2H nuclear magnetic resonance study of deuterated water dynamics in perfluorosulfonic acid ionomer Nafion

We have employed deuteron nuclear magnetic resonance (NMR) spectroscopy in order to study the dynamics of the deuterated water (D₂O) molecules introduced into a perfluorosulfonic acid ionomer Nafion (NR-211) film. According to the ²H NMR spectral analysis, the deuterated water molecules at low temperatures occupied either relatively rigid or mobile sites up to the temperature T_M=240 K where all the deuterated water molecules became mobile. The temperature-dependent NMR linewidths sensitively reflected the motional narrowing of the rigid and mobile sites, and the NMR chemical shift reflected significant changes in the hydrogen bonds of the deuterated water. While a slow- to fast-limit motional transition was manifested at T_M in the laboratory-frame NMR spin–lattice relaxation, the rotating-frame spin–lattice relaxation indicated no bulk liquid water state down to 200 K.     

Photoexcited Eu2+ spin dynamics in EuFe2As2

Employing temperature dependent time-resolved optical femtosecond spectroscopy, we investigated the quasiparticle and Eu²⁺ spin relaxation dynamics in EuFe₂As₂ (EFA). As previously reported in other undoped iron-based pnictides, we observe the quasiparticle relaxation bottleneck due to the charge gap opening in the spin density wave (SDW) state below T _SDW = 189 K. Below the Eu²⁺ antiferromagnetic (AFM) spin ordering temperature, T _AFM = 19 K, we observe another slower relaxation component, which we attribute to the Eu²⁺ AFM order dynamics. The slow dynamics of this component suggests a weak coupling between the Eu²⁺ spins and the carriers in the Fe-d derived bands.     

Study of the two-domain processing structure in the superfluid3He-B

The systematic experimental and theoretical investigation of the longlived induction signal, known to exist in the³He-B, has shown that even very small nonuniformity of a steady magnetic fieldH ₀ changes qualitatively the precession pattern arising in the pulsed NMR experiments after tipping of the magnetization. The spin supercurrents redistribute magnetization within the experimental cell to produce the precessing structure, consisting of two domains. In one-domain, situated in the higher field region, magnetizationM has its equilibrium value and is parallel toH ₀. In the other domain the angle betweenM andH ₀ is slightly larger than? ₀=arc cos (?1/4). The structure precesses with frequency, equal to the Larmor frequency at the site of the wall, separating the domains. The relaxation of this structure goes via the growth of the equilibrium domain at the expense of the precessing domain; therefore in the course of the relaxation the frequency of the precession has to decrease with time. The calculated rate decrease agrees with the observed value. Experiments were carried out directly demonstrating the existence of the two-domain structure. After the formation of the two-domain structure, as well as after a perturbation of the structure by short r.f. pulses, low frequency (≈200 Hz) modulation of the induction signal is observed due to vibration of the structure. These vibrations are the standing spin waves in the precessing domain, their frequency being proportional to the size of the domain. The observed dependence of the frequency on other parameters is in agreement with theoretical calculations. The analysis of the data on the vibration and relaxation of the two-domain structure enables us to find the spin wave velocity and the spin diffusion coefficient in³He-B. Further investigation of the two-domain structure enables the study of spin supercurrents in³He-B.     

Probing the tilting mode in fission with γ-ray multiplicity techniques

The γ-ray multiplicities of the fragments from a number of ⁴He-induced fission reactions have been measured as a function of fragment emission angle. The value of M_γ is found to vary with angle in qualitative agreement with the predictions of statistical models of fission-fragment angular distributions. The observed variation is rather weak, on the order of 5%. The data are compared with several models. Calculations assuming a rigidly rotating, transition-state nucleus predict a much stronger angular dependence of the fragment spin than indicated by the data. The agreement is significantly improved if a fragment-spin enhancement effect is included in these calculations. The fragment spins are explored within the framework of the statistical scission model and the collective mode model. Both of these models predict large fragment spins and thus a relatively weak angular dependence of the total fragment spin. Neither model provides a completely satisfactory explanation of the data. Depending on the assumptions made in the calculations, the models either predict too strong an angular dependence of the total fragment spin or spins which seem incompatible with M_γ.     

