Nuclear spin relaxation in strongly disordered superconductors

The influence of nonmagnetic impurity and spin-orbit scattering on the nuclear spin-lattice relaxation rate in strongly disordered superconductors is presented. Using Anderson's exact-eigenstate formalism, it is shown that there exist two effects of disorder onT ₁ ^–1 . Firstly, nonmagnetic impurity and spin-orbit scattering enhances the magnitude of the relaxation rate in the same manner as in the normal dirty metal due to the diffusive nature of quasiparticle motion. Secondly, the Hebel-Slichter peak becomes suppressed due to the disorder enhancement of the quasiparticle inelastic scattering rate due to phonon, Coulomb, and/or spin-fluctuation interactions. Comparison with the available experimental data is made.     

Low-energy electronic spin excitations between filling factors ν=1 and studied by optically detected nuclear magnetic resonance

We report measurements of the spin relaxation time (T_1n) for nuclei in the potential well confining a high-mobility two-dimensional electron system at a single GaAs–GaAlAs heterojunction. At low temperatures nuclear spin relaxation is dominated by electron–nuclear spin scattering: we find that T_1n displays sharp maxima at incompressible states throughout the hierarchy of the fractional quantum Hall effect. This behaviour is consistent with the existence of low-energy spin excitations only where the electron system is compressible. Our measurements also provide evidence for a gap in the spin excitation spectrum at .     

Hebel-Slichter peak and superconducting energy gap in Rb3C60 observed by muon spin relaxation

Muon spin relaxation has been observed in both the normal and superconducting states of Rb₃C₆₀ (T _c=29.3K). The field dependence of theT ₁ spin relaxation rate is due to muonium undergoing spin-exchange scattering with conduction electrons, making this the first observation of muonium in a metal. The temperature dependence ofT ₁ ^–1 shows a Hebel-Slichter coherence peak just belowT _c which is not seen in¹³C spin relaxation. The peak can be fit assuming spin relaxation due to interaction with the quasiparticle excitations of a BCS superconductor provided the density of states is broadened relative to that of BCS. Such fits yield a value for the zero temperature energy gap, ₀/k _B , of 53(4)K, consistent with weak-coupling BCS.     

Effect of boundaries and impurities on electron–phonon dephasing

Electron scattering from boundaries and impurities destroys the single-particle picture of the electron–phonon interaction. We show that quantum interference between ‘pure‘ electron–phonon and electron–boundary/impurity scattering may result in the reduction as well as to the significant enlargement of the electron dephasing rate. This effect crucially depends on the extent, to which electron scatterers, such as boundaries and impurities, are dragged by phonons. Static and vibrating scatterers are described by two dimensionless parametersq_Tl and q_TL, where q is the wavevector of the thermal phonon, l is the total electron mean-free path, L is the mean-free path due to scattering from static scatterers. According to the Pippard ineffectiveness condition , without static scatterers the dephasing rate at low temperatures is slower by the factor 1 / ql than the rate in a pure bulk material. However, in the presence of static potential the dephasing rate turns out to be 1 / qL times faster. Thus, at low temperatures electron dephasing and energy relaxation may be controlled by electron boundary/impurity scattering in a wide range.     

Calculation of host nuclear relaxation in dilute Kondo alloys for T ⪡ Tk

We present a microscopic calculation of the host nuclear spin-lattice relaxation rate as a function of impurity-host distance r for dilute Kondo alloy at T ? T_k. The net relaxation rate involves two main parts. One, dependent up-on the local conduction electron density of states, exhibits kinematic oscillations which are due to resonant scattering. The other part, due to the impurity spin fluctuations, is shown to dominate the first mechanism allowing the Korringa relation to hold in systems with low T_k (such as Cu:Fe). In A?:Mn both mechanisms are of equal importance, and the net host relaxation rate and the excess Knight shift do not satisfy a Korringa relation.     

