The electrodynamic response of heavy-electron materials with magnetic phase transitions

We have investigated the electrodynamic response of the heavy-electron compounds U₂Zn₁₇, UPd₂Al₃, UCu₅ and URu₂Si₂. Particular emphasis has been devoted to the optical evidence of the antiferromagnetic phase transitions at T_N = 9.7 K, 14 K, 15 K and 17 K for U₂Zn₁₇, UPd₂Al₃, UCu₅ and URu₂Si₂, respectively. In the excitation spectrum of UCu₅ and URu₂Si₂, we found an absorption in the far-infrared, which develops below T_N and is ascribed to the excitation across a spin-density-wave type gap, suggesting that the antiferromagnetic phase transition might be itinerant in nature, and invokes a Fermi surface instability. Since this gap-like feature is absent in U₂Zn₁₇ and UPd₂Al₃, we argue that these latter compounds belong to a characteristically different class of antiferromagnets, representative of the heavy-electron compounds with an ordering of essentially localized magnetic moments. The antiferromagnetic ordering then leads to a suppression of the spin-flip mechanism below T_N. At low temperatures, we observe for all compounds the formation of a narrow Drude-like resonance in the optical conductivity, which is ascribed to the electrodynamic response of the heavy-quasiparticles, and is indicative of the progressive development of the manybody coherent Kondo state, coexisting with both types of magnetic ordering. In this review, we also present the evolution of the optical properties due to Ni- and Redoping in UCu₅ and URu₂Si₂, respectively. The optical evidence of the itinerant antiferromagnetic ordering is suppressed in both compounds upon doping and particularly for the URu₂Si₂ compound this is consistent with a crossover to a ferromagnetic ground state upon Re-doping.     

μSR studies of heavy fermion systems

We have performed both zero field and high transverse field measurements at dilution refrigerator temperatures on a number of heavy electron systems, examining the superconducting and magnetic properties of these interesting materials. Among the materials studied to date are UBe₁₃, URu₂Si₂ and U₆Fe. The magnetic field penetration depth in the superconducting state of UBe₁₃ is greater than 10000 Å, as no increase in the transverse field relaxation rate is observed belowT _c . A sharp increase in the precession frequency is seen, starting atT _c . This frequency shift shows little temperature dependence at low temperature; we found no clear evidence for unconventional superconductivity in this material. Zero field measurements in URu₂Si₂ show the weak antiferromagnetic transition at 17.5 K. Finally, we we found no clear evidence for unconventional superconductivity in this material. Zero field measurements in URu₂Si₂ show the weak antiferromagnetic transition at 17.5 K. Finally, we have observed relaxation in high transverse field due to the formation of a flux lattice in U₆Fe, a material where the electron effective mass is rather lighter than in other heavy fermion systems. The relaxation exhibits a sharp onset atT _c=3.9 K, and is flat at low temperatures as expected for a conventional superconductor.     

Appearance of anisotropic non s-wave superconductivity above the critical pressure of antiferromagnetic CeRhIn5

We have carried out ¹¹⁵In nuclear quadrupole resonance (NQR) measurements in CeRhIn₅. At ambient pressure, CeRhIn₅ undergoes an antiferromagnetic AF phase transition at K. The ¹¹⁵In NQR spectrum has shown the appearance of a small internal field in the direction perpendicular to the tetragonal c-axis. With application of a hydrostatic pressure, the AF state is suppressed and the superconductivity appears just above the critical pressure (P = 17 kbar). The nuclear spin lattice relaxation rate 1/T₁ of ¹¹⁵In measured at P = 27 kbar indicates the occurrence of the superconductivity in the nearly AF region. In the superconducting state, 1/T₁ has no Hebel-Slichter coherence peak just below of 2 K and has a power law T-dependence (T³) down to 300 mK. This is consistent with anisotropic superconductivity, with line nodes in the superconducting energy gap: non-s-wave superconductivity occurs in CeRhIn₅. Received 5 July 2000     

