NMR paramagnetic relaxation enhancement: test of the controlling influence of zfs rhombicity for S = 1

Prior theoretical work has predicted that the NMR paramagnetic relaxation enhancement (NMR-PRE) produced by electron spin S = 1 ions is highly sensitive to orthorhombic terms in the static zero field splitting (zfs) tensor. Zfs orthorhombicity (which implies chemical inequivalence of the three principal directions of the zfs-principal axis system and is described by the zfs E-parameter) is predicted to suppress the NMR-PRE profoundly relative to the reference cylindrical zfs-limit situation. This expectation was tested experimentally by a comparison of the zfs-limit NMR-PRE produced by [Ni(II)(en)(3)](2+) (en = ethylenediamine), a trigonal complex which lacks zfs-rhombicity, with the zfs-limit NMR-PRE produced by two orthorhombic complexes, [Ni(II)(en)(2)(H(2)O)(2)](2+) and [Ni(II)(en)(H(2)O)(4)](2+). As predicted, the zfs-limit NMR-PRE produced by the orthorhombic complexes in the proton resonance of a dioxane probe species in the solvent was strongly suppressed (by factors of approximately 5 and 7, respectively) relative to the comparable measurement on the trigonal complex. The suppression of the NMR-PRE due to the orthorhombic zfs terms is counteracted by an applied Zeeman field, leading to a predicted rise in the NMR-PRE with increasing Zeeman field strength; this rise occurs when the Zeeman energy is comparable to the orthorhombic zfs splitting, 2E. This second prediction of theory was likewise confirmed: the expected rhombicity-induced magnetic field dependence in the NMR-PRE was observed for the orthorhombic complexes but not for the trigonal complex.     

Relaxation of a quadrupolar nucleus in a strong magnetic field

Longitudinal relaxation of spin systems (S = 1, 3/2, 3) containing isolated quadrupolar nuclei are studied. The characteristic features of the relaxation behavior are identified in strong magnetic fields in the presence of chemical shift anisotropy. Two mechanisms are established that favor involvement of high rank multipoles in the relaxation process: an autocorrelation mechanism and a cross correlation mechanism. Multipoles of odd rank are involved in the relaxation of nuclei with spin S > 1 as a result of the autocorrelation mechanism (in this case, due to quadrupole interactions). The cross correlation mechanism, due to correlations between the chemical shift anisotropy and the quadrupole interactions, favors the appearance of multipoles of even rank. Expressions are presented for the multipole cross relaxation and longitudinal relaxation rates for spin systems with S = 1, 3/2, 3. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 1, pp. 18–25, January–February, 2006.     

Efficiency of paramagnetic relaxation enhancement in off-resonance rotating frame

Transferring from laboratory frame to off-resonance rotating frame for the (1)H spin can compensate the relaxivity loss for paramagnetic agents at the magnetic field strength higher than 3 Tesla and enhance water relaxation rate constant significantly. A comprehensive theory for calculating the relaxation rate constants in the off-resonance rotating frame is described. This theory considers the contributions from both inner shell and outer shell water. The derived relaxation rate constants and relaxation enhancement efficiency as a function of the magnetic field strength and the effective field parameters are directly correlated to the structures, dynamics and environments of paramagnetic agents. To validate the theoretical predictions, we have measured the relaxation enhancement efficiency for a series of macromolecule conjugated gadolinium chelates at 9.4 Tesla. The experimental results confirmed the theoretical predictions. The theory also predicts the relaxation enhancement for T(2)-type paramagnetic agents at high magnetic fields. Promising fields of applications include situations where T(1)- or T(2)-type paramagnetic agents are used for labeling molecular/cellular events.     

射频场照射下多自旋体系弛豫的理论计算

根据Liouville-von Neumann方程，对射频场照射下多自旋体系的弛豫进行了理论描述，并用WBR理论推导出了体系的弛豫方程组，给出了各类弛豫速率的理论计算公式.在此基础上，编制了弛豫方程组数值解的计算程序，分别用此程序和Bloch方程计算了双自旋体系在不同情况下的稳态解，并对计算结果进行了简要的分析和讨论. 关键词： 核磁共振 弛豫 射频场 多自旋体系     

Intrinsic electron spin relaxation due to the D'yakonov–Perel' mechanism in monolayer MoS2

Intrinsic electron spin relaxation due to the D'yakonov–Perel' mechanism is studied in monolayer Molybdenum Disulphide. An intervalley in-plane spin relaxation channel is revealed due to the opposite effective magnetic fields perpendicular to the monolayer Molybdenum Disulphide plane in the two valleys together with the intervalley electron–phonon scattering. The intervalley electron–phonon scattering is always in the weak scattering limit, which leads to a rapid decrease of the in-plane spin relaxation time with increasing temperature. A decrease of the in-plane spin relaxation time with the increase of the electron density is also shown.     