The spin exchange interaction effect on Tc equation of anisotropic impure superconductors

We study the influence of spin exchange interaction of impurity scattering on critical temperature of anisotropic impure superconductors. The model of random non-magnetic and magnetic impurity are revised to cover the effect of spin exchange interaction. The sign of magnitude of the second-order Born scattering has been changed after consideration of the spin exchange interaction that also effects the form of T_c equation. We can get the general T_c equation that can be described well by anisotropic impure superconductors and covers all models done before.     

Relaxation times and line widths of isotopically-substituted nitroxides in aqueous solution at X-band

Optimization of nitroxides as probes for EPR imaging requires detailed understanding of spectral properties. Spin lattice relaxation times, spin packet line widths, nuclear hyperfine splitting, and overall lineshapes were characterized for six low molecular weight nitroxides in dilute deoxygenated aqueous solution at X-band. The nitroxides included 6-member, unsaturated 5-member, or saturated 5-member rings, most of which were isotopically labeled. The spectra are near the fast tumbling limit with T₁∼T₂ in the range of 0.50–1.1 μs at ambient temperature. Both spin–lattice relaxation T₁ and spin–spin relaxation T₂ are longer for ¹⁵N- than for ¹⁴N-nitroxides. The dominant contributions to T₁ are modulation of nitrogen hyperfine anisotropy and spin rotation. Dependence of T₁ on nitrogen nuclear spin state m_I was observed for both ¹⁴N and ¹⁵N. Unresolved hydrogen/deuterium hyperfine couplings dominate overall line widths. Lineshapes were simulated by including all nuclear hyperfine couplings and spin packet line widths that agreed with values obtained by electron spin echo. Line widths and relaxation times are predicted to be about the same at 250 MHz as at X-band.     

Giant heat capacity and nuclear-spin diffusion in GaAs/AlGaAs heterostructures near ν=1

We report low temperature (T) heat capacity (C) data on a multiple-quantum-well GaAs/AlGaAs sample in the quantum-Hall regime. Relative to its low field magnitude, C exhibits up to ≈10⁵-fold enhancement near Landau level filling v=1 where skyrmions are the expected ground state of the confined two-dimensional electrons. We attribute this striking behavior to a skyrmion-induced enhancement of the coupling between the nuclear spin system and the lattice. The data are consistent with the Schottky nuclear heat capacity of Ga and As atoms in the quantum wells, except at very low T where C vs. T exhibits a remarkably sharp peak suggestive of a phase transition in the electronic system. Our quasi-adiabatic experiments provide quantitative evidence that the sharp peak in C vs. T is due to an enhanced nuclear-spin diffusion from the GaAs quantum wells into the AlGaAs barriers. We discuss the physical origin of this enhancement in terms of the possible Skyrme solid–liquid phase transition.     

The NSW interaction with nuclear local modes in antiferromagnets

The nuclear spin wave (NSW) relaxation rates due to the interaction with nuclear impurity local modes (NILM) in antiferromagnets are considered in the framework of the Keldysh formalism based on the spin operator diagram technique. It is shown that the NSW relaxation frequency due to the scattering on the fluctuations of impurity nuclear spins is of resonance character. The NSW damping due to the resonance absorption by NILM depends strongly on the NSW amplitude N, which accounts for the “hard” excitation of NSW's in parallel pumping experiments /6/. The NSW relaxation rates due to the processes involving two NSW's and one impurity nuclear excitation are also calculated.     

Negative resistivity anomaly of unstable 4f impurities in metals

The minimum of the resistivity of dilute alloys with unstable Ce and Pr impurities is usually attributed to an abnormal increase of the spin scattering cross section of the inner 4f electron at low temperatures (4f Kondo effect). By comparison with the resistivity increments of stable rare earth impurities, we show that nearT=0 the anomalous increment is in fact consistent with simple potential scattering from the outer 5d6s valence electrons of fractional valent impurities. The observed decrease of the increment at elevated temperatures is too large to be due to 4f spin scattering in the unitarity limit or to a valence change. This decrease therefore implies some kind of shunting of the impurity potential scattering by an unknown mechanism connected with the valence instability of the impurity.     