High magnetic field behavior of strongly correlated uranium-based compounds

Magnetic fields are now available to 100?T (pulsed), 45?T (static) at temperatures below 0.3?K. Such technical developments allow the study and tuning of (quantum) phase transitions, unusual magnetic structures and (high-temperature) superconductors in a variety of quantum materials. An especially important class of strongly correlated electron materials is the heavy Fermi liquids (HFLs) displaying numerous reduced-moment antiferromagnets, quantum critical points, unconventional superconductivity, hidden order (HO) and other mysterious ground states. Among the ‘heavy fermions’, the duality of 5f electrons in uranium-based compounds introduces interesting behavior that can be affected by large magnetic fields. I list a few such heavy fermion materials to be considered: URu₂Si₂ and its tunable hidden state, UBe₁₃ and UPt₃ as very HFL paramagnets that become superconducting, the magnetic superconductors UPd₂Al₃ and UNi₂Al₃, and the ferromagnetic s UGe₂, URhGe and UCoGe. There are also the suggested metamagnetic Fermi-surface reconstructed intermetallic compounds such as UPt₂Si₂ and UCo₂Si₂. Present research attention focuses on the high-field behavior (30–40?T) of URu₂Si₂ and its destruction of HO. These and other U-based systems, e.g. UAu₂Si₂, UIrGe, etc., expand the opportunities of high magnetic field studies far into the future.     

New aspects on URu2Si2 and CeTIn5 (T=Rh, Ir, Co) observed by high pressure NMR and NQR

NMR and NQR studies on two interesting systems (URu₂Si₂, CeTIn₅) were performed under high pressure. (1) URu₂Si₂: In the pressure range 3.0 to 8.3 kbar, we have observed new ²⁹Si NMR signals arising from the antiferromagnetic (AF) region besides the previously observed ²⁹Si NMR signals which come from the paramagnetic (PM) region in the sample. This gives definite evidence for spatially-inhomogeneous development of AF ordering below T ₀ of 17.5 K. The volume fraction is enhanced by applied pressure, whereas the value of internal field (∼91 mT) remains constant up to 8.3 kbar. In the AF region, the ordered moment is about one order of magnitude larger than 0.03 μB. (2) CeTIn₅: The pressure and temperature (T) dependences of nuclear spin-lattice relaxation rate 1/T ₁ of ¹¹⁵In in CeTIn₅ have shown that the superconductivity (SC) occurs close to an AF instability. From the T dependences of 1/T ₁ and Knight shift below T _c. CeTIn₅ has been found to exhibit non-s wave (probable d wave) SC with even parity and line nodes in the SC energy gap.     

Unusual behavior of nuclear relaxation in CeCu2Si2 “possible evidence for triplet superconductivity”

Nuclear relaxation of ⁶³Cu in the superconducting state of the Kondo-lattice system CeCu₂Si₂ has been studied with the use of the ⁶³Cu nuclear quadrupole resonance technique under zero field and down to 65mK. The nuclear spin-lattice relaxation rate (1/T₁) decreases drastically just below T_c=0.67 K down to 0.5T_c without the apparent enchanced behavior and then is found to be almost temperature independent below 0.3T_c. These results suggest that the superconductivity in CeCu₂Si₂ is not in the usual BCS regime. The analysis based upon the existing triplet pairing model with an anisotropic energy gap describes well the behavior from T_c down to 0.5T_c, while the temperature independence below 0.3T_c remains unexplained.     

Generalized Fulde-Ferrell-Larkin-Ovchinnikov state in heavy-fermion and intermediate-valence systems

Anomalous properties of the magnetization, the crystal dilatation, and other physical quantities observed in the mixed state of compounds such as UPd₂Al₃ and CeRu₂ suggest the occurrence of a new state near H _c2. In such compounds with large spin susceptibility and high H _c2, a new inhomogeneous superconducting state is theoretically predicted to occur in high magnetic fields. In this inhomogeneous state which is shown to be a generalized Fulde-Ferrell-Larkin-Ovchinnikov state, the order parameter is spatially modulated, and planar nodes of the order parameter are periodically aligned perpendicular to the vortices. Various theoretical predictions are compared with experimental results on UPd₂Al₃ and CeRu₂ related to this new superconducting high-field state.     

