Kondo anomaly of impurity spin resonance linewidth

Using the method of Baym and Kadanoff a kinetic equation is derived for the impurity susceptibility in thes-d model. Summing up the most important diagrams the impurity self-energy can be expressed in terms of Suhl'sT-matricest andτ. The contribution of the spin non flip amplitudet to the spin relaxation time is cancelled by a corresponding vertex correction. Thus the final result can be expressed in terms of the spin flip amplitudeτ alone which causes an anomalous temperature dependence of the relaxation time.     

Relaxational model near the Lifshitz point

The critical dynamics of a relaxational model near the Lifshitz point is studied by the ε expansion. The dynamical exponents z are calculated numerically for the uniaxial (m = 1) and biaxial (m = 2) cases.     

Paramagnetische Relaxation von CeCl3·7H2O im Temperaturbereich von 1,1 bis 4,2°K

The paramagnetic relaxation of a single crystal of CeCl₃·7H₂O has been studied by the dispersion-absorption-method at temperatures between 1,1 and 4,2°K. Alternating magnetic fields with frequencies between 5 and 2660 Hz and parallel magnetic fields up to 4000 Oe have been used. The spin lattice relaxation time has been determined as a function of temperature. At two special rangesH ₁ andH ₄ of the magnetic field a second, temperature-independent dispersion-absorption region has been observed besides the temperature-dependent spin-lattice relaxation (double relaxation). At two other special magnetic fieldsH ₂ andH ₃ the anomalous field dependence of the high frequency adiabatic susceptibility suggests a second dispersion-absorption-region ocurring at frequencies, which we cannot attain experimentally. In all cases cross relaxation processes are combined with the spin lattice relaxation.     

Zur Definition von Relaxationszeit und Korrelationszeit in magnetischen Resonanzexperimenten

Kubo's general definition of relaxation and correlation times in magnetic spin systems, applicable to non-exponential processes, is evaluated for several non-exponential relaxation and correlation functions known from nmr experiments. The new definition eliminates the arbitrary factors usually encountered in the time constants of nonexponential irreversible processes. For the correlation time of the well-known “translational two-spin model”, three different values are used in the literature; our definition leads toτ _t =1/5 d²/D (d=distance of closest approach between the two spins,D=diffusion coefficient of the related molecules), which is an intermediate value to the conventional abbreviationsτ _t =1/5d ²/D andτ _t =1/6d ²/D.     

Steady state signal in the limit of weak optical pumping with D1 or D2 line

The simplified rate equations for electronic polarization of alkali atoms in the hyperfine ground states are shown for circularly polarizedD ₁ andD ₂ lines in the limit of weak pumping. The rate equations include effects due to collisional and spin exchange relaxation of atoms in the ground state. Analytical forms of the repopulation pumping terms are shown assuming the standardJ-randomization model for relaxation of alkali atoms in resonant² P _J states and neglecting energy transfer. Analyses of the analytical steady state solutions have been performed to determine the conditions at which the longitudinal electronic orientation of alkali atoms 〈S _z〉 and the orientation of atoms in hyperfine sublevels 〈S _z〉 _f pass through zero.     

Relaxation effects in Mössbauer spectra of bridged seven-coordinate Fe3+ pairs

The compound [Fe₂L(H₂O)₄] (ClO₄)₄.H₂O which contains pairs of Fe³⁺ ions within a binucleating macrocycle derived from Schiff base condensation of 2,6-diacetylpyridine and 1,3-diamino-2-hydroxy-propane has been studied by magnetic susceptibility measurements and⁵⁷Fe Mössbauer spectroscopy between 4.2 K and 300 K, and its crystal structure determined. The spectra show relaxation effects at all temperatures. Spectra taken at 4.2 K in applied fields of about 3 T showed thatV _zz is positive and η～0. The spectra were fitted using a stochastic model of a magnetic hyperfine field relaxing parallel to thez axis, giving relaxation times of 10^?9?10^?10 s.     

