Neutron scattering studies on heavy-fermion superconductors

We review recent neutron scattering studies on uranium-based heavy-fermion superconductors. The coupling between magnetic and superconducting order parameters was observed in UPt₃, UPd₂Al₃, URu₂Si₂, and UNi₂Al₃. In UPd₂Al₃, the superconducting gap appears in the spin excitation spectra. These results are indicative of the strong interplay between magnetism and superconductivity. We also report the unusual behaviors of the weak antiferromagnetic ordering, the long-range magnetic correlation in UPt₃ at ultra-low temperatures, and the pressure-induced magnetic transition from the weak (0.02μ_B/U) to a high moment state (0.4μ_B/U) at 1.5 GPa in URu₂Si₂.     

The resonance peak in the high-Tc cuprates

I present a theory in which the resonance peak observed in inelastic neutron scattering experiments on YBa₂Cu₃O_6+x and Bi₂Sr₂CaCu₂O_8+x arises from a dispersing spin mode. I argue that it is heavily damped in the normal state and becomes visible in the superconducting state due to a drastic decrease in the spin damping. I show that a spin-fermion model correctly describes the doping dependence of the peak position and of its integrated intensity. Finally, I derive a criterion for the existence of the resonance peak in other cuprate superconductors.     

Interplay of structure and magnetism in ruthenocuprates: a Raman scattering and dilatometry study

We present a Raman scattering and dilatometry study of polycrystalline samples of the magnetic superconducting ruthenocuprates RuSr₂Gd_2−xCe_xCu₂O_10+δ (RuGd₁₂₂₂) and RuSr₂GdCu₂O₈ (RuGd₁₂₁₂). In the Raman spectra a high-temperature diffusive-like laser-tail develops below the magnetic ordering temperature (T_M) into an underdamped peak which shifts up to 130 cm⁻¹. A line assigned to O(Ru) phonons hardens, narrows and strengthens strongly below T_M. Finally, a phonon peak appears below T_M at 590 cm⁻¹. These three magnetic-order-dependent features are observed for RuGd₁₂₁₂ and for RuGd₁₂₂₂ with x=1.0, but do not appear for x=0.5. Dilatometry measurements, on the other hand, evidence a change of the expansion coefficient at T_M. These results point to a structural effect accompanying the magnetic order, and suggest a complex interplay of spin and lattice degrees of freedom in these ruthenocuprates.     

Suppression of antiferromagnetic spin fluctuation in Zn-substituted YBa2Cu3O7

We have prepared Zn-substituted YBa₂Cu_3−xZn_xO₇ (YBCO, x=0.0–0.09) and performed ^63,65Cu nuclear quadrupole resonance (NQR) measurements for the plane site at 300 and 100 K as a function of Zn concentration. The substitutional effects are observed in resonant frequencies and linewidths of spectra, and relaxation times as well as in the superconducting transition temperature. The spin–lattice relaxation rate 1/T₁ is reduced for the higher Zn concentration and the reduction is more significant at 100 K. The ratio of ^63,65Cu spin–lattice relaxation rates suggests that a magnetic contribution due to the antiferromagnetic spin fluctuation becomes weak as the Zn concentration increases. These effects confirm that the antiferromagnetic spin fluctuation of Cu 3d spins is suppressed by the Zn substitution due to the absence of local moment at the zinc site.     

Nuclear magnetic resonance study of the electron-doped high-temperature superconducting cuprates

Nuclear magnetic resonance (NMR) measurements have been made on two of the electron-doped high-temperature superconducting cuprates (HTSCs), Pr_2−xCe_xCuO₄ and Sr_0.9La_0.1CuO₂ that represent the two known electron-doped structures. The results are compared with the more-studied hole-doped HTSCs. We show that the electron and hole-doped HTSCs probe a similar antiferromagnetic spin fluctuation spectrum in the normal state, which provides support for theories of superconductivity where the pairing is mediated by antiferromagnetic spin fluctuations and the superconducting order parameter has a d_x²−y² symmetry. Contrary to results from underdoped and hole-doped HTSCs, there is no evidence for a normal-state pseudogap in the NMR data from measurements on the electron-doped HTSCs. Therefore, the electron-doped HTSCs can be better compared with overdoped and hole-doped HTSCs where the normal-state pseudogap is absent. The antiferromagnetic spin fluctuation spectrum as probed by the Cu spin–lattice relaxation rate, is independent of the doped electrons per Cu. A similar effect is observed in the overdoped and hole-doped HTSC, Y_1−xCa_xBa₂Cu₃O_7−δ for a hole concentration range of 0.063. The anomalous Cu NMR linewidth anisotropy observed in the electron-doped HTSCs suggests a small and static spin variation for temperatures up to room temperature.     

