On the theory of NMR spin echoes in solids

A general expression in terms of two-time correlation functions is derived for the spin echo responses to 90°-τ-β⁰_φ pulse sequences of quadrupolar spins coupled through dipolar interactions. The second moments of the correlation function are calculated for a system of spin one nuclei and shown to be in accordance with the experimental observations. Furthermore, results are presented for the fourth moments.     

Use of composite refocusing pulses to form spin echoes

The radiofrequency pulses used in NMR are subject to a number of imperfections such as those caused by inhomogeneity of the radiofrequency (B(1)) field and an offset of the transmitter frequency from precise resonance. The effect of these pulse imperfections upon a refocusing pulse in a spin-echo experiment can be severe. Many of the worst effects, those that distort the phase of the spin echo, can be removed completely by selecting the echo coherence pathway using either the "Exorcycle" phase cycle or magnetic field gradients. It is then tempting to go further and try to improve the amplitude of the spin-echo signal by replacing the simple refocusing pulse with a broadband composite 180° pulse that compensates for the relevant pulse imperfection. We show here that all composite pulses with a symmetric or asymmetric phase shift scheme will reintroduce phase distortions into the spin echo, despite the selection of the echo coherence pathway. In contrast, all antisymmetric composite pulses yield no phase distortion whatsoever, both on and off resonance, and are therefore the correct symmetry of composite refocusing pulse to use. These conclusions are verified using simulations and (31)P MAS NMR spin-echo experiments performed on a microporous aluminophosphate.     

Exchange and dipolar fields in phosphorus-doped silicon measured by electron spin echoes

The instantaneous diffusion effect of Klauder and Anderson has been observed in electron spin echo measurements on phosphorus donors in silicon. Our results give the size and radial dependence of exchange and dipolar interactions between donors. Previous studies of the spin-packet width in this system are re-interpreted.     

N.M.R. dipolar echoes in solids containing spin-1/2 pairs

The proton echo responses to resonant 90°-τ-β_90° (XY) and 90-τ-β_0° (XX) pulse sequences in powdered crystalline hydrates are reported. The echo produced by the XY sequence consists of two components: one is proportional to sin² β and the other to sin² β cos² β; the former component decays much faster than the latter on increasing the pulse spacing τ. In contrast, the XX sequence produces a single component echo of the form - sin² β cosβ. The maximum echo amplitudes for the sequences 90°-τ-90°_90° and 90°-τ-54°44′_0° exhibit a gaussian dependence on τ² over at least 95 per cent of their decays. The decay constant for the 90-τ-90°_90° echo corresponds to M ₂(inter) = 5/6 M ₂ ^vv(inter), where M ₂ ^vv(inter) is the interpair second moment calculated by the van Vleck procedure. These observations can be explained in terms of a simple model consisting of a planar arrangement of two spin-1/2 pairs provided the interpair dipolar hamiltonian is truncated so that [?^o _a(intra) + ?^{o, t} _d(inter), ?_z] = 0 and [?^o _a(intra), ?^{o, t} _d(inter)] = 0.

The model predicts the echo behaviour only if the spin-1 character of the eigenfunctions of ?^o _d(intra) + ?_z is preserved in the presence of the interpair interactions. It is shown that the XX echo and the sin² β cos² β components of the XY sequence originate solely in the interpair interactions and contain no contributions from the intrapair interactions. The decay of the maximum echo amplitude with increasing τ is caused by the incomplete refocusing of the interpair interactions by the XX and XY sequences; the correct decay is only determined provided the interpair dipolar hamiltonian is correctly truncated. The model also accounts for the proton echo behaviour in solid hydrogen reported by Metzger and Gaines.

Interestingly, the N.M.R. behaviour observed for these spin-1/2 pair systems is largely determined by the eigenfunctions of the spin Hamiltonian with M_z = 0.     

Long-lived NMR echoes in solids

A new type of long-lived NMR echo in solids with homogeneously broadened dipolar spectra is discussed. The echo can be generated by a simple two-pulse Hahn sequence in solid samples, where dipolar-coupled nuclei have different chemical shifts. We present general considerations and simple theoretical models which explain some features of this phenomenon.     