On the dynamical coupling between the dipolar and tunneling system of CH3-groups in solids at high temperatures

For methyl groups a dynamical coupling has been predicted between the dipolar and tunnelling systems, also at high temperatures where the observable tunnelling frequency at thermal equilibrium ω_t is zero. This is experimentally confirmed by observed non-exponential dipolar relaxation for ω₀²τ_c² ? 1.     

Pulsed ESR on the organic ion radical salt: 3,3′-diethyl-4,4′-dimethyl-2,2′-thiazolocyanine-[TCNQ]2

We present firstT _1e ^?1 andT _2e ^?1 measurements on the organic ion radical salt 3,3′-diethyl-4,4′-dimethyl-2,2′-thiazolocyanine-(TCNQ)₂ as function of temperature and of orientation. The electronic spin diffusion constant could be determined directly by the electron spin echo field gradient technique:D (300 K)=0.03±0.02 cm²/sec. Pulsed ESR experiments have — in comparison to conventional cw-ESR — the advantage to monitor viaT _1e ^?1 andT _2e ^?1 the spectral density of dynamical processes at different frequencies. This is shown in a general manner on 3,3′-diethyl-4,4′-dimethyl-2,2′-thiazolocyanine-(TCNQ)₂. Between 300 and 60 K,T _1e ^?1 andT _2e ^?1 are close in amplitude and have a similar temperature dependence. At 60 K their degeneracy is lifted, yielding a quantitative value for the effective spin exchange between localized spinsτ _ex ^?1 sec^?1 and via the absolute value of the relaxation an average distance of the localized centers of about 12 Å. The dynamical data as evaluated above cannot be correlated with the conductivity, clearly indicating that the conduction electrons are a minority, not being monitored by the ESR-experiments.     

Dynamics of a dissipative two level system. II

The problem of quantum coherence in a symmetric double well potential with a dimensionless damping coefficient α for classical motion is studied within a spin 1/2-boson model. The experimentally measured probabilityp(t) of refinding a definite initial state after timet is approximately expressed by the transverse spin relaxation function ?(t), which is determined from a three-pole approximation, that incorporates both the correct long and short time behaviour. For a bare tunnelsplitting δ small compared to the heat bath cutoffω _c we find, that the oscillating component of ?(t) is negligible compared to the relaxational one unless α is of orderΔ/ω _c . Thusp(t)?(1+exp(?νt))/2 with a mean tunneling rateν proportional to \(\tilde \Delta = \Delta (\Delta /\omega _c )^{\frac{\alpha }{{2 - \alpha }}} \) for α < 2 andT ? \(\tilde \Delta \) and proportional toΔ ²/ω _c ·(T/ω _c ) ^α?1 otherwise. The results apply directly to recent measurements of the dynamics of flux states in a SQUID.     

On the paramagnetic resonance and the longitudinal relaxation of ferromagnets in the critical region above Tc

Uniform dynamical susceptibility of cubic ferromagnets above T_c in magnetic field is investigated. Resonance frequences and damping constants are determined in the limiting cases of low and strong magnetic field. It is shown that in the exchange temperature region when 4πχ ? 1 owing to spin diffusion the uniform susceptibility is depended non-trivially on the frequency and the magnetic field. From this dependence the temperature behaviour of spin diffusion coefficient can be determined.     

Time resolved ADMR applied to the triplet state of the primary donor of bacterial photosynthetic reaction centers

The population and depopulation kinetics of the triplet sublevels of reaction centers ofRhodobacter (Rb.) sphaeroides strains R26 and GA were determined at 9 K by time resolved absorption detected magnetic resonance (ADMR) using the RF pulse method. The comparison of the saturation and pulse methods of time resolved ADMR proofs the latter to be superior. The kinetic behavior of the 2|E| signal was investigated for the first time. It exhibits an unexpected slow decaying component with a rate comparable to thez-level decay. Using a simple kinetic 4-level model for the triplet dynamics we conclude that this slow component as well as the sign of the ADMR signal of the 2|E| transition can be explained by a selective spin lattice relaxation channel connecting the triplet sublevelsx andz.     