(110)-GaAs量子阱中光生载流子对电子自旋弛豫的影响

我们实验研究了(110)-GaAs量子阱中光生载流子对电子自旋弛豫的影响。通过测量量子阱的荧光寿命和光学吸收计算,我们能得到不同泵浦光功率下的带间吸收所产生的空穴浓度;相对应地,通过双色磁光科尔旋转技术,我们测量了该GaAs量子阱中电子自旋的动力学过程。结合两者,我们得到了电子自旋弛豫速率与空穴浓度的关系。实验结果表明电子自旋弛豫速率与空穴浓度呈线性依赖关系,验证了BirAronov-Pikus机制主导该体系的电子自旋弛豫。     

半导体量子阱中电子自旋弛豫和动量弛豫

根据电子自旋轨道耦合对自旋极化弛豫影响的DP机理进一步导出了半导体中电子自旋弛豫与动量弛豫及载流子浓度的关系，并采用飞秒抽运探测技术在室温下测量AlGaAs/GaAs 多量子阱中载流子浓度在 1×10¹⁷—1×10¹⁸cm^-3范围内，电子自旋弛豫时间由58ps增加至82 ps的变化情况，与理论计算值符合，说明了随着载流子浓度的增加，载流子间的频繁散射加速了电子动量驰豫，减弱了电子自旋轨道耦合作用，从而延长了电子自旋寿命. 关键词： 电子自旋轨道耦合 电子自旋弛豫和动量弛豫 飞秒光谱技术     

1H spin–lattice relaxation in water solution of 209Bi counterparts of Gd3+contrast agents

ABSTRACT

¹H spin–lattice relaxation studies of water solutions of Bismuth-ethylenediamine-tetraacetic acid (Bi-EDTA), Bismuth-ethylenediamine-tetrakis(methylenephosphonic) acid (Bi-EDTP), Bismuth-1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetic acid (Bi-DOTA), Bismuth-1,4,7,10-tetraazacyclododecane-1,4,7,10-tetrakis(methylenephosphonic acid) (Bi-DOTP) and Bismuth-1,4,7,10-tetraazacyclododecane-1,4,7-triacetic acid (Bi-DO3A) have been performed in order to compare Quadrupole Relaxation Enhancement (QRE) effects with Paramagnetic Relaxation Enhancement (PRE) from the perspective of exploiting the first one as a novel contrast mechanism for Magnetic Resonance Imaging (MRI). The selected compounds can be considered as ²⁰⁹Bi counterparts of Gd³⁺ complexes. The relaxation experiments have been performed in a broad frequency range of 5?kHz–30?MHz. The relaxation contribution associated with QRE has been extracted from the data and compared with PRE. Similarities and differences between the two effects have been discussed.     

嵌段共聚物溶致液晶相中水的2H-NMR动力学分析

采用D₂O 的²H-NMR线型和弛豫分析了PEO-PPO-PEO/D₂O/对二甲苯体系的层状和六角液晶相的动力学行为. 通过实验测得了两个不同体系的自旋 晶格弛豫时间T₁、自旋-自旋弛豫时间T₂和²H-NMR 谱. ²H-NMR 谱均为具有四极劈裂的粉末谱线型，且在谱图的中心，β_LD=54.7°时存在一个倒峰. 倒峰的出现直接表明引起体系中弛豫的主要动力学过程处于极窄化区域. 采用NMR弛豫模型，通过调节动力学参数，使理论模拟的²H-NMR谱、弛豫时间、倒峰的大小与实验的对应量相吻合，求得了体系的动力学参数.     

13C spin-lattice relaxation in natural diamond: Zeeman relaxation in fields of 500 to 5000 G at 300 K due to fixed paramagnetic nitrogen defects