As-NMR/NQR study of pressure-induced superconductivity in CaFe2As2

⁷⁵As-zero-field nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) measurements are performed on CaFe₂As₂ under pressure. At P=4.7 and 10.8 kbar, the temperature dependence of nuclear-spin-lattice relaxation rate (1/T₁) measured at tetragonal phase show no coherence peak just below T_c and decrease with decreasing temperature. The superconductivity is of gapless at P=4.7 kbar but evolves to multiple gaps at P=10.8 kbar. We find that the superconductivity appears near a quantum critical point. Both electron correlation and superconductivity disappear in the collapsed tetragonal phase. A systematic study under pressure indicates that electron correlations play a vital role in forming Cooper pairs in this compound.     

238U Mössbauer study on the magnetic properties of uranium-based heavy fermion superconductors

We have performed ²³⁸U Mössbauer spectroscopy of uranium-based heavy fermion superconductors, UPd₂Al₃ and URu₂Si₂, in order to investigate their physical properties, mainly their magnetic properties. The slow relaxation of magnetic hyperfine interaction in a paramagnetic state and the static hyperfine field has been observed in an antiferromagnetic ordered state for each compound. The line-widths have maximum at their characteristic temperatures where their magnetic susceptibilities have maximum values.     

Electronic phase transitions in the spinless Falicov-Kimball model

We have studied thedV/dI vs.V characteristics of point contacts between the heavy fermion superconductor URu₂Si₂ and the conventional superconductors Zn and NbTi. Contacts between URu₂Si₂ and Zn do not show Josephson effects; instead Andreev reflection type structures occur, which are related to both, the heavy fermion and the conventional superconductor. In contrast, contacts between URu₂Si₂ and NbTi become superconducting at low currents. A closed-loop setup with two NbTi contacts on URu₂Si₂ showed SQUID oscillations in a small magnetic field. Our data give evidence that the contacts should be described as superconductor/normal/superconductor junctions with a thick normal layer on the URu₂Si₂ side of the contact with proximity induced superconductivity in theN-layer in the case of NbTi. With such a model the occurrence or absence of superconductivity can be explained and also the suppression of Andreev-scattering which is frequently observed for contacts between heavy fermion superconductors and normal metals.     

NQR investigations of the high-Tc superconductor Ba2YCU3O7

NQR measurements of ^63,65Cu in both the normal and superconducting state are reported for the Cu1 and Cu2 sites in Ba₂YCu₃O₇. An anomalous behaviour in the vicinity and below T_c is observed: after a steep decrease at T_c the quadrupole frequency increases with decreasing temperature.     

Exotic superconducting state embedded in the hidden order state of URu2Si2

The heavy-fermion compound URu₂Si₂ has mystified researchers since the superconducting state (T_c = 1.45 K) is embedded within the enigmatic ‘‘hidden order” phase (T_h = 17.5 K). Here, we report charge and thermal transport measurements on ultraclean single crystals of URu₂Si₂ with very large residual-resistivity-ratio down to 30 m K (∼T_c/50), which reveal a number of unprecedented superconducting properties. The results provide strong evidence for a new type of unconventional superconductivity with two distinct gaps having different nodal topology. We propose a gap function with chiral d-wave form Δ(k) = Δ₀k_z(k_x + ik_y). We also demonstrate that a distinct flux line lattice melting transition with outstanding characters occurs well below the upper critical fields even at sub-Kelvin temperature. The intriguing superconducting state of URu₂Si₂ adds a unique and exciting example to the list of unconventional superconductors.     

La NMR and As NQR study of the As-based filled skutterudite LaOs4As12

We report experimental results of nuclear magnetic resonance (NMR) at the La site and nuclear quadrupole resonance (NQR) at the As site in the normal state of the superconducting compound LaOs₄As₁₂. Measurements have been performed on powder sample obtained from high quality single crystals. The temperature dependences of the nuclear spin-lattice relaxation rates, 1/T₁, of ⁷⁵As and ¹³⁹La nuclei were measured. No scaling between them was found indicating a local character of relaxation processes. The relaxation of ⁷⁵As nuclei can consistently be understood in terms of antiferromagnetic spin fluctuations, as deduced from the T-dependence of (1/T₁T)=C/(T−θ)^1/2.     