Anomalous pulse-angle and phase dependence of Hahn’s electron spin echo and multiple-quantum echoes of the spin correlated radical pair P700+A 1 − in photosystem I

In a spin-correlated radical pair system, anomalous pulse-angle and phase dependence of electron spin echo and multiple-quantum echoes were theoretically calculated by Tanget al. (J. Chem. Phys.106, 7471 (1997)). The maximum intensity of the out of phase signal at 45 degree of spin rotation angle was experimentally verified in two-pulse echoes of the light-induced P700⁺A ₁ ^? radical pair in Photosystem I. The values,D = 1.64 G andJ = 0.00 G, fit well with the experimental ESEEM spectra. Single and double quantum echoes were observed at the value oft = τ andT = 2τ with the laser flash-t-P1_70,ζ1-τ-P2_{140, ζ2}-T pulse sequence, which led to determination of the relaxation time T₂₃ between the singlet and triplet ¦T₀〉 states. The relaxation times of the zero and single quantum transitions were determinedT ₂₃ ≈ 100 ns andT ₂ = 1000 ns, respectively. The field sweep ESE signal shape can be fitted with the hyperfine inhomogeneities of 7 G for P700⁺ and of 10 G for A ₁ ^? .     

Relaxation modes in glassy polymers: A temporal analysis by the simplex method of isothermal depolarisation current measurements

Molecular dynamics associated to relaxation phenomena in the glass transition temperature domain is often investigated by means of thermostimulated depolarisation current TSDC technique. It is a very sensitive method and the data are traditionally obtained according to two protocols leading to the well known complex spectra and elementary spectra. The aim of this work is to use a new TSDC protocol which analyses the relaxation current kinetics obtained after submitting the sample to an electrical field pulse at a constant temperature. A new temporal analysis of the return equilibrium isothermal transient current I(T) is proposed. The signal fitting is obtained by a simplex optimisation method. The entire signal recorded for all the temperatures can be fitted with a sum of two exponentials allowing the definition of two different relaxation times called τ₁ and τ₂. This new protocol has been used to analyse the glass transition domain of amorphous PET.     

Spectral distribution of relaxation times in spin glasses

Recent neutron scattering measurements on spin glasses show that the dynamics of the spin systems can be best described in terms of wide spectral distribution of relaxation times evolving continuously with decreasing temperature but which is devoid of any critical behaviour, either speeding up or slowing down, at any finite temperature including the spin glass “freezing temperature T_sg”. It is argued that the latter temperature itself is dependent on the time constant of measurement for all spin glasses in general; the observed variation with frequency being less pronounced in some systems than others owing to some special characteristics of their spin dynamics such as, for example, the presence of parallel channels of rapid relaxation provided by the Korringa coupling in metallic spin glasses. The neutron scattering measurements presented here enable us to propose plausible forms for the density of relaxation times of the spin system and to show that the logarithmic frequency dependence of the freezing temperature observed in low frequency ac susceptibility measurements follows naturally from a uniform density of relaxation times at these frequencies.     

Manifestation of liquid-state and solid-state properties in electron relaxation of paramagnetic ions in solutions: Non-Markovian processes

The linewidth δH and the spin-spin relaxation time T ₂ for Gd³⁺, Mn²⁺, and Cr³⁺ ions in aqueous, water-glycerol, and water-poly(ethylene glycol) solutions at paramagnetic ion concentrations providing the dipole-dipole mechanism of spin relaxation are measured using two independent methods, namely, electron paramagnetic resonance (EPR) and nonresonance paramagnetic absorption in parallel fields. Analysis of the experimental results indicates a gradual crossover from pure liquid-state (diffusion) to quasi-solid-state (rigid lattice) spin relaxation. It is demonstrated that the limiting cases are adequately described by standard, universally accepted formulas for dipole-dipole interactions in the liquid-state (the correlation time of translational motion satisfies the condition τ _c ?τ₂) and solid-state (τ _c ?τ₂) approximations. A complete theoretical treatment of the experimental dependences (including the observed gradual crossover of spin relaxation) is performed in the framework of the non-Markovian theory of spin relaxation in disordered media, which is proposed by one of the authors. Within this approach, the collective memory effects for spin and molecular (lattice) variables are taken into account using the first-order and second-order memory functions for spin-spin and spin-lattice interactions. A correlation between the spin magnitude and the temperature-viscosity conditions corresponding to the crossover to non-Markovian relaxation is revealed, and the situations in which structural transformations occurring in the solutions favor the crossover to solid-state spin relaxation are analyzed.     

