K a rate of about 20 μ s^-1 is seen in the polycrystal while in the single crystal it is only about 5 μ s^-1. Even more revealing is the fact that longitudinal field decoupling spectra at very low temperatures demonstrate an essentially static spin system to be present in the polycrystalline material while the single crystal shows definite dynamic spin properties. We conclude that, in the presence of the distortion, long range magnetic order occurs below 0.9 K while in tetragonal symmetry long range order is suppressed (probably due to frustration) and spin fluctuations remain for T\rightarrow0. This revised version was published online in July 2006 with corrections to the Cover Date.