Numerical and experimental studies of long-range magnetic dipolar interactions

We describe several numerical methods developed to analyze the behavior of spin polarized liquids in the presence of long-range magnetic dipolar interactions and external field gradients. Two of the methods use a discrete lattice of spins. In the first we calculate the magnetic field from the lattice of spins directly, either in the rotating frame, or in the lab frame. In the second method we include the dipolar fields from linear magnetization gradients analytically and calculate the dipolar fields from higher order gradients in Fourier space, where they are a local function of the magnetization. In the third method the magnetization is expanded in a Taylor series and the dipolar fields are calculated analytically for each term. The results of these calculations are compared to experimental data, in which we use two superconducting quantum interference device magnetometers adjacent to a spherical sample of hyperpolarized liquid 129Xe to detect the evolution of magnetization gradients. In particular, we observe an increase by a factor of 100 of the spin dephasing time in a longitudinal magnetic field gradient due to dipolar interactions of the spins. While each of the numerical techniques has certain limitations, they are generally in agreement with each other and with experimental data.     

Fourier decompositions and pulse sequence design algorithms for nuclear magnetic resonance in inhomogeneous fields

In this paper, we introduce algorithms based on Fourier synthesis for designing phase compensating rf pulse sequences for high-resolution nuclear magnetic resonance (NMR) spectroscopy in an inhomogeneous B0 field. We show that using radio frequency pulses and time varying linear gradients in three dimensions, it is possible to impart the transverse magnetization of spins phase, which is a desired function of the spatial (x,y,z) location. Such a sequence can be used to precompensate the phase that will be acquired by spins at different spatial locations due to inhomogeneous magnetic fields. With this precompensation, the chemical shift information of the spins can be reliably extracted and high resolution NMR spectrum can be obtained.     

Effect of internal gradients in the nuclear magnetic resonance measurement of the surface-to-volume ratio

We consider a system of spins diffusing in a static inhomogeneous (nonuniform-gradient) magnetic field B in a restricted geometry and in the presence of surface relaxation. We show that the short-time diffusional decay of nuclear magnetization is controlled by the field scattering kernel F(t) identical with [B(t)-B(0)](2), which is a measure of the average field inhomogeneity sampled by the spins in time t and does not depend on the particular sequence of radio-frequency pulses used. Magnetization in arbitrary sequences can be straightforwardly computed by evaluating elementary integrals of F(t). Diffusion takes place while the field is on, so that the spins precess as they diffuse, in contrast to the simpler problem of purely classical diffusion considered in [P. P. Mitra, P. N. Sen, and L. M. Schwartz, Phys. Rev. B 47, 8565 (1993)] which is applicable only to the ideal pulsed-field gradient experiment. We compute the short-time asymptotic form of F(t) and find that it depends on the surface-to-volume ratio (S/V) of the pore space as well as on the average of the gradients over the bounding surface. In a system with nonuniform gradients that vary faster near the surface than in the bulk, as for internal susceptibility fields, this gradient surface average may be much larger than the gradients in the bulk, significantly enhancing the apparent S/V. We discuss the application of our results to the widely used Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence as well as proposing a modification of it, which we term "padded" CPMG, that may be preferable in systems with significant surface relaxation. We indicate how each sequence can be used to probe the internal fields.     

Diffusive diffraction phenomenon in a porous polymer material observed by NMR using radio-frequency field gradients

Pulsed field gradient NMR diffusion experiments can, in principle, lead to the "diffusive diffraction" phenomenon. In practice, its observation by gradients of the static magnetic field is difficult in real systems because they involve internal gradients due to the static magnetic field (necessary for polarizing nuclear spins). This latter drawback can be circumvented by using gradients of the radio-frequency (rf) field (the other magnetic field used in any NMR experiment). For the first time, by means of rf gradients, a so-called diffusive diffraction peak has been observed in a real porous system and its position provides a value of the mean distance between pores; this can be further complemented by the mean pore size determined from the dependence of the apparent diffusion coefficient with respect to the diffusion interval.     