Dephasing of spin echoes by multiple heteronuclear dipolar interactions in rotational echo double resonance NMR experiments

The application of rotational echo double resonance (REDOR) nuclear magnetic resonance (NMR) for accurate distance measurements has thus far been largely restricted to isolated heteronuclear two-spin systems. In the present paper, the informational content of REDOR curves is explored for systems characterized by multi-spin interactions. To this end, numerical REDOR simulations are presented for cases in which single observe spins S are dipolarly coupled to groups of spins I in distinct geometries. To develop the utility of REDOR for characterizing dipolar couplings in unknown and/or ill-defined geometries, the validity ranges and systematic errors of certain analytical approximations are studied. In the limit of short dipolar evolution times where 0 < deltaS/S0 < or = 0.2 to 0.3, the REDOR difference signal intensity increases approximately proportional to the square of the dipolar evolution time. Here, the curvature depends simply on the second moment M2 characterizing the overall strength of the heterodipolar coupling, irrespective of specific molecular geometries. Fitting experimental REDOR data in this manner produces slight systematic underestimates of M2. However, these errors tend to be counterbalanced by additional systematic errors made by neglecting weak couplings to more remote spins and distribution effects caused by disorder. Based on these findings, the results suggest a convenient method of obtaining site-resolved second moment information in disordered materials.     

Diffusion measurements with the aid of nutation spin echoes appearing after two inhomogeneous radiofrequency pulses in inhomogeneous magnetic fields

Nutation echoes are generated by radiofrequency (RF) pulses with an inhomogeneous amplitude, B(1) = B(1)(r), in inhomogeneous magnetic fields, B(0) = B(0)(r). The two gradients of strengths G(1) and G(0), respectively, must be aligned in parallel for a maximum echo signal. After two RF pulses, two echoes appear at times tau(a) = 2 tau(1) + tau(2) + (G(1)/G(0))tau(1) and tau(b) = 2 tau(1) + tau(2) + 2(G(1)/G(0))tau(1), where tau(1) is the RF pulse duration and tau(2) the interpulse interval. It is shown that these echoes can favorably be employed for the determination of self-diffusion coefficients even in the poor experimental situation one often faces in low-resolution or low-field NMR. The signal intensity is comparable to that of ordinary Hahn echoes. Diffusion coefficients and spin-lattice relaxation times can be evaluated from the same experimental data set if both nutation echoes are recorded. Test experiments are in good agreement with literature data. Applications of the technique to "inside out" NMR, well logging NMR, surface coil NMR, toroid cavity NMR, etc., are suggested.     

Generating spin currents in semiconductors with the spin Hall effect

We investigate electrically induced spin currents generated by the spin Hall effect in GaAs structures that distinguish edge effects from spin transport. Using Kerr rotation microscopy to image the spin polarization, we demonstrate that the observed spin accumulation is due to a transverse bulk electron spin current, which can drive spin polarization nearly 40 microns into a region in which there is minimal electric field. Using a model that incorporates the effects of spin drift, we determine the transverse spin drift velocity from the magnetic field dependence of the spin polarization.     

Calculation of dipolar correlation function in solids with internal mobility

A general equation for the dipolar correlation function, to be used to analyze various kinds of independent internal motions, described by some correlation times tau(cm) (m = 1,2 em...k), has been obtained. The obtained expression has been used to analyze the temperature dependencies of different NMR measured values: second moment: spin-lattice relaxation times; amplitude of solid echoes signals.     

Multiple spin echoes in inhomogeneously broadened NMR systems

New types of spin echoes produced by refocusing the magnetic moments dephased during a long rf excitation pulse are observed in inhomogeneously broadened NMR systems. The experimental results are in good agreement with the theoretical predictions.     

Sensitivity enhancement of NMR spectra of half-integer spin quadrupolar nuclei in solids using hyperbolic secant pulses

The experimental factors influencing the enhancements achievable for the central NMR transition, m(I)=1/2-->m(I)=-1/2, of spin-3/2 and spin-5/2 nuclei in the solid state using hyperbolic secant, HS, pulses for population transfer are investigated. In the case of powder samples spinning at the magic angle, it is found that the spinning frequency, the bandwidth and the frequency offset of the HS pulse play a crucial role in determining the maximum enhancements. Specifically, the bandwidth must be set to the spinning frequency for maximum signal enhancements. The (87)Rb NMR enhancement obtained for RbClO(4) using HS pulses was relatively insensitive to the magic angle spinning frequency; however, in the case of Al(acac)(3), the (27)Al enhancement increased with MAS frequency. In order to obtain an adiabatic HS sweep, one should optimize the rf field for a given pulse duration or optimize the pulse duration for a given rf field.     