Electron spin relaxation of copper(II) ions in diamagnetic crystals

The electron spin-lattice and spin-spin phase relaxation measurements of Cu²⁺ ions in various crystals are reviewed and discussed. Examples of the Debye temperature determination from a wide temperature range measurements of the spin-lattice relaxation time T₁ are shown. An influence of the Jahn-Teller dynamics on T₁ is presented. The phase relaxation described by the phase memory time T_M is affected by temperature due to the spin packet width modulation by molecular motions. The T_M is anisotropic in crystals and can be different for different hyperfine lines of an EPR spectrum.     

Spin dynamic in mixed antiferromagnet with competing anisotropies Fe0.6Co0.4TiO3 probed by positive muons

The positive muon spin relaxation method is applied to probe the spin dynamics in the random mixture of two antiferromagnets with competing anisotropies Fe_0.6Co_0.4TiO₃. In the S_∥-ordered phase between the paramagnetic phase and the oblique antiferromagnetic phase, the characteristic relaxation is observed, revealing that the spin component S_⊥ which has not a long-range order is dynamically fluctuating. The correlation time of this fluctuated spin component is estimated to be 10⁻⁷∼10⁻⁵s.     

Spin dynamics investigated by EPR in the paramagnetic regime of La2/3Ca1/3Mn1−x Me x O3 (Me = Al, In) manganites

We report an electron paramagnetic resonance (EPR) investigation of the spin dynamics in the paramagnetic regime of the colossal magnetoresistive manganites La_2/3Ca_1/3Mn_1?x Me _x O₃ (Me=Al, In;x≤0.05). The temperature dependences of the EPR linewidth and integral intensity have been analyzed in terms of the bottleneck spin relaxation and small-polaron hopping models. The exchange coupling integral between Mn³⁺ and Mn⁴⁺ ions and the polaron activation energy decrease with increasing doping level. A discussion is given concerning the factors which could explain the observed changes.     

Exotic decays of the muon and heavy leptons in gauge theories

We have studied the decay ?₁ → ?₂ + γ for arbitrary like charged spin $\text{1}\text{2}$ leptons in a manner which is applicable to a large class of models. Our computations assume that this process is induced by one loop diagrams. When the leading effect is cancelled by a leptonic G.I.M. mechanism, we find an extremely large enhancement of O(M_W⁴/M_L⁴) in Λ(μ^?→e^?+e⁺e^?)/Λ(μ^?→e^?+γ) if the intermediate lepton is charged.     

Determination of the nonlinear relaxation exponent: A Monte Carlo study

The nonlinear relaxation exponent Δ_M^nl for the order parameter is obtained through a standard Monte Carlo study of the two-dimensional Ising model. We find that Δ_M^nl is about 2.1 as predicted by renormalization group results but larger than some earlier Monte Carlo estimates. For the linear relaxation exponent Δ_M¹ our data suggest a slightly higher value as expected by scaling laws.     

Magnetic properties of Sm-based bulk metallic glasses

We perform detailed investigation on the magnetization and specific heat of Sm-based ternary bulk metallic glasses with different Co contents at low temperature. A low temperature cluster spin-glass phase below T_f ∼25 K is evidenced for all samples. This cluster spin-glass behavior is ascribed to competition among the multi-fold magnetic interactions and the intrinsic structural inhomogeneity. The magnetic relaxation behavior of the spin-glass phase can be well described using the stretched exponential dynamics. The magnetic hysteresis under field-cooling condition and spin dynamics further demonstrate the low temperature cluster spin-glass behavior. It is revealed that the Co atoms play an important role in modulating the physical properties of the present Sm-based ternary metallic glasses.     

