Quasielastic magnetic scattering of neutrons by heavy-fermion systems

A theory of quasielastic scattering by a spin liquid with resonating valence bonds is constructed. It is demonstrated that the dependence of the scattering cross section of the spin liquid on the energy transfer has the same shape as the quasielastic peak observed experimentally in heavy-fermion systems. It is shown that a consequence of fact that the excitations of the spin-liquid state obey Fermi statistics is that the total quasielastic scattering cross section oscillates as a function of the momentum transfer. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 6, 480–485 (25 September 1998)     

Magnetic order in a Kondo lattice: A neutron scattering study of CeCu2Ge2

Elastic and inelastic neutron scattering studies of the Kondo lattice CeCu₂Ge₂ were performed. AtT _N=4.1 K an incommensurate magnetic order develops with an ordering wave vectorq ₀=(0.28, 0.28, 0.54) and an ordered moment µ _s =0.74 µB. The crystalline electric field splits the 4f ¹-J-multiplet of the Ce ion into a ground state doublet and a quartet at 191 K. The wave function of the ground state yields an ordered moment of 1.54µB. Thus, due to the onset of the formation of a Kondo singlet the magnetic moment is considerably reduced. The magnetic relaxation rate was investigated via quasielastic neutron scattering. The temperature dependence of (T) is characteristic of heavy-fermion systems with a high temperature square root dependence and a limiting low temperature value, yielding a Kondo temperatureT _K10K. The quasielastic component of the scattered neutron intensities persists down to the lowest temperatures, well belowT _N. This quasielastic line is regarded as a characteristic feature of heavy-fermion systems and corresponds to the enhanced value of the linear term of the specific heat.     

Strongly correlated quantum spin liquid in herbertsmithite

Strongly correlated Fermi systems are among the most intriguing and fundamental systems in physics. We show that the herbertsmithite ZnCu₃(OH)₆Cl₂ can be regarded as a new type of strongly correlated electrical insulator that possesses properties of heavy-fermion metals with one exception: it resists the flow of electric charge. We demonstrate that herbertsmithite’s low-temperature properties are defined by a strongly correlated quantum spin liquid made with hypothetic particles such as fermionic spinons that carry spin 1/2 and no charge. Our calculations of its thermodynamic and relaxation properties are in good agreement with recent experimental facts and allow us to reveal their scaling behavior, which strongly resembles that observed in heavy-fermion metals. Analysis of the dynamic magnetic susceptibility of strongly correlated Fermi systems suggests that there exist at least two types of its scaling.     

Anomalous influence of an external magnetic field on spin fluctuations in magnetic semiconductors with strong p-d hybridization and the colossal magnetoresistance effect

The colossal magnetoresistance effect in magnetic semiconductors based on lanthanum manganites has been investigated in terms of the model allowing for the effects of p-d hybridization and electronelectron Coulomb correlations. The influence of an external magnetic field on spin fluctuations has been considered under the conditions where the chemical potential is in a narrow heavy-fermion band formed in the hybridization gap. It has been shown that, in the vicinity of the Curie point T _C, the strong spin anharmonicity leads to an anomalously strong suppression of spin fluctuations by the external magnetic field, a phenomenon contributing significantly to the formation of colossal negative magnetoresistance.     

Neutron scattering on the strongly correlated electron CeNi Cu system: from non-magnetic behaviour to long-range magnetic order

The ground state of the strongly correlated electron CeNi_1-xCu_x compounds has been investigated by means of neutron scattering experiments. Thus, magnetic diffraction was performed for compounds showing long-range magnetic order (x > 0.2). An evolution from a collinear ferromagnetic structure for x =0.6 to a simple antiferromagnetic one for CeCu takes place through some more complex magnetic structures for intermediate compositions. The magnetic moments are continuously reduced when the Ni content increases reflecting the progressive enhancement of the Kondo screening. The large reduction found for x =0.6 compound is discussed and the existence of a spin glass like component of the magnetic moment cannot be discarded. From the quasielastic spectra, we have obtained the Kondo temperatures which are close to the magnetic ordering ones. The quasielastic line-width evolves from a linear temperature dependence to a T ^1/2 behaviour when approaching the non-magnetic limit. Then, this system provides an interesting example for the evolution of unstable 4 f shell relaxation regimes when modifying the hybridisation strength. Received 22 May 2000     