Positron spin relaxation in solids

Summary The positron spin relaxation in a longitudinal magnetic field was investigated in some solids where Ps formation occurs. The experimental results indicate that this relaxation manifests itself in those organic compounds where the positron can excite low-lying triplet states. The values of positron slowing-down time, obtained by adopting a schematic model, range from 13 to 28 ps. This work was supported by CISM (Centro Interuniversitario di Struttura della Materia) of Ministero della Pubblica Istruzione, and by GNSM (Gruppo Nazionale di Struttura della Materia) of CNR.     

Spontaneous spin textures in dipolar spinor condensates

We have mapped out a detailed phase diagram that shows the ground state structure of a spin-1 condensate with magnetic dipole-dipole interactions. We show that the interplay between the dipolar and the spin-exchange interactions induces a rich variety of quantum phases that exhibit spontaneous magnetic ordering in the form of intricate spin textures.     

Phonon-assisted spin diffusion in solids

The spin flip-flop transition rate is calculated for the case of spectral spin diffusion within a system of dipolarly coupled spins in a solid where the lattice vibrations are present. Long-wavelength acoustic phonons time-modulate the interspin distance r_ij and enhance the transition rate via the change of the 1/r³_ij term in the coupling dipolar Hamiltonian. The phonon-assisted spin diffusion rate is calculated by the golden rule in the Debye approximation of the phonon density of states. The coupling of the spins to the phonons introduces temperature dependence into the transition rate, in contrast to the spin diffusion in a rigid lattice, where the rate is temperature-independent. The direct (one-phonon absorption or emission) processes introduce a linear temperature dependence into the rate at temperatures not too close to T = 0. Two-phonon processes introduce a more complicated temperature dependence that again becomes simple analytical for temperatures higher than the Debye temperature, where the rate is proportional to T², and in the limit T → 0, where the rate varies as T⁷. Raman processes (one-phonon absorption and another phonon emission) dominate by far the phonon-assisted spin flip-flop transitions.     

Rotary echoes due to magnetic dipolar interaction in a multi-level NMR system

A new type of rotary echo which is due to magnetic dipolar interaction has been observed in a multi-level NMR system. From the echo-envelope decay we can estimate a second moment due to a part of dipolar interaction participating only in the resonant transition.     

Revision of spin echoes in pure nuclear quadrupole resonance

Goldman's spin-1/2 formalism has been used for describing the response of an I=3/2 spin system to a two-pulse sequence in a pure nuclear quadrupole resonance experiment. A detailed analysis of the polarization evolution and quadrupolar echo generation is carried out through the use of explicit expressions for secular homo- and heteronuclear dipolar interactions. In striking contrast with previous studies, it is predicted that Van Vleck's second moments governing a classical solid-echo or Hahn sequence differ from those obtained by equivalent means in magnetic resonance. In fact, it is shown that, although measured moments still complement each other, the combined use of standard sequences does not allow the separate determination of homo- and heteronuclear dipolar contributions to the linewidth, not even in an indirect manner. In this context, the importance and potential usefulness of a crossed coil probe are also briefly discussed.     

Stochastic dipolar recoupling in nuclear magnetic resonance of solids

I describe a nuclear magnetic resonance (NMR) technique, called stochastic dipolar recoupling (SDR), that permits continuous experimental control of the character of spin dynamics between coherent and incoherent limits in a system of magnetic dipole-coupled nuclei. In the fully incoherent limit of SDR, spin polarization transfers occur at distance-dependent rates without the quantum mechanical interferences among pairwise dipole-dipole couplings that often limit the feasibility or precision of structural studies of solids by NMR. In addition to facilitating structural studies, SDR represents a possible route to experimental studies of effects of decoherence on the dynamics of quantum many-body systems.     

Negative muon spin rotation in solids

Experimental advances in solid state physics research using polarized negative muons (in the ground state of muonic atoms) are reviewed. The main subject is studies of ^– hyperfine interactions in magnetic materials. Basic principles and distinctive features of the ^–SR method are also presented, and possible future developments are briefly discussed.     

Storage of intense optical pulses in solids

Possibility to store optical information in media with fast relaxations is studied in case of arbitrary intensities of probe and control pulses. Analytical solution of the self-consistent system of equations for propagation and density matrix is obtained with allowance for the first non-stationary corrections. A new scheme of storage is proposed which allows an essential reduction of the optical length needed for storage.