Al NMR studies of NpPd5Al2

We present ²⁷Al NMR studies for a single crystal of the Np-based superconductor NpPd₅Al₂. We have observed a five-line ²⁷Al NMR spectrum with a center line and four satellite lines separated by first-order nuclear quadrupole splittings. The Knight shift clearly drops below T_c. The temperature dependence of the ²⁷Al nuclear spin-lattice relaxation rate shows no coherence peak below T_c, indicating that NpPd₅Al₂ is an unconventional superconductor with an anisotropic gap. The analysis of the present NMR data provides evidence for strong-coupling d-wave superconductivity in NpPd₅Al₂.     

139La and63Cu-NQR of high-T c oxide superconductors

Nuclear quadrupole resonances (NQR) of¹³⁹La in La_2−xM_xCuO₄ (M=Ba, Sr) and⁶³Cu in YBa₂CU₃O₇ have been investigated with substitution of Cu by magnetic impurities. For La-system, the strong enhancement of the nuclear relaxation rate, 1/T ₁ atT _c ^*≈10 K (suggesting the occurrence of magnetic instability with hole-doping), is suppressed by 3D-antiferromagnetism induced by magnetic impurities. In the superconducting region, fluctuations of Cu moments at low temperatures remain extremely fast as at high temperatures. For Y-system, Fe-ions are substituted for both Cu(1) and Cu(2) sites, But Co-ions are preferentially substituted to Cu1 sites. The peaks in the relaxation rate of Cu indicate the appearance of magnetic ordering without destroying superconductivity for the 0.5%-Fe doped sample.     

Molecular motions in chloramphenicol studied by35Cl nuclear quadrupole and1H nuclear magnetic resonance spectroscopy

The³⁵Cl nuclear quadrupole resonance (NQR) frequency (v_Q), nuclear quadrupole spinlattice relaxation time (T_1Q),¹H nuclear magnetic resonance second moment (M₂) and nuclear magnetic spin-lattice relaxation timeT ₁) were measured for polycrystalline chloramphenicol (drug) as a function of temperature. Hindered rotation of the CHC1₂ group and the phenyl ring was detected, the relevant activation energies were determined. The rotations are discussed in detail.     

Nuclear magnetic resonance study of the heavy-fermion system URu2Si2

Nuclear magnetic resonance (NMR) and relaxation studies on ²⁹Si have been carried out on the heavy Fermion system URu₂Si₂. Above the Kondo temperature of about 60 K, the nuclear relaxation time T₁ is nearly temperature independent, which is consistent with the occurrence of fluctuations of localized U moments. Below about 60 K T₁ is inversely proportional to temperature suggesting that the system behaves like a Fermi liquid. A sharp increase in T₁ occurs below 17 K which is probably associated with the opening of an energy gap at the Fermi surface due to the formation of a spin density wave state. Below about 10 K, T₁ reacquires the inverse temperature dependence observed in the 17 K ∼ 60 K temperature range.     

Electronic structure and lattice dynamics of domeykite Cu<Subscript>3</Subscript>As according to nuclear quadrupolar resonance of<Superscript>75</Superscript>As and<Superscript>63,65</Superscript>Cu

The temperature dependences of nuclear quadrupole resonance (NQR) frequencies, the line width and nuclear relaxation of⁷⁵As and^63,65Cu, as well as the electrical resistivity in domeykite Cu₃As are studied in the temperature range of 4.2-300 K. The comparison of the calculated with the measured lattice contribution to the NQR frequencies points at a substantial role played by the conduction electrons in creating the electric field gradient at the nuclei sites. The temperature dependence of the copper and arsenic nuclear spin-lattice relaxation linear at 4.2<T<200 K and that of the electric resistivity (30<T<200 K) prove the metallic character of the conductivity of domeykite. The enhancement of nuclear relaxation, the narrowing of copper and arsenic NQR line widths are considered as arising due to the ionic movement starting beyond 200 K. This movement influences the electric resistivity, most likely due to the inreasing density of states at the Fermi surface.     

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.