About long-lived nuclear spin states involved in para-hydrogenated molecules

This study deals with a spin system constituted of three nonequivalent protons, two of them originating from para-hydrogen (p-H(2)) after a hydrogenation reaction carried out in the earth magnetic field. It is shown that three singlet states are created provided indirect (J) couplings exist between the three spins, implying hyperpolarization transfer toward the third spin. Upon insertion of the sample in the NMR (Nuclear Magnetic Resonance) high field magnet, the following events occur: (i) the longitudinal two-spin orders which are parts of the singlet states survive; (ii) the other two terms (of these singlet states) tend to be destroyed by magnetic field gradients but at the same time are partly converted into differences of longitudinal polarizations. Nuclear spin relaxation is studied by appropriate NMR measurements when evolution takes place in the high field magnet or in the earth field. In the former case, relaxation is classical although complicated by numerous relaxation rates associated with both longitudinal two-spin orders and longitudinal polarizations. In the latter case, an equilibration between the singlet states first occur, their disappearance being thereafter driven by relaxation rates which remain very small because of the absence of any dipolar contribution. Thus, even in the case of a three-spin system, long-lived states exist; this unexpected property could be very useful for many applications.     

Analytical formulas for the magnetic field produced by a spin or a paramagnetic current density in the case of Gaussian basis functions

We present a derivation of simple formulas for the evaluation at any point of space of the magnetic field produced by a spin or a paramagnetic orbital current when Cartesian Gaussian basis functions are used, as is often the case in quantum chemistry. These formulas can be useful to plot the magnetic field vector density obtained from ab initio calculations or from a density operator fitted on experimental data. The magnetic field density is the observable probed in polarized neutron diffraction (PND) experiment, for it is, in fact, with this quantity that the neutron spins interact and not with the spin or magnetization density. The formulas make extensive use of the confluent hypergeometric function. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 11–15, 2001     

Spintronics and spintronics materials

The review concerns the fundamentals of spintronics (spin-transport electronics). The material covers spin-spin interactions and spin relaxation in semiconductors as well as spin and spin injection related effects in the condensed matter. Examples of promising spintronic devices are given, requirements for spintronic materials are formulated, methods of synthesis of spintronic materials are described, and the physicochemical properties of some materials are characterized. Organic spintronic materials are briefly outlined and the state-of-the art in the field of research on inhomogeneous magnetic semiconducting materials possessing high-temperature ferromagnetism is described. The emphasis is placed on the chemical bonding and electronic structure of magnetic impurities in semiconductors, consideration of the nature of ferromagnetism, and on the character of exchange interactions between localized spins in novel spintronic materials.__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 2255–2303, November, 2004.     

Magnetic resonance imaging of the manipulation of a chemical wave using an inhomogeneous magnetic field

The effects of applied magnetic fields on the traveling wave formed by the reaction of (ethylenediaminetetraacetato)cobalt(II) (Co(II)EDTA2-) and hydrogen peroxide have been studied using magnetic resonance imaging (MRI) . It was found that the wave could be manipulated by applying pulsed magnetic field gradients to a sample contained in a vertical cylindrical tube in the 7.0 T magnetic field of the spectrometer. Transverse field gradients decelerated the propagation of the wave down the high-field side of the tube and accelerated it down the low-field side. This control of the wave propagation eventually promoted the formation of a finger on the low-field side of the tube and allowed the wave to be maneuvered within the sample tube. The origin of these effects is rationalized by considering the Maxwell stress arising from the combined homogeneous and inhomogeneous magnetic fields and the magnetic susceptibility gradient across the wave front.     

The Stern-Gerlach experiment and the effects of spin relaxation

The classical Stern-Gerlach experiment is analyzed with an emphasis on the spin dynamics. The central question asked is whether there occurs a relaxation of the spin angular momentum during the time the particle passes through the Stern-Gerlach magnet. We examine in particular the transverse relaxation, involving angular momentum exchange between the spin of the particles and the spins of the magnet. A method is presented describing relaxation effects at an individual particle level. This leads to a stochastic equation of motion for the spins. This is coupled to a classical equation of motion for the particle translation. The experimental situation is then modeled through simulations of individual trajectories using two sets of parameter choices and three different sets of initial conditions. The two main conclusions are: (A) if the coupling between the magnet and the spin is solely described by the Zeeman interaction with the average magnetic field the simulations show a clear disagreement with the experimental observation of Stern and Gerlach. (B) If one, on the other hand, also allows for a T(2) relaxation time shorter than the passage time one can obtain a practically quantitative agreement with the experimental observations. These conclusions are at variance with the standard textbook explanation of the Stern-Gerlach experiment.     