Magnetic properties of high-T c superconductors from NQR and NMR measurements

NMR and NQR spectra and spin-lattice relaxation measurements carried out in LASCO and YBCO-type crystals are presented and analyzed in order to derive insights on the correlations and spin-dynamics of the Cu²⁺ ions and on the microscopic mechanisms of high-T _c superconductivity. As an illustrative example on how the magnetic correlation length and spin dynamics properties can be extracted from the relaxation rateW, the³⁵Cl NMR data in the two-dimensional Heisenberg system Sr₂CuCl₂O₂, around the paramagnetic-antiferromagnetic (PA-AF) transition are first considered. Then the¹³⁹La NQR relaxation measurements in La_2?xSr_xCuO₄ are briefly reviewed and it is shown how a simple picture of localized Cu²⁺ magnetic moments, whose spin fluctuation times are controlled by the charge defects induced by the doping, leads in a direct way to quantitative estimates for the progressive shift, on cooling, of the spectral density of the low-frequency spin excitations towards the high frequency range. This phenomenon can be described in terms of effective spin at the Cu²⁺ ions, and its similarities with the analogous effect of progressive delocalization in Heavy Fermions systems are pointed out. Thus, the superconducting transition appears to occur in an unconventional Fermi liquid with AF correlations among itinerant pseudoparticles, possibly involving a mechanism not directly related to the magnetic correlated dynamics. In fact, a universal behavior of the relaxation rates as a function of temperature is observed, regardless of the transition temperatureT _c. The independence ofT _c from the low frequency static and dynamical spin properties is also indicated by⁸⁹Y Knight shifts and from⁶³Cu relaxation rates in systems like YBa₂Cu₄O₈ (Y124), whereT _c can be changed by atomic substitutions and by controlling the oxygen stoichiometry. The effect of an external magnetic field on the correlated spin dynamics of the AF Fermi liquid is investigated and from a comparison of Cu NQR relaxation and NMR relaxation in oriented powder of YBCO and LASCO it is shown that the external field has the small but unambiguous effect of depressing the relaxation rates aboveT _c, besides strongly enhancing them in the superconducting phase. A maximum in the ratio \({{W\left( {NQR} \right)} \mathord{\left/ {\vphantom {{W\left( {NQR} \right)} {W\left( {\vec H\left\| {\vec c} \right.} \right)}}} \right. \kern-0em} {W\left( {\vec H\left\| {\vec c} \right.} \right)}}\) is thus observed around 80 K, either in LASCO or in YBCO, again indicating that the transition could be driven by a mechanism not directly involving the spin dynamic properties. To study the role of the fluxions belowT _c ⁸⁹Y NMR shifts and spectra in oriented powders of YBCO are analyzed. Information on the spin susceptibility and on the structure of the vortex lattice is obtained. In addition, from the temperature behavior of the linewidth a motional narrowing related to flux melting is evidenced. The effective correlation time for the vortex motion is derived and it is discussed why μ⁺SR cannot detect it in view of the different rigid-lattice line broadening.     

Dynamical susceptibility of the ising model in a transverse magnetic field

An approximate expression is obtained for the dynamical susceptibility, χ_zz(q, ω), of the spin one half, simple cubic Ising model in a transverse magnetic field, which is appropriate to the disordered state (〈S_z〉 = 0). The susceptibility along the direction of the field is shown to contain a thermal part with a relative weight proportional to the difference between the isothermal and adiabatic susceptibilities and a width determined by the thermal diffusion constant.     