Relaxation of the shallow acceptor center in germanium

Polarized negative muons were used to study relaxation mechanisms of shallow acceptors in germanium. In p-type germanium at low temperatures relaxation of the muon spin was observed, indicating that the muonic atom (gallium-like acceptor center) formed via capture of the negative muon by a host atom is in the paramagnetic state and its magnetic moment is relaxing. The relaxation rate of the muon spin was found to depend on temperature and on concentration of gallium impurity. We conclude that to the relaxation of the magnetic moment of the Ga acceptor in Ge there contribute both scattering of phonons and quadrupole interaction between the acceptors. We estimate, for the first time, the hyperfine interaction constant for the gallium acceptor in germanium as 0.11 MHz.     

Spin fluctuations and high temperature superconductivity

Theory of spin fluctuations for itinerant magnetism and its application to high temperature superconductivity are reviewed. After a brief introduction to the whole subject the developments of the self-consistent renormalization theory of spin fluctuations are summarized with particular emphasis on critical properties at the quantum phase transitions. Most of the anomalous properties in the normal state of high-T_c cuprates are understood as due to the critical behaviours for the two dimensional antiferromagnetic metals. By analysing the nuclear magnetic relaxation rate and the T-linear term of resistivity, the set of parameters to specify the spin fluctuations are determined. It is shown that by using the parameters thus obtained one can describe other quantities as well, e.g. optical conductivity. Then we proceed to the theory of superconductivity by the spin fluctuation mechanism. After some discussion on the weak coupling treatments, the strong coupling theory is reviewed. It is shown that the set of parameters determined by the normal state properties of the high-T _c cuprates just give a transition temperature of the right order of magnitude. Among the parameters, the most sensitive one for T _c is the frequency spread of the spin fluctuations. This fact enables us to present a possible unified picture of the antiferromagnetic spin fluctuation-induced superconductors, including heavy fermion superconductors and organic superconductors. This point of view may be confirmed to a certain extent by microscopic calculations based on the fluctuation exchange approximation for the two-dimensional Hubbard models representing not only the cuprates but also organic and trellis lattice compounds. The review is concluded with some discussions on future problems, e.g. the pseudo spin-gap in the under-doped region.     

Nuclear spin lattice relaxation of191mIr in Fe

Thermal cycling of the lattice temperature was used to determine the nuclear spin lattice relaxation of^191m IrFe in polarizing fields of 0.05 to 1.3 T. At low temperatures, the relaxation time is not very much shorter than the lifetime of^191m Ir. In the first part of the paper, the master equation formalism is extended to include a finite lifetime. Our result for the reduced relaxation constant, ² C _K =(1.48±0.11)·10¹⁴ K s^–1 T^–2 (high field limit) is in serious disagreement with that of a spin echo measurement of¹⁹³IrFe, but fits much better into the general systematics. A comparison of relaxation rates for 3d-, 4d-, and 5d-impurities in Fe is given. As a by-product, a Kapitza conductivity constant ofl _K =1.5 mW cm^–2 K^–4±30% was found between Fe and dilute³He/⁴He.     

Indirect magnetic exchange interaction mediated by bound Landau states in 2DES

The possibility of indirect exchange coupling mediated by Landau electrons bound to magnetic impurities in 2DES is studied here. The importance of the resonance scattering of the Landau electrons with the impurities is emphasized due to its spin selectivity which results in strong spin polarization of the localized Landau states. The bound Landau states act as mediators of the superexchange interaction resulting in an antiferromagnetic interaction between the nuclear spins of the impurities. The coupling constant, between these nuclear spins, J, is presented for the case of a weak scattering limit and found to depend strongly on the ratio of the impurity separation over the magnetic length. Possible applications of these results may include a long-range mechanism for coupling between two nuclear spins to be used as a qubits interaction with a spacing distance of the order of the magnetic length.     

