Knight Shift Data and Superconducting Tc Modeling Based on an Effective Hole Model

The superconducting T _c of cuprates have been modeled on a linear scaling with hole concentration per CuO₂ plane and a deleterious influence of bond resonance with the apical system (effective hole formalism). In cases where distribution between various hole reservoirs is not trivial, Knight shift can provide actual hole concentrations. It is shown here that when Knight shift data are used in an effective hole algorithm, satisfactory T _c predictions can be made, corroborating the deleterious influence on T _c of apical O and earlier assumptions concerning hole distributions. For the case of stacking of more than two CuO₂ planes, the inner plane has to be treated as an infinite layer analog in the effective hole model. A separation into inner and outer planes with different dopings is indeed observed by Knight shift, with higher doping in the latter. This is explained here as being due to a tendency to equalize an effective doping degree, as the outer planes lose holes in resonance of bonding with the apical system.     

Ferromagnetic Correlations in Ca-Doped Sr2RuO4: 87Sr NMR Study

Magnetic properties on Sr_2–x Ca _x RuO₄ have been investigated by a microscopic probe of ⁸⁷Sr-NMR in order to understand the magnetic character on spin-triplet superconductor of Sr₂RuO₄, which has multibands on the Fermi surface. With substituting Ca for Sr which gives rise to crystal distortion, the Knight shift (K) and the nuclear spin-lattice relaxation rate divided by temperature (1/T _{1 T}) increases progressively up to x=1.5. The Korringa relation from K and 1/T ₁ T becomes smaller, indicative of development of ferromagnetic fluctuations with increasing Ca content. This suggests that the q-independent spin fluctuations originating from the 2-dimensional band are changed to the ferromagnetic ones by the Ca doping.     

Electronic Inhomogeneity and Possible Pseudogap Behavior of Spin Susceptibility in the Electron-Doped Superconductor Sr0.93La0.07CuO2: 63Cu NMR Study

The magnetic susceptibility, NMR spectra, nuclear spin-lattice relaxation rate (T ₁ ^–1) and the echo-decay rate (T ₂ ^–1) of ⁶³Cu were measured for the electron-doped infinite-layer superconductor Sr_0.93La_0.07CuO₂/T _c ^onset = 42.4 K). The results obtained revealed a clear tendency toward frustrated phase separation in this nominally underdoped high-T _c material. Above T _c the ⁶³Cu Knight shift is found to decrease upon cooling giving an evidence for a pseudogap-like decrease of the spin susceptibility. It is shown that unusual anisotropy of the ⁶³Cu Knight shift in the electron-doped CuO₂ layer can be understood as a compensation effect between the isotropic hyperfine coupling, mediated by the 4s Fermi-contact and 3d core-polarization exchange interactions, and the anisotropic on-site spin-dipolar hyperfine interaction of the Cu nuclei with the itinerant carriers, whose states near the Fermi energy have a sizeable admixture of Cu(4p_z) and/or Cu(3d_z ²) orbitals.     

Electronic Inhomogeneity and Possible Pseudogap Behavior of Spin Susceptibility in the Electron-Doped Superconductor Sr0.93La0.07CuO2: 63Cu NMR Study

The magnetic susceptibility, NMR spectra, nuclear spin-lattice relaxation rate (T ₁ ^?1)_α and the echo-decay rate (T ₂ ^?1) of ⁶³Cu were measured for the electron-doped infinite-layer superconductor Sr_0.93La_0.07CuO₂/T _c ^onset = 42.4 K). The results obtained revealed a clear tendency toward frustrated phase separation in this nominally underdoped high-T _c material. Above T _c the ⁶³Cu Knight shift is found to decrease upon cooling giving an evidence for a pseudogap-like decrease of the spin susceptibility. It is shown that unusual anisotropy of the ⁶³Cu Knight shift in the electron-doped CuO₂ layer can be understood as a “compensation effect” between the isotropic hyperfine coupling, mediated by the 4s Fermi-contact and 3d core-polarization exchange interactions, and the anisotropic on-site spin-dipolar hyperfine interaction of the Cu nuclei with the itinerant carriers, whose states near the Fermi energy have a sizeable admixture of Cu(4p_z) and/or Cu(3d_z ²) orbitals.     