Heavy fermions in transition metals and transition-metal oxides

Heavy-fermion formation in transition metals and transition-metal oxides is reviewed and compared to observations in canonical f-derived heavy-fermion systems. The work focuses on the dynamic susceptibilities which reveal a characteristic temperature and frequency dependence and which can be unambiguously determined via nuclear magnetic resonance and electron-spin resonance measurements as well as via quasielastic neutron-scattering studies. Different routes to heavy-fermion behaviour are discussed, amongst them Kondo systems, frustrated magnets, and electronically correlated systems close to a metal-insulator transition. From a theoretical point of view, utilizing dynamical mean-field theory, we show that dynamic susceptibilities as calculated for the Hubbard model and for the periodic Anderson model look qualitatively rather similar. These different theoretical concepts describe an universal behaviour of the temperature dependent dynamic susceptibility.Received: 15 May 2003, Published online: 9 September 2003PACS: 71.27.+a Strongly correlated electron systems; heavy fermions - 71.30.+h Metal-insulator transitions and other electronic transitions - 76.60.-k Nuclear magnetic resonance and relaxation - 76.30.Kg Rare-earth ions and impurities     

Nuclear and muon hyperfine techniques in the study of heavy-fermion superconductors

Nuclear magnetic resonance and relaxation, and the related techniques of muon spin rotation and relaxation, have been used to study local spin polarization and quasiparticle excitations in the heavy-fermion superconductors CeCu₂Si₂, pure and thoriated UBe₁₃, and UPt₃. Measurements of nuclear and positive muon Knight shifts, linewidths, and spinlattice relaxation rates give some hints as to the nature of Cooper pairing in these exotic materials.     

Long-range antiferromagnetic order in CeCu5.5Au0.5

The magnetic ordering previously discovered in CeCu_6–xAu_x heavy-fermion alloys is shown to be of long-range antiferromagnetic type by elastic neutron scattering performed on a polycrystalline sample. The data are compatible with an incommensurate wave vector (0.17, 0, 0.514). Although a definite assignment needs a single-crystal study, the magnetic structure is clearly different from the type of magnetic correlations in pure CeCu₆ found in inelastic scattering.     

Muon spin relaxation in CeCu2Si2 and muon knight shift in various heavy-fermion systems

Positive muon spin precession has been observed in various heavy-fermion systems in the transverse external magnetic field. In the superconductor CeCu_2.1Si₂, the relaxation rate of muon spins increases rapidly with decreasing temperature below T_C. This is interpreted as the results of the inhomogeneous fields due to the imperfect penetration of the external field into the type-II superconducting state. The magnetic-field penetration depth λ is derived from the observed muon spin relaxation rate. λ is about 1200 ∢ at T∼0.5T_C, and the temperature dependence of λ is consistent with the relation expected for a BCS superconductor. We have also measured the muon Knight shift K_μ in the normal (or paramagnetic) state of various heavy-fermion systems. K_μ is large and negative (about −1000∼−3000 ppm at T=10 K) for CeCu₂Si₂, UPt₃ and CeAl₃, while more complicated signals are measured in CePb₃ and CeB₆. The negative muon Knight shift in the non-magnetic heavy-fermion systems is discussed in terms of the Kondo-coupling between the conduction- and f-electrons.     

Magnetic correlations in heavy fermion CeAl3 compound

To study the effect of hybridization on inter-ion correlations the measurements of the intensity of the quasielastic scattering on momentum transfer in Ce_0.9Y _0.1Al₃, Ce_0.9La_0.1Al₃ and CeAl₃ have been performed. Some hints that quasielastic magnetic scattering more sensitive to regularity in rare-earth sublattice than to the hybridization have been obtained. We also get some indications on the presence of ferromagnetic inter-ion correlations. In a contrast to quasielastic scattering the inelastic part of spectra is very sensitive to the hybridization.     

Fermi surface topology and the superconducting gap function in UPd2Al3: a neutron spin-echo study

We report on a single crystal neutron spin-echo investigation of the low-energy dynamic response in the heavy-fermion superconductor UPd2Al3 in the vicinity of the antiferromagnetic wave vector Q(0)=(0 0 0.5). Well inside the superconducting phase, antiferromagnetic quasielastic scattering, which is present in the normal state, is absent for relaxation times up to 10 ns, equivalent to an energy resolution of approximately 1 microeV. This places strong constraints on possible models for this magnetic superconductor.     