Influence of high magnetic fields on the low temperature heat capacity of the itinerant electron ferromagnet Sc3In

The low temperature (1.3–20 K) heat capacity of the weak itinerant electron ferromagnet Sc₃In was measured in magnetic fields up to 10 T. The measurements were made on three different samples containing 24.1, 24.3 and 24.4 at.% In with Curie temperatures at H = 0 of 5.5, 6.0 and 6.3 K, respectively. The heat capacity peak at T_c becomes smaller with increasing fields and at 9.98 T the magnetic entropies are only 11 to 19% of the zero field value. Above T_c the spin fluctuation contribution to heat capacity, which is enhanced by the magnetic field at low fields (<≈ 5 T), is quenched at high fields ( ≈ 5 T). Our results show that the spin fluctuations in Sc₃In are almost completely quenched by the magnetic fields of ≈ 10 T, and that the characteristics spin fluctuation temperature, T_s, of this itinerant electron ferromagnet is about the same as T_c.     

NMR study of local hole distribution, spin fluctuation and superconductivity in Tl2Ba2Ca2Cu3O10

⁶³Cu, ¹⁷O and ²⁰⁵Tl NMR have been performed in the high-T_c superconductor Tl₂Ba₂Ca₂Cu₃O₁₀ whose T_c(max) is 127 K. The hole densities at Cu and oxygen sites in the CuO₂ plane have been extracted from the nuclear quadrupole frequency ν_Q. The striking feature is that the Cu holes are significantly transferred to oxygen site due to strong hybridization between Cu and oxygen. From an analysis of T₁ and T_2G, it has been found that the spectral weight of the spin fluctuation is transferred to higher energy compared to YBa₂Cu₃O₇, while the magnetic correlation length ξ does not differ much. Thus, it is suggested that the higher T_c is due to higher characteristic energy of spin fluctuations, i.e. the superconductivity is spin fluctuation mediated. The superconducting properties are consistently explained by a d-wave superconductivity model with a finite density of states (DOS) at the Fermi level. We show that the disorder of the Ca/TlO layer caused by the partial inter-substitution of Tl and Ca is responsible for the potential scattering to produce such a DOS. It is found that if such a potential scattering were absent, T_c would go up to 132 K which is quite close to the record T_c realized in the Hg based compound.     

Dispersion of neutron spin resonance mode in Ba0.67K0.33Fe2As2

We report an inelastic neutron scattering investigation on the spin resonance mode in the optimally hole-doped iron-based superconductor Ba_0.67K_0.33Fe₂As₂ with T_c=38.2 K. Although the resonance is nearly two-dimensional with peak energy E_R≈14 meV, it splits into two incommensurate peaks along the longitudinal direction ([H, 0, 0]) and shows an upward dispersion persisting to 26 meV. Such dispersion breaks through the limit of total superconducting gaps ∆_tot=|∆_k|+|∆_k+Q|(about 11-17 meV) on nested Fermi surfaces measured by high resolution angle resolved photoemission spectroscopy (ARPES). These results cannot be fully understood by the magnetic exciton scenario under s^±-pairing symmetry of superconductivity, and suggest that the spin resonance may not be restricted by the superconducting gaps in the multi-band systems.     

Quenching of spin fluctuations by high magnetic fields

The quenching of spin fluctuations by magnetic fields has been observed in heat capacity and electrical resistivity measurements at low temperatures for a series of highly exchange enhanced magnetic materials. These include: the weak itinerant electron ferromagnets Sc₃In, Zr_1−xHf_xZn₂ (0 x 0.2) and Ni₃Al; the strong Pauli paramagnets RCo₂ (R = Sc, Y and Lu), TiBe₂ and Pd_1−xNi_x (0 x 0.01); and the heavy fermion systems CeSn₃, CeSi_x (x ≈ 1.85) an d UAl₂. The reported quenching of spin fluctuations in scandium and palladium by magnetic fields is reviewed, and it appears that the initial observations and conclusions are incorrect, and that fields greater than 10 and 40 T, respectively, will be necessary to quench spin fluctuations in these metals. The behaviors of these spin fluctuators have been grouped into six classes.     