Magnetic field and temperature dependence of the Knight shift in superconductors of small dimensions

The magnetic field dependence of the paramagnetic Knight shift in weak-coupling superconductors is evaluated within the framework of the BCS-Gor'kov theory for samples of small dimensions. The behavior of the monotonic and oscillatory parts of the Knight shift are examined in detail in the regimesT0 andTT _c ^– .     

Multiple Superconducting Gaps and Anisotropic Spin Fluctuations in Hole-Doped and Electron-Doped Iron-Pnictides: NMR Studies

We present extensive ⁷⁵As-NMR data on the electron-doped pnictides PrFeAsO_0.89F_0.11 (T _c=45 K), LaFeAsO_0.92F_0.08 (T _c=23 K), and the hole-doped Ba_0.72K_0.28Fe₂As₂ (T _c=31.5 K) single crystal. We find that the Fe antiferromagnetic spin fluctuations are anisotropic and are weaker compared to underdoped copper-oxides or cobalt-oxide superconductors. The spin lattice relaxation rate 1/T ₁ decreases below T _c with no coherence peak and shows a step-wise variation at low temperatures. The Knight shift decreases below T _c and shows a step-wise T variation as well. These results indicate spin-singlet superconductivity with multiple gaps.     

Clues Obtained from the Oxygen Isotope Effect on NMR/NQR Parameters Observed in YBa2Cu4O8

Nuclear magnetic and nuclear quadrupole resonance (NMR, NQR) techniques have a precision allowing one to determine rather small isotope effects. Well-defined oxygen stoichiometry and negligible oxygen diffusion makes YBa₂Cu₄O₈ an ideal compound for studies of small isotope effects that require experimental results not hampered by reproducibility problems. We report on high-precision measurements of the temperature dependence of plane-^63,65Cu NMR/NQR parameters such as Knight shift, spin–lattice relaxation rate R = 1/T ₁, NQR line frequency _Q and NQR linewidth _Q, as well as ⁸⁹Y Knight shift, performed in normal and superconducting ¹⁶O and ¹⁸O exchanged YBa₂Cu₄O₈.     

NMR studies of Nd2−x Ce x CuO4

Copper NMR has been studied as a function of temperature in a number of superconducting Nd_2−x Ce _x CuO₄ samples. The electric field gradient is very small and the Knight shift is 2380 ppm at room temperature, both of these implying that the copper is in a Cu⁺ state. The Knight shift decreases with temperature particularly belowT _c . The spin contribution to the Knight shift is estimated to be ∼ 200 ppm (about a factor ten smaller than in YBa₂Cu₃O₇) indicating thatN _s (E _F ) at the copper sites is small in this material.     

Knight Shift Data and Superconducting T c Modeling Based on an Effective Hole Model

The superconducting T _c of cuprates have been modeled on a linear scaling with hole concentration per CuO₂ plane and a deleterious influence of bond resonance with the apical system (effective hole formalism). In cases where distribution between various hole reservoirs is not trivial, Knight shift can provide actual hole concentrations. It is shown here that when Knight shift data are used in an effective hole algorithm, satisfactory T _c predictions can be made, corroborating the deleterious influence on T _c of apical O and earlier assumptions concerning hole distributions. For the case of stacking of more than two CuO₂ planes, the inner plane has to be treated as an infinite layer analog in the effective hole model. A separation into inner and outer planes with different dopings is indeed observed by Knight shift, with higher doping in the latter. This is explained here as being due to a tendency to equalize an effective doping degree, as the outer planes lose holes in resonance of bonding with the apical system.     

Clues Obtained from the Oxygen Isotope Effect on NMR/NQR Parameters Observed in YBa2Cu4O8

Nuclear magnetic and nuclear quadrupole resonance (NMR, NQR) techniques have a precision allowing one to determine rather small isotope effects. Well-defined oxygen stoichiometry and negligible oxygen diffusion makes YBa₂Cu₄O₈ an ideal compound for studies of small isotope effects that require experimental results not hampered by reproducibility problems. We report on high-precision measurements of the temperature dependence of plane-^63,65Cu NMR/NQR parameters such as Knight shift, spin–lattice relaxation rate R = 1/T ₁, NQR line frequency ν_Q and NQR linewidth δν_Q, as well as ⁸⁹Y Knight shift, performed in normal and superconducting ¹⁶O and ¹⁸O exchanged YBa₂Cu₄O₈.     