Nuclear-spin-lattice relaxation in a bilayer quantum Hall system

We examined the electron spin degree of freedom around the total Landau-level filling factor ν=1 in a bilayer system via nuclear spins. In a balanced bilayer system, nuclear-spin-lattice relaxation rate 1/T₁, which probes low-energy electron spin fluctuations, increases gradually as the system is driven from the quantum Hall (QH) state through a phase transition to the compressible state. This result demonstrates that the electron spin degree of freedom is not frozen either in the QH or compressible states. Furthermore, as the density difference between the two layers is increased from balanced bilayer to monolayer configurations, 1/T₁ around ν=1 shows a rapid yet smooth increase. This suggests that pseudospin textures around the bilayer ν=1 system evolves continuously into the spin texture for the monolayer system.     

Kondo effect in spin glasses: Electrical resistivity

We investigate the influence of the Kondo effect on the electrical resistivity of spin glasses. Our approximation reduces in the limit of vanishing impurity concentrations to the Suhl-Nagaoka theory for the Kondo effect. The magnetic impurity interactions are taken into account in the form of time dependent two-spin correlation functions which can be measured by neutron scattering. The dynamics of the impurity spins leads to a partial destruction of the Kondo effect. For the resistivity this can be described by a temperature dependent effective spinS _eff ² (T) withS _eff ² 0 forT0 andS _eff ² S(S+1) forT, and by a reduction of the Kondo temperatureT _K. Sufficiently strong interactions lead toT _K=0. We obtain a resistivity maximum at a temperatureT _m due to the interplay of the Kondo effect and the spin dynamics;T _m depends onT _K and on the excitation spectrum, and therefore on parameters such as impurity concentration or pressure. The ratioT _m/T_f (T _f is the freezing temperature) is calculated for a single relaxation time and for a square density of relaxation modes and is compared with experimental data forAuCr,AuMn,AgMn, andCuMn. The influence of other possible modes on various spin glass properties is discussed.SFB 125 Aachen-Jülich-Köln     

Nuclear magnetic resonance in icosahedral Al-Pd-Mn alloys

²⁷Al and⁵⁵Mn nuclear magnetic resonance shift,K, and²⁷Al spin lattice relaxation time,T ₁, have been measured for the six-dimensional face-centered icosahedral quasicrystals, Al_75-x Pd₁₅Mn_10+x withx=0, 2 and7. The Al₇₅Pd₁₅Mn₁₀ quasicrystal exhibits a temperature independent Knight shiftK and(T ₁ T)^–1=0.022±0.002 (K s)^–1 in a temperature range from room temperature to 5 K because there exist no Mn atoms with local magnetic moment. The replacement of Al with Mn drastically decreases the²⁷AlK, the⁵⁵MnK andT ₁ of²⁷Al, andthe²⁷AlK becomes negative. There is an additional contribution to the spin lattice relaxation time independent of temperature. This is considered to be due to the presence of a localized magnetic moment in the replaced Mn atoms.     

Hyperfine coupling of12B in noble metals and Al; enhancement of the conduction-electron spin susceptibility by e-e exchange

We have remeasured the Korringa contributionT _1e to the nuclear spin lattice relaxation time of the interstitial¹²B in nobel metals and in Al. TheT _1e T times the squared Knight shiftK of¹²B taken from the literature, that is the Korringa product of¹²B, shows that the conduction-electron spin susceptibility is exchange enhanced similarly to that sensed by the matrix nucleus. The enhancement factors are equal within the experimental errors for both interstitial and matrix positions in Cu and Ag. The enhancement factors at the boron and at the matrix position are different in Au and Al.     

Muon spin relaxation measurements in kagomé lattice system SrCr8Ga4O19

Dynamical spin fluctuations in SrCr_8–xGa_4+xO₁₉ a frustrated spin system on a kagomé lattice, is examined by the longitudinal field muon spin relaxation technique. This system shows a spin-glass (SG)-like cusp in the susceptibility atT _g=3.5(2) K. The slowing down of Cr spin fluctuations is found to occur over a very wide temperature rangeT _g<T<30T _g. AsT/T _g 0 these fluctuations remain without static polarization (order parameter). Such strong fluctuations belowT _g have not been observed before in a conventional SG system.