Local-moment and itinerant antiferromagnetism in the heavy-fermion system Ce(Cu1−xNix)2Ge2

Elastic and inelastic neutron-scattering studies on the system Ce(Cu_1?xNi_x)₂Ge₂ are reported. These measurements are complemented by measurements of the magnetic susceptibility, high-field magnetization, heat capacity, thermal expansion, electrical resistivity and thermopower. The results reveal an interesting T-x phase diagram consisting of two different antiferromagnetic phases for x < 0.2 and 0.2 < x < 0.75, respectively, and a heavy-Fermi-liquid regime at higher Ni concentrations. The experimental results are interpreted in terms of an alloying-induced transition from local-moment to itinerant heavy-fermion magnetism. Fingerprints of this latter phase are a strongly reduced ordered moment and a short incommensurate ordering wave vector, in accord with theoretical predictions. A surprisingly good agreement between theory and experiment is found for x > 0.5. Further experimental evidence for different types of antiferromagnetic ordering derives from a line-shape analysis of the quasielastic neutron-scattering intensity, from magnetization and thermopower experiments.     

Advances in the study of intermediate-valence and heavy-fermion effects in rare-earth and uranium systems

Summary Three intermetallic systems, Yb−Al, U−Au and Ce−Co, are studied as most typical examples of intermediate-valence, heavy-fermion and coexistence of both intermediate-valence and heavy-fermion effects, respectively. YbAl₂ and YbAl₃, the two phases stable at low temperatures in the equilibrium phase diagram of Yb−Al, are both intermediate-valence systems with Yb valence values of 2.33 and 2.79 at room temperature. The modulation of these values by variations of external parameters like temperature, pressure and chemical substitutions with proper atoms was studied by structural, magnetic and spectroscopical techniques. Two phases are given also by U with Au at low temperatures with compositions UAu₂ and U₁₄Au₅₁: both systems exhibit heavy-fermion properties although with different ordering mechanisms. U₁₄Au₅₁ is an antiferromagnetic heavy-fermion system with a Nèel temperature around 23 K, UAu₂ shows spin-fluctuating behaviour with a saturation in theT→0 K magnetic susceptibility. Effects of substitutions with thorium were investigated only in U₁₄Au₅₁: competition between strong antiferromagnetic coupling and Kondo-like behaviours is observed. The Ce-rich side of the Ce−Co phase diagram shows a single Ce₂₄Co₁₁ phase stable at room temperature interest in the present work but in CeCo₂, which was demonstrated to be intermediate valent by resonant photoemission and XAS experiments and to exibit low magnetic moment and superconducting transition. The coexistence of intermediate-valence and heavy-fermion behaviours observed in Ce₂₄Co₁₁ and of intermediate valence and superconductivity in CeCo₂ is shown by the analyses of XPS, XAS and magnetic experiments with suitable phenomenological models. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

Investigations of magnetic excitations in a La2CuO4 single crystal

A detailed neutron scattering study is carried out of magnetic excitations in pure La₂CuO₄ in the low energy region up to 15 meV, at temperatures in the vicinity of the transition temperatureT _N to the paramagnetic state. In particular the question of existence of propagating spin waves in this energy region is addressed. The experimental results show that the energy region studied (up to 15 meV) is characterized by aquasielastic peak of the width of order 4 meV (at 300 K). Thus the magnetic correlation function has relaxational behavior in the studied energy region, no indications for propagating spin waves are obtained. The measured quasielastic width agrees well with existing theories. Polarized neutrons and polarization analysis are also used to identify the magnetic origin of the observed scattering.     

Magnetic relaxation spectra of YbPd2Si2

We present the results of inelastic neutron scattering experiments on the intermediate-valent system YbPd₂Si₂ to investigate the magnetic relaxation behaviour. We have performed measurements on polycrystalline samples with neutrons of incident energyE ₀=3.1 meV at temperatures between 1.5 K and 250 K, and withE ₀=12.7 meV andE ₀=50.8 meV at temperatures between 5 K and 50 K using time-of-flight spectrometers. At temperaturesT>50 K we find a pure quasielastic magnetic response with a rather broad linewidth typical for intermediate-valent systems. AtT50 K an inelastic excitation line appears at about 21 meV; its intensity increases with decreasing temperature. In the same temperature range (T<50 K) the quasielastic linewidth decreases rapidly and atT=5 K the quasielastic response has been apparently transformed to a second inelastic feature at about 4.7 meV. The width of this low-energy excitation fits well to the temperature dependence of the quasielastic linewidth forT>5 K.     