Tl-NMR Study on High–Tc Oxides TlM2CaCu2O7–δ(M=Ba, Sr) : Spin-Gap in Underdoped and Overdoped Systems

The Spin–lattice relaxation rate and the Knight shift have been measured for Tl–based cuprates TlBa ₂ CaCu ₂ O ₇₊ (TB1212) and TlSr ₂ Y _l–x Ca _x Cu ₂ O ₇₊ (TS1212). In the underdoped sample of TS1212 with Tc=34K. (T ₁ ) ^–1 showed a gap–like behavior from the temperature T _SG=120K. As for the slightly overdoped sample of TB1212 with T _c =80K, both the Knight shift and (T ₁ ) ^–1 showed a significant decrease from 160K, suggesting the existing of the spin-gap not only around q(, ) but also q0.     

Effect of Normal-State Pseudogap on Physical Quantities in Hubbard Model for Underdoped High-T c Cuprates

We develop the strong-coupling theory of coexisting charge-density-wave (CDW) and superconductivityd-wave gaps within the framework of the FLEX (fluctuation exchange) approximation for the two-dimensional Hubbard model. For nested sections of the Fermi surface these equations reduce to the previous FLEX equations for superconductivity where the squared energy gap _s ² in the denominator of the Green's function is replaced by ( _s ² + _c ² ) (here _s is the superconductivity and _c the CDW gap). We solve these equations by taking for _c a phenomenologicald-wave gap. The resulting neutron scattering intensity, spin-lattice relaxation rate 1/T₁ , Knight shift, resistivity, and photoemission intensity are in qualitative agreement with the data on underdoped high-T_c cuprates. TheT_c for superconductivity decreases and the crossover temperature T_* for 1/T₁Tincreases with increasing gap amplitude of _c which is in qualitative agreement with the phase diagram for underdoped cuprates.     

Nuclear spin-lattice relaxation rate in Kondo superconductors in the gapless state

The host nuclear spin-lattice relaxation rates in Kondo superconductors in the gapless state are derived within the framework of the Matsuura, Ichinose, and Nagaoka (MIN) theory of the Kondo effect. The relaxation rates for both low-T _K and high-T _K Kondo superconductors are obtained. The temperature dependence of the relaxation rate in low-T _K Kondo superconductors in the gapless state arising from the pair breaking by the Kondo impurity is obtained. The dependence of the relaxation rate for high-T _K Kondo superconductors in the gapless state on the external magnetic field producing the gapless state is also obtained.     

Pseudogap Ground State and Its Doping Evolution in Bi2Sr2?x La x CuO6+δ : Removing the Superconducting State by the Application of Very High Magnetic Fields

We present results for the pseudogap ground state and its doping evolution in single-layered copper-oxide Bi₂Sr_2?x La _x CuO_6+?? . We apply very high magnetic fields up to 44 T to remove the superconducting state and reveal the hidden low temperature (T) normal state. Through ⁶³Cu-NMR Knight shift and spin-lattice relaxation rate measurements, we find that there remains a finite density of states (DOS) at the Fermi level in the zero-T limit when the superconductivity is removed, which indicates that the pseudogap ground state is a metallic state with a finite volume of Fermi surface. The residual DOS in the pseudogap ground state decreases with decreasing doping (increasing x), but remains quite large even at the vicinity of the magnetically ordered phase of x?? 0.8. The result indicates that the superconductivity emerges from the remaining Fermi surface and coexists with the pseudogap.     

NMR studies of spin dynamics in cuprates

We report recent NMR results in cuprates. The oxygen Knight shift and the Cu nuclear spin-lattice relaxation rate in Bi_2.1Sr_1.94Ca_0.88Cu_2.07O₈₊ single crystals revealed a gapless superconducting state, which can be most naturally explained by a d-wave pairing state and the intrinsic disorder in this material. The Cu nuclear spin-spin relaxation rate in underdoped YBa₂Cu₃O_6.63 shows distinct temperature dependence from the spin-lattice relaxation rate, providing direct evidence for a pseudo spin-gap near the antiferromagnetic wave vector.     