Conductivity peaks broadening in the quantum Hall regime

We argue that it is the hopping transport that is responsible for broadening of the σ_xx peaks. Explicit expressions for the width Δν of a peak as a function of the temperature T, current J and frequency ω are found. It is shown that Δν grows with T as (T/T₁)^κ, where κ is the inverse localization-length exponent. The current J is shown to act like the effective temperature T_eff(J) ∝ J^1/2 if . Broadening of the ohmic ac-conductivity peaks with frequency ω is found to be determined by the effective temperature      

Superconductivity of compressed platinum powder at very low temperatures

Superconductivity of compressed, high-purity platinum powder (average grain size 2–3 μm) was found by measurements of resistivity, AC susceptibility and magnetization. The transition temperature into the superconducting state T_c and the critical magnetic field B_c strongly depend on the packing fraction f of the samples: we found 0.62T_c(0)1.38 mK and 6.6B_c(0)67 μT for 0.8f0.5, respectively. The temperature dependence of the critical magnetic fields can be described by B_c(T)=B_c(0)(1−(T/T_c)²). The discussion of these results includes possible explanations for the origin of superconductivity in this new superconducting material.     

Final-state interactions and single-spin asymmetries in semi-inclusive deep inelastic scattering

Recent measurements from the HERMES and SMC Collaborations show a remarkably large azimuthal single-spin asymmetries A_UL and A_UT of the proton in semi-inclusive pion leptoproduction γ^*(q)p→πX. We show that final-state interactions from gluon exchange between the outgoing quark and the target spectator system lead to single-spin asymmetries in deep inelastic lepton–proton scattering at leading twist in perturbative QCD; i.e., the rescattering corrections are not power-law suppressed at large photon virtuality Q² at fixed x_bj. The existence of such single-spin asymmetries requires a phase difference between two amplitudes coupling the proton target with J^z_p=±1/2 to the same final-state, the same amplitudes which are necessary to produce a nonzero proton anomalous magnetic moment. We show that the exchange of gauge particles between the outgoing quark and the proton spectators produces a Coulomb-like complex phase which depends on the angular momentum L^z of the proton's constituents and is thus distinct for different proton spin amplitudes. The single-spin asymmetry which arises from such final-state interactions does not factorize into a product of distribution function and fragmentation function, and it is not related to the transversity distribution δq(x,Q) which correlates transversely polarized quarks with the spin of the transversely polarized target nucleon.     

Nucleon–nucleon scattering observables in large-Nc QCD

Nucleon–nucleon scattering observables are considered in the context of the large N_c limit of QCD for initial states with moderately high momenta (pN_c). The scattering is studied in the framework of the time-dependent mean-field approximation. We focus on the dependence of those observables on the spin and isospin of the initial state which may be computed using time-dependent mean-field theory. We show that, up to corrections, all such observables must be invariant under simultaneous spin and isospin flips (i.e., rotations through π/2 in both spin and isospin) acting on either particle. All observables of this class obtained from spin unpolarized measurements must be isospin independent up to 1/N_c corrections. Moreover, it can be shown that the leading correction is of relative order 1/N_c² rather than 1/N_c.     

Doping dependence of bilayer resonant spin excitations in (Y, Ca)Ba2Cu3O6+x

Resonant magnetic modes with odd and even symmetries were studied by inelastic neutron scattering experiments in the bilayer high-Tc superconductor Y1-xCa+Ba2Cu3O6+y over a wide doping range. The threshold of the spin excitation continuum in the superconducting state, deduced from the energies and spectral weights of both modes, is compared with the superconducting d-wave gap, deduced from electronic Raman scattering in the B1g symmetry on the same samples. Above a critical doping level of delta approximately =0.19, both mode energies and the continuum threshold coincide. We find a simple scaling relationship between the characteristic energies and spectral weights of both modes, which indicates that the resonant modes are bound states in the superconducting energy gap, as predicted by the spin-exciton model of the resonant mode.     