Quasi-equilibria in reduced Liouville spaces

The quasi-equilibrium behaviour of isolated nuclear spin systems in full and reduced Liouville spaces is discussed. We focus in particular on the reduced Liouville spaces used in the low-order correlations in Liouville space (LCL) simulation method, a restricted-spin-space approach to efficiently modelling the dynamics of large networks of strongly coupled spins. General numerical methods for the calculation of quasi-equilibrium expectation values of observables in Liouville space are presented. In particular, we treat the cases of a time-independent Hamiltonian, a time-periodic Hamiltonian (with and without stroboscopic sampling) and powder averaging. These quasi-equilibrium calculation methods are applied to the example case of spin diffusion in solid-state nuclear magnetic resonance. We show that there are marked differences between the quasi-equilibrium behaviour of spin systems in the full and reduced spaces. These differences are particularly interesting in the time-periodic-Hamiltonian case, where simulations carried out in the reduced space demonstrate ergodic behaviour even for small spins systems (as few as five homonuclei). The implications of this ergodic property on the success of the LCL method in modelling the dynamics of spin diffusion in magic-angle spinning experiments of powders is discussed.     

Sub-100 nm confinement of magnetic nanoparticles using localized magnetic field gradients

Ferromagnetic rods containing thin sections of diamagnetic metal create intense magnetic field gradients that attract and confine magnetic nanoparticles to regions of space as small as 20 nm. The rods (80 nm diameter) comprised alternating sections of CoNi ( approximately 350 nm) and Au (20-160 nm) formed by electrodeposition into porous polycarbonate membranes. Upon magnetizing the rods, large magnetic gradients (106-107 T/m) form at the boundaries between ferromagnetic and diamagnetic sections. These gradients attract and confine magnetic nanoparticles to attoliter volumes of space surrounding the rod. This method provides a new tool for generating intense, highly localized magnetic field gradients, by design, and confining magnetic nanoparticles in these gradients.     

Separation of the different orders of NMR multiple-quantum transitions by the use of pulsed field gradients

Any order of transition can be detected separately in a two-dimensional multiple-quantum spin-echo experiment by applying a matching pair of pulsed field gradients. The method is based on the fact that the rate of defocusing and refocusing in an inhomogeneous magnetic field is proportional to the order of coherence. Natural line widths can be obtained for each order of transition.     

Dipolar-induced dephasing of triplet electron spins

In this paper, magnetic dipolar-induced spin dephasing is considered for localized electronic triplet spin states in solids. Using a projection operator formalism, expressions are derived to describe the Hahn-echo decay behavior for an ensemble of triplet spins at zero- and low-magnetic field strengths. For triplet states localized on non-axially symmetric molecules (or defects) it is shown that, at zero field, cross-relaxation with rapidly relaxing spins is essential in the dipolar-induced dephasing process; secular spin-spin interactions become important only in the presence of a static magnetic field or hyperfine couplings. The results are used to relate experimental dephasing data previously obtained for photoexcited triplet states of axially- and non-axially symmetric defects in CaO.     

Spin amplification in solution magnetic resonance using radiation damping

The sensitive detection of dilute solute spins is critical to biomolecular NMR. In this work, a spin amplifier for detecting dilute solute magnetization is developed using the radiation damping interaction in solution magnetic resonance. The evolution of the solvent magnetization, initially placed along the unstable -z direction, is triggered by the radiation damping field generated by the dilute solute magnetization. As long as the radiation damping field generated by the solute is larger than the corresponding thermal noise field generated by the sample coil, the solute magnetization can effectively trigger the evolution of the water magnetization under radiation damping. The coupling between the solute and solvent magnetizations via the radiation damping field can be further improved through a novel bipolar gradient scheme, which allows solute spins with chemical shift differences much greater than the effective radiation damping field strength to affect the solvent magnetizations more efficiently. Experiments performed on an aqueous acetone solution indicate that solute concentrations on the order of 10(-5) that of the solvent concentration can be readily detected using this spin amplifier.     