Electron spectrum and heat capacity of heavy fermions in the canted phase of antiferromagnetic intermetallides

The energy spectrum of heavy fermions in an external magnetic field is calculated for canted magnetic sublattices of antiferromagnetic intermetallides. This makes it possible to determine low-temperature features of electronic heat capacity of heavy-fermion antiferromagnets with the metal-type ground state taking into account the structural rearrangement of the magnetic subsystem. The calculated temperature dependences of the magnetization, heat capacity, and Sommerfeld constant in the vicinity of the point of transition to the antiferromagnetic phase correlate with experimental data obtained for heavy-fermion antiferromagnets PuGa₃, Ce₂Au₂Cd, YbNiSi₃, and PuPd₅Al₂.     

Evidence for anisotropic kondo behavior in Ce0.8La0.2Al3

We have performed an inelastic neutron scattering study of the low energy spin dynamics of the heavy fermion compound Ce0.8La0.2Al3 as a function of temperature and external pressure up to 5 kbar. At temperatures below 3 K, the magnetic response transforms from a quasielastic form, common to many heavy fermion systems, to a single well-defined inelastic peak, which is extremely sensitive to external pressure. The scaling of the spin dynamics and the thermodynamic properties are in agreement with the predictions of the anisotropic Kondo model.     

Quasi-one-dimensional quantum spin liquid in the Cu(C<Subscript>4</Subscript>H<Subscript>4</Subscript>N<Subscript>2</Subscript>)(NO<Subscript>3</Subscript>)<Subscript>2</Subscript> insulator

We analyze measurements of the magnetization, differential susceptibility and specific heat of quasi-onedimensional insulator Cu(C₄H₄N₂)(NO₃)₂ (CuPzN) subjected to magnetic fields. We show that the thermodynamic properties are defined by quantum spin liquid formed with spinons, with the magnetic field tuning the insulator CuPzN towards quantum critical point related to fermion condensation quantum phase transition (FCQPT) at which the spinon effective mass diverges kinematically. We show that the FCQPT concept permits to reveal and explain the scaling behavior of thermodynamic characteristics. For the first time, we construct the schematic T–H (temperature-magnetic field) phase diagram of CuPzN that contains Landau–Fermi-liquid, crossover and non-Fermi liquid parts, thus resembling that of heavy-fermion compounds.     

Spin relaxation in the amorphous spin glass Al2Mn3Si3O12

Neutron scattering measurements on the amorphous spin glass Al₂Mn₃Si₃O₁₂ have been made using the time-of-flight method. The scattering lawS(Q, ) reveals a quasielastic line with temperature andQ-dependent linewidth and an elastic line with constant intensity between 15 and 294K. The linewidth of the quasielastic scattering diminishes with decreasing temperature following an Arrhenius law at least down to 15K. Deviations from this exponential form are strictly correlated with an increase of the elastic intensity below 15K. We favour the opinion that this effect is caused by the instrumental resolution rather than by the onset of spin glass freezing.     

Interplay between unconventional superconductivity and heavy-fermion quantum criticality: CeCu2Si2 versus YbRh2Si2

In this paper the low-temperature properties of two isostructural canonical heavy-fermion compounds are contrasted with regards to the interplay between antiferromagnetic (AF) quantum criticality and superconductivity. For CeCu₂Si₂, fully-gapped d-wave superconductivity forms in the vicinity of an itinerant three-dimensional heavy-fermion spin-density-wave (SDW) quantum critical point (QCP). Inelastic neutron scattering results highlight that both quantum critical SDW fluctuations as well as Mott-type fluctuations of local magnetic moments contribute to the formation of Cooper pairs in CeCu₂Si₂. In YbRh₂Si₂, superconductivity appears to be suppressed at T???10?mK by AF order (T_N?=?70?mK). Ultra-low temperature measurements reveal a hybrid order between nuclear and 4f-electronic spins, which is dominated by the Yb-derived nuclear spins, to develop at T_A slightly above 2?mK. The hybrid order turns out to strongly compete with the primary 4f-electronic order and to push the material towards its QCP. Apparently, this paves the way for heavy-fermion superconductivity to form at T_c?=?2?mK. Like the pressure – induced QCP in CeRhIn₅, the magnetic field – induced one in YbRh₂Si₂ is of the local Kondo-destroying variety which corresponds to a Mott-type transition at zero temperature. Therefore, these materials form the link between the large family of about fifty low-T unconventional heavy – fermion superconductors and other families of unconventional superconductors with higher T_cs, notably the doped Mott insulators of the cuprates, organic charge-transfer salts and some of the Fe-based superconductors. Our study suggests that heavy-fermion superconductivity near an AF QCP is a robust phenomenon.