NMR of 89Y in the Copper-Oxide Spin-Chain Compound Ca2+x Y2−x Cu5O10

We report NMR lineshape, spin-lattice relaxation time T ₁, and spin-spin relaxation time T ₂ data at 17 MHz (8.07 T) for ⁸⁹Y in the copper-oxide spin-chain compound Ca_2+x Y_2–x Cu₅O₁₀. For x=0, a broad, asymmetric line with width 90 kHz is observed for T=250–300 K. The spectra exhibit an appreciable average shift (H/H+0.7%) and sharpen at lower temperature, possibly due to increasing intrachain ferromagnetic correlations. T ₁ and T ₂ decrease with decreasing temperature. The Tl data imply a short correlation-time limit, with _e=3–5×10^–11 s. The T ₂ data apparently include a contribution from dipolar interactions with copper nuclei. Relaxation time data for a doped (x=0.5) compound surprisingly show more rapid relaxation.     

Relaxation times of molecular ions OH− in glasses at very low temperature

This paper presents a detailed study of the temperature dependence of the longitudinal relaxation time T ₁ and of the coherence time T ₂ of a population of ionic molecular impurities in silica glass. Electric dipolar echoes taken in a temperature range 4–22 mK and a frequency of 370 MHz show that T ₁ is governed by a one-phonon process; consequently T ₁ varies like T ^–1; experimental data show that T ₂ also varies like T ^–1 and this in contradiction with predictions which lead to T ^–2. The relaxation of the spontaneous and stimulated echoes shows that there is a wide distribution of relaxation times (T ₁ and T ₂) ; from the amplitude of the signal it is also possible to extract both the longitudinal and the transverse electric moment; the coupling constant of the impurities with the strain is found to be as large as 3 eV.     

Nuclear spin-lattice relaxation in a Kondo superconductor

The nuclear spin-lattice relaxation rate R _s in a Kondo superconductor has been calculated numerically in the framework of the Müller-Hartmann-Zittartz depairing theory. The calculations have been performed in the case of the usual Korringa mechanism for certain concentrations of magnetic impurities and some typical values of T _K/T _c0, where T _K is the Kondo temperature and T _c0 is the superconducting transition temperature in the absence of magnetic impurities. The temperature variation of R _s shows very interesting behavior for values of T _K/T _c0corresponding to the reentrance behavior of superconductivity. Results are compared with the experimental data on the La(Ce)Al₂ system obtained by MacLaughlin, Alloul, and Daugherty. Other possible relaxation mechanisms in the La(Gd, Ce)Al₂ systems are also discussed.     

Nuclear relaxation in the superconducting state of (MDT-TTF)2AuI2

We report the results of our attempt to measure the proton nuclear relaxation rate, 1/T ₁, in the superconducting state of the title material. The relaxation rate in the superconducting state at a field of 1 T was found much longer than that in the normal state, but it became clear that the dominant contribution came from the normal core region. The nuclear relaxation at zero field was examined by using the field cycling technique. An ln(t) term in the relaxation curve was observed at low temperatures, suggesting the contribution of the creeping motion of vortices. We discuss the possibility to determine the intrinsic temperature dependence of 1/T ₁ in the superconducting state.     

Charging Effects on Nuclear Spin Relaxation in Quantum Dots

We study the mechanism of nuclear spin relaxation in quantum dots due to the electron exchange with 2D gas. We show that the nuclear spin relaxation rate T ₁ ^–1 is dramatically affected by the Coulomb blockade (CB) and can be controlled by gate voltage. In the case of strong spin–orbit (SO) coupling the relaxation rate is maximal in the CB valleys whereas for the weak SO coupling the maximum of 1/T ₁ is near the CB peaks. The physical mechanism of nuclear spin relaxation rate at strong SO coupling is identified as Debye–Mandelstam–Leontovich–Pollak–Geballe relaxational mechanism.