Measuring of mass and spin of dark matter particles at ILC

In many models stability of dark matter particles D (with mass M _D ) is ensured by a new conserved quantum number which we call the D-parity. We consider models which also contain charged D-odd particle D ^± (with mass M _±). We study the process e ⁺ e ^? ?? D ⁺ D ^? followed by decay of D ^± to D and gauge bosons W (either on-shell or off-shell). Measuring the end points of the energy distribution of W??s would determine M _D and M ^±. However, the hadron mode of W decay would lead to low precision in this measurement. while the information from the lepton mode looks incomplete. I show that it is sufficient to measure the energy distribution of a single lepton (for definiteness ??) in the process e ⁺ e ^? ?? ?? + 2jets + large missing E _T . The well identified singularities in this distribution allow for determination of M _D and M _± with a high precision. After that, measuring the corresponding cross section will allow one to determine the spin of D particles.     

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.     

N.M.R. solid echoes in systems of dipolar-coupled inequivalent spins-1 or dipolar-coupled inequivalent pairs of spins-1/2

Proton solid-echo transverse relaxation functions for many thermotropic and lyotropic mesophases, mapped by measurement of the echo amplitude S_yx (t′ = τ) as a function of τ using a P_y (90°)-τ-P_x (90°)-t′ sequence, yield gaussian behaviour of the form exp [-½M ^E ₂τ²] for decays up to 20–30 per cent of the value at τ = 0. M ^E ₂, the second moment for the dipolar interactions between the spin-½ pairs, is related to the van Vleck second moment M ^VV ₂ through a factor f. Whilst experiments suggested a value of 0·70–0·72 for f = M ^E ₂/M ^VV ₂, simple models that ignored the non-equivalence of the dipolar-coupled spin-pairs had predicted f = 0·65. In this paper we derive an exact analytic expression for the spin response of a model of two dipolar-coupled inequivalent spins-1 to the pulse sequence P_y (90°)-τ-P _α(β)-t′, and show that the present model, with the quenching of the spin-flip terms of the dipolar hamiltonian, resolves the afore-mentioned discrepancy. We also reconcile the differences between the experimental and the earlier predicted values of f for deuteron N.M.R. spin echoes in perdeuterated solids.     

Correlated spin dynamics in 2-D quantum Heisenberg antiferromagnets from NMR relaxation in copper formiate tetradeuterate

Proton nuclear magnetic resonance (NMR) T₁ in a single crystal of copper formiate tetradeuterate is used to study the correlated Cu²⁺ spin dynamics and to derive the temperature behavior of the in-plane magnetic correlation length. The results are compared with the predictions of recent theoretical models for the spin dynamics in planar quantum Heisenberg antiferromagnets in a wide temperature range (from the Néel temperature up to a reduced temperatureT/J ～ 1.4, withJ in-plane exchange integral). In particular, it is shown that, in contrast to the predictions of the nonlinear σ model, no crossover to a quantum critical regime occurs and that the experimental findings are well reproduced by deriving the NMR relaxation rate in the framework of the standard mode-mode coupling theory.     

H NMR study of the phase transitions of trissarcosine calcium chloride single crystals at low temperature

The ¹H NMR line-width and spin-lattice relaxation time T₁ of TSCC single crystals were studied. Variations in the temperature dependence of the spin-lattice relaxation time were observed near 65 and 130 K, indicating drastic alterations of the spin dynamics at the phase transition temperatures. The changes in the temperature dependence of T₁ near 65 and 130 K correspond to phase transitions of the crystal. The anomalous decrease in T₁ around 130 K is due to the critical slowing down of the soft mode. The abrupt change in relaxation time at 65 K is associated with a structural phase transition. The proton spin-lattice relaxation time of this crystal also has a minimum value in the vicinity of 185 K, which is governed by the reorientation of the CH₃ groups of the sarcosine molecules. From this result, we conclude that the two phase transitions at 65 and 130 K can be discerned from abrupt variations in the ¹H NMR relaxation behavior, and that ¹H nuclei play important roles in the phase transitions of the TSCC single crystal.     