High-resolution NMR spectra in inhomogeneous fields via IDEAL (intermolecular dipolar-interaction enhanced all lines) method

Intermolecular double-quantum technique is used to yield high-resolution NMR spectra in inhomogeneous magnetic fields. The method exploits the distant dipolar interactions between the solvent and solute nuclear spins. Chemical shifts, J couplings, multiplicity patterns, and relative areas are retained with the method. Except for a 1.5-fold change in the scale factor of J couplings, other parameters are consistent with those extracted from one-dimensional spectra obtained in a homogeneous field.     

Spin exchange interactions and magnetic structures of extended magnetic solids with localized spins: theoretical descriptions on formal, quantitative and qualitative levels

Low-energy excitation energies of a magnetic solid with localized spins are probed by magnetic susceptibility, neutron scattering and Raman scattering measurements, and are analyzed using a spin Hamiltonian with a set of spin exchange parameters. The nature and values of the spin exchange parameters deduced from this analysis depend on what spin exchange paths one includes in the spin Hamiltonian. In this article, we review how spin exchange interactions of magnetic solids with localized spins are described on formal, quantitative and qualitative theoretical levels, investigate antisymmetric and anisotropic interactions for general spin dimers, and discuss the spin exchange interactions and magnetic structures of various extended magnetic solids on the basis of spin dimer analysis. Strongly interacting spin exchange paths of a magnetic solid are determined by the overlap between its magnetic orbitals, so that the strongly interacting spin unit of a magnetic solid does not necessarily have the same geometrical feature as does the arrangement of its magnetic ions or spin-carrying molecules. Therefore, in interpreting results of magnetic susceptibility, inelastic neutron scattering or Raman scattering measurements, it is essential to employ a set of spin exchange parameters chosen on the basis of proper electronic structure considerations. Spin dimer analyses based on extended Hückel tight binding calculations provide a reliable and expedient means to study the relative strengths of superexchange and super-superexchange spin exchange interactions.     

Restricted diffusion in NMR in arbitrary inhomogeneous magnetic fields and an application to circular layers

The multiple correlation function technique is a versatile approach for the computation of the nuclear magnetic resonance (NMR) magnetization of spins diffusing in inhomogeneous fields. The difficulties in deriving the required interaction matrices are one of the main limitations of this technique. In this work, methods to compute the interaction matrices of general magnetic field profiles from those of linear fields by basic matrix manipulations are presented. As an example, susceptibility induced magnetic field profiles that are generated by cylindrical capillaries residing in homogeneous magnetic fields are considered.     

Background-Free Detection of Spin-Exchange Dynamics at Ultra-Low Magnetic Field

Ultra-low field nuclear magnetic resonance spectroscopy (NMR) and imaging (MRI) inherently suffer from a low signal-to-noise ratio due to the small thermal polarization of nuclear spins. Transfer of polarization from a pre-polarized spin system to a thermally polarized spin system via the Spin Polarization Induced Nuclear Overhauser Effect (SPINOE) could potentially be used to overcome this limitation. SPINOE is particularly advantageous at ultra-low magnetic field, where the transferred polarization can be several orders of magnitude higher than thermal polarization. Here we demonstrate direct detection of polarization transfer from highly polarized ¹²⁹Xe gas spins to ¹H spins in solution via SPINOE. At ultra-low field, where thermal nuclear spin polarization is close to background noise levels and where different nuclei can be simultaneously detected in a single spectrum, the dynamics of the polarization transfer can be observed in real time. We show that by simply bubbling hyperpolarized ¹²⁹Xe into solution, we can enhance ¹H polarization levels by a factor of up to 151-fold. While our protocol leads to lower enhancements than those previously reported under extreme Xe gas pressures, the methodology is easily repeatable and allows for on-demand enhanced spectroscopy. SPINOE at ultra-low magnetic field could also be employed to study ¹²⁹Xe interactions in solutions.