Magnetic properties and peculiarity of magnetic states in dilute antiferromagnets Mn1−x Zn x F2

The dependence of magnetic moment and susceptibility on temperature, magnetic field and frequency of some single crystals Mn_1?x Zn _x F₂ (x≈x _e=0.75—percolation limit) were experimentally investigated. Our experiments show that (Bazhan and Petrov 1984; Cowleyet al 1984; Villain 1984) in these crystals the nonequilibrium magnetic state of spinglass type with finite correlation length appears as temperature decreasesT<T in weak magnetic fields. This state is determined by fluctuation magnetic moments √nμ (wheren is the number of magnetic ions, corresponding to finite correlation length andμ the magnetic moment Mn⁺¹). In the experiments in low magnetic fields and frequencies there are no peculiarities in the magnetic susceptibility temperature dependence atT≠T _f. At temperaturesT>T _f andT<T _f magnetic susceptibility is determined by 1 $$\chi \left( {T > T_f } \right) = \frac{{N\left\langle \mu \right\rangle ^2 }}{{3k\left( {T + \theta } \right)}} = \frac{N}{n}\frac{{\left\langle {\sqrt n \mu } \right\rangle ^2 }}{{3k\left( {T + \theta } \right)}} = \chi \left( {T< T_f } \right)$$ . In strong magnetic fields and large frequencies there are peculiarities in thex(T) dependence atT=T _f. AtT<T _f and strong magnetic fieldsX(T)=x ₀ andT<T _f and at large frequenciesx(T)=x ₀+α/T. The dependences of magnetic susceptibility on the frequency are determined by the magnetic system relaxation. Calculations and comparison with experiments show that the relaxation of the investigated magnetic systems atT<T _f follows the relaxation lawM(t)=M(0) exp[?(t/τ) ^r ], suggested in Palmeret al (1984) for spin-glasses relaxation taking into account the time relaxation distributionτ ₀....τ _max in the system and its ‘hierarchically’ dynamics.     

Estimation of water content and water mobility in the nucleus and cytoplasm of Xenopus laevis oocytes by NMR microscopy

NMR microscopy is a noninvasive approach for studying cell structure and properties. Spatially resolved measurement of the relaxation times T₁ and T₂ provided information on the water proton spin density and water mobility in different parts of Xenopus laevis oocytes. The spin-lattice relaxation time T₁ was determined using a saturation-recovery sequence and the common spin-echo sequence with increasing repetition times, while the transverse relaxation time T₂ was measured by means of the spin-echo sequence with varying echo times. From the relaxation times, the mole fractions of possible reorientational correlation times τ_c for different types of intracellular water were calculated according to a simple two-phase model. The values for T₁, T₂, and proton spin density (i.e., water content) are: nucleus ⪢ animal cytoplasm > vegetal cytoplasm. Based on the estimation of τ_c, nearly 90% of the nuclear water and 74.4% of the water of the animal pole was considered as free mobile water, whereas 55.5% of the water of the vegetal pole appeared as bound water.     

Phenomenology of local scale invariance: from conformal invariance to dynamical scaling

Statistical systems displaying a strongly anisotropic or dynamical scaling behaviour are characterized by an anisotropy exponent θ or a dynamical exponent z. For a given value of θ (or z), we construct local scale transformations, which can be viewed as scale transformations with a space–time-dependent dilatation factor. Two distinct types of local scale transformations are found. The first type may describe strongly anisotropic scaling of static systems with a given value of θ, whereas the second type may describe dynamical scaling with a dynamical exponent z. Local scale transformations act as a dynamical symmetry group of certain non-local free-field theories. Known special cases of local scale invariance are conformal invariance for θ=1 and Schrödinger invariance for θ=2.The hypothesis of local scale invariance implies that two-point functions of quasiprimary operators satisfy certain linear fractional differential equations, which are constructed from commuting fractional derivatives. The explicit solution of these yields exact expressions for two-point correlators at equilibrium and for two-point response functions out of equilibrium. A particularly simple and general form is found for the two-time autoresponse function. These predictions are explicitly confirmed at the uniaxial Lifshitz points in the ANNNI and ANNNS models and in the aging behaviour of simple ferromagnets such as the kinetic Glauber–Ising model and the kinetic spherical model with a non-conserved order parameter undergoing either phase-ordering kinetics or non-equilibrium critical dynamics.