On Hahn-echo measurements of short 29Si T2 times in some silica-based materials

The Hahn-echo ²⁹Si NMR experiments performed for determinations of T₂ times in static supermicroporous materials SiO₂–Al₂O₃–MnO and SiO₂–MnO have shown the large loss in the echo intensity, observed at shortest echo delays. The relaxation patterns “intensity—τ”, where the echo-intensity initially increases with increasing τ values and then it “normally” reduces due to spin–spin relaxation, are formally treated and discussed.     

Frequency response of the low-temperature ionic conductivity of single crystals R 1 − y M y F3 − y (R = La-Er; M = Ca, Sr, Ba, Cd)

The frequency response (10^?1–10^?7 Hz) of the ionic conductivity σ of R _{1 ? y} M _y F_{3 ? y} single crystals (R is a rare-earth element, and M stands for an alkaline-earth element and Cd) with a tysonite structure is studied over a wide temperature range (114–410 K), which includes (for the first time for these phases) the interval below room temperature. The dependences σ(ν) obtained are discussed within the hopping relaxation model. The characteristics of the relaxation and migration processes and the carrier concentration and mobility are determined.     

Nuclear magnetic relaxation induced by the relaxation of electron spins

A physical mechanism responsible for the relaxation of nuclear spins coupled by the hyperfine interaction to relaxed electron spins in materials with spin ordering is proposed. The rate of such induced nuclear spin relaxation is proportional to the dynamic shift of the nuclear magnetic resonance (NMR) frequency. Therefore, its maximum effect on the NMR signal should be expected in the case of nuclear spin waves existing in the system. Our estimates demonstrate that the induced relaxation can be much more efficient than that occurring due to the Bloch mechanism. Moreover, there is a qualitative difference between the induced and Bloch relaxations. The dynamics of nuclear spin sublattices under conditions of the induced relaxation is reduced to the rotation of m₁ and m₂ vectors without any changes in their lengths (m ₁ ² (t) = m ₂ ² (t) = m ₀ ² (t)= const). This means that the excitation of NMR signals by the resonant magnetic field does not change the temperature T _n of the nuclear spin system. This is a manifestation of the qualitative difference between the induced and Bloch relaxations. Indeed, for the latter, the increase in T _n accompanying the saturation of NMR signals is the dominant effect.     

Application of microwave amplitude modulation technique to measure spin-lattice and spin-spin relaxation times accurately with a continuous-wave EPR spectrometer: Solution of Bloch’s equations by a matrix technique and least-squares fitting

A matrix technique to calculate signals recorded using the microwave amplitude-modulation technique is described. The calculations are carried out for spin packets, on and off resonance, to take into account inhomogeneous broadening. Both, the transverse component of magnetization representing the continuous-wave signal in a resonator, such as a cross-looped resonator, as well as the signal (electromotive force) induced in a pickup coil oriented parallel to the external magnetic field, are calculated for an arbitrary value of the coefficient of modulation. This is accomplished by solving the relevant Bloch equations in the rotating frame for the case when the amplitude of the microwave field is modulated by a sinusoidal wave, using Fourier expansions of the longitudinal and transverse components of the magnetization in Bloch equations. This results in a series of coupled equations inM _α(n) (α=y,zz), the magnetic moments of vaarious orders, leading to a penta-diagonal matrix of infinite dimension. These equations are then truncated and solved by a fast matrix technique to calculateM _α(n), required to calculate the modulation signals as functions of the amplitudemodulation frequency Ω. It is outlined how to exploit the expressions for the modulation signals to estimate the spin-lattice relaxation timesT ₁ and spin-spin relaxation timesT ₂ accurately by the leastsquares procedure, fitting simultaneously all signals obtained for spin packets, on and off resonance, at various modulation frequencies. Illustrative examples are provided.