Synthesis, crystal structure and inelastic neutron scattering in the infinite-layer compounds Sr1−xNdxCuO2

For the first time large samples of the nominal composition Sr_1−xNd_xCuO₂ (x=0.07, 0.15) 10 g in mass each have been prepared using a high-pressure technique. Neutron-diffraction and X-ray measurements have shown that the main phase in the samples obtained is of the infinite-layer structure which has been refined in the tetragonal P4/mmm space group. Both samples are not superconducting. Inelastic neutron scattering has been employed to search for crystalline-electric-field transitions in these compounds. The observed low-energy spectra exhibit one inelastic line of magnetic origin at 18 meV, comparable in energy with a crystalline-electric-field excitation in the high-T_c superconductor NdBa₂Cu₃O_x.     

Effects of the spin–orbit coupling on magnetic and superconducting properties in iron-based superconductors

We analyze the magnetic properties through two-orbital Hubbard model with the spin–orbit coupling (SOC) interaction in the iron-based superconductors. With the help of the Ising approximation for the Hund’s coupling between the itinerant electrons and the localized spins, we give a self-consistent account of the various magnetic orders observed in pnictides and the pairing symmetry. We also calculate the local density of states (LDOS) of the vortex state when a magnetic field is applied. The LDOS without SOC shows no resonant peak at the vortex core center in the superconducting state, while it shows an obvious resonant peak when SOC is applied.     

Charge susceptibility and charge correlation function in the d---p model

The properties of the charge fluctuation are investigated in the d---p model with the repulsion U_pd between holes on the nearest-neighbor Cu and O sites and the infinite on-site repulsion U_d at the Cu site. We calculate the charge susceptibility χ^c(q, iω_n) and the charge correlation function S^c(q) = TΣ_ωn χ^c(q, iω_n). It is found that S^c(q) has a peak at the Γ point and a maximum in a ring around the Γ point. The former is due to Tχ^c(q, 0). Its intensity is proportional to temperature T and strongly enhanced by U_pd. The latter is due to TΣ_{ωn ≠ 0} χ^c(q, iω_n) and shows a weak T and U_pd dependence. The intensity of the diffuse X-ray scattering on taking the charge fluctuation into account is also calculated. The result is consistent with the experiments in La_2−δSr_δCuO₄.     

Elastic proton-proton scattering: Excitation functions from 0.45 to 2.5 GeV

Excitation functions of the differential cross sections dσ/dgw, analyzing powers A_N and spin correlation parameters A_NN, A_SS and A_SL have been measured with internal targets at the Cooler Synchrotron COSY. Data were taken continously during the acceleration and deceleration of the internal beam for kinetic energies between 450 and 2500 MeV and scattering angles 30° σ_cm 90°. Details of the experimental method are presented. The results provide excitation functions and angular distributions of high precision and internal consistency. No evidence for narrow structures are found. Upper limits on the coupling of narrow resonances to elastic scattering in the mass range √s = 2.2…2.8 GeV are deduced. The data have significant impact on phase shift solutions.     

Stray-field imaging of quadrupolar nuclei of half integer spin in solids

A report is presented on the observation of Hahn echoes from the following quadrupolar nuclei of half integer spin (I) in polycrystalline solids in the large static magnetic field gradient (37.5 T/m) which exists in the fringe field of a superconducting solenoid: ⁷Li, ²³Na, ¹¹B, ⁶⁵Cu (I = 3/2); ²⁷Al (I = 5/2); ⁵¹V, ⁵⁹Co (I = 7/2); and ¹¹⁵In (I = 9/2). ²³Na echo-trains from NaCl (with non-selective excitation) and from Na₂SO₄ (with selective excitation) are compared quantitatively for two different RF pulse sequences: 90_x-(τ-90_y-τ-echo-)_n and 90_x-(τ-90_x-τ-echo-)_n. The signals obtained from RF pulses corresponding to non-selective 90 ° pulses were shown to be quantitative, whereas in the selective case smaller signals were obtained since only the central transition contributed. The loss of signal from this cause can be distinguished from small signals resulting from low density of nuclei by use of the second sequence. A ⁷Li image obtained from LiF in a cylindrical glass-vial is shown.     

Composite scalars in ee collisions and radiative Z decays

Starting point is the hypothesis that the observed Z→e⁺e⁻γ decays are mediated by a (composite) spin 0 boson X with 40m_X50 GeV. The consequences for e⁺e⁻→e⁺e⁻, e⁺e⁻→γγ and e⁺e⁻→ hadrons at PETRA are explored. PETRA experiments turn out to be sensitive up to masses m_X50 GeV; the best indicator for m_X 48 GeV is the angular distribution of Bhabha scattering.