¹³C Spin–lattice relaxation (SLR) times in the laboratory frame have been measured at room temperature as a function of field in the range of 500 to 5000 G on two natural type Ib and Ia diamonds after dynamic nuclear polarization. Each of the diamonds contains two types of fixed paramagnetic centers with overlapping inhomogeneous electron paramagnetic resonance (EPR) lines. EPR techniques have been employed to identify these defects and to determine their concentrations and relaxation times at X-band. Three different nuclear SLR paths, namely that due to electron SLR and two types of three spin processes, are discussed. The one three-spin process (TSP) (type 1) involves a simultaneous transition of two electron spins belonging to the same hyperfine EPR line and a ¹³C spin while the other process (type 2) involves two electron spins belonging to different hyperfine EPR lines and a ¹³C spin. It is shown that the thermal contact between the ¹³C nuclear Zeeman and electron dipole–dipole interaction reservoirs decreases with an increase in field intensity, thus forming a bottleneck in the ¹³C relaxation path due to the type 1 TSP. The contribution of TSP of type 1 dominates that due to electron SLR and the type 2 TSP in relaxing the ¹³C nuclei in type Ib diamond from about 1200 to 5000 G, while for type Ia diamond it dominates from 500 up to about 2200 G. In type Ia diamond over the range 2200 to 5000 G it seems that the type 2 TSP, which involves electrons of neighboring P2 hyperfine lines, dominates that of electron spin–lattice and the type 1 TSP. Over the range 500 to about 1200 G, a field-dependent electron SLR mechanism associated with N3 centers appears to dominate the ¹³C SLR.     

Determination of the electron relaxation rates in paramagnetic metal complexes: applicability of available NMR methods

Four different approaches for determining the electron relaxation rates in paramagnetic metallo-proteins are investigated, using a paramagnetic Ni2+ complex of a protein as an example. All four approaches rely on the determination of the longitudinal paramagnetic relaxation enhancements, R1p, of the 1H nuclei and the backbone 15N nuclei. Three of the methods utilize the field dependence of the R1p rates. It is found that the applicability of each of these methods depends on whether the fast-motion condition, omegaS2tau2<1, applies to the electron relaxation, omegaS being the Larmor frequency of the electron spin S and tau the correlation time of the electron relaxation. If the fast-motion condition is fulfilled, the electron relaxation rate can be obtained from the ratio of the R1p rates of one or more protons at two magnetic field strengths (method A). On the other hand, if the fast-motion condition does not apply, more elaborate methods must be used that, in general, require a determination of the R1p rates over a larger range of magnetic field strengths (method C). However, in the case of paramagnetic metal ions with relatively slow electron relaxation rates only two magnetic field strengths suffice, if the R1p rates of a hetero nucleus are included in the analysis (method B). In the fourth method (method D), the electron relaxation is estimated as a parameter in a structure calculation, using distance constraints derived from proton R1p rates at only one magnetic field strength. In general, only methods B and C give unambiguous electron relaxation rates.     

Paramagnetic Proton Nuclear Spin Relaxation Theory of Low-Symmetry Complexes for Electron Spin Quantum NumberS=

A generalization of the modified Solomon–Bloembergen–Morgan (MSBM) equations has been derived in order to describe paramagnetic relaxation enhancement (PRE) of paramagnetic complexes characterized by both a transient (Δ^ZFS_t) and a static (Δ^ZFS_s) zero-field splitting (ZFS) interaction. The new theory includes the effects of static ZFS, hyperfine coupling, and angular dependence and is presented for the case of electron spin quantum numberS= , for example, Mn(II) and Fe(III) complexes. The model gives the difference from MSBM theory in terms of a correction term δ which is given in closed analytical form. The theory may be important in analyzing the PRE of proton spin–lattice relaxation dispersion measurements (NMRD profiles) of low-symmetry aqua–metal complexes which are likely to be formed upon transition metal ions associated with charged molecular surfaces of biomacromolecules. The theory has been implemented with a computer program which calculates solvent water protonT₁NMRD profiles using both MSBM and the new theory.     

Effect of temperature,electric and magnetic field on spin relaxation in single layer graphene: A Monte Carlo simulation study

In this article, we employ the semiclassical Monte Carlo approach to study the spin polarized electron transport in single layer graphene channel. The Monte Carlo method can treat non-equilibrium carrier transport and effects of external electric and magnetic fields on carrier transport can be incorporated in the formalism. Graphene is the ideal material for spintronics application due to very low Spin Orbit Interaction. Spin relaxation in graphene is caused by D'yakonov-Perel (DP) relaxation and Elliott-Yafet (EY) relaxation. We study effect of electron electron scattering, temperature, magnetic field and driving electric field on spin relaxation length in single layer graphene. We have considered injection polarization along z-direction which is perpendicular to the plane of graphene and the magnitude of ensemble averaged spin variation is studied along the x-direction which is the transport direction. This theoretical investigation is particularly important in order to identify the factors responsible for experimentally observed spin relaxation length in graphene.     

R(1rho) relaxation for two-site chemical exchange: general approximations and some exact solutions

Analytic expressions for the nuclear magnetic spin relaxation rate constant for magnetization spin-locked in the rotating reference frame under an applied radiofrequency field, R(1rho), are obtained for two-site chemical exchange. The theoretical approach is motivated by Laguerre's method and obtains R(1rho) as the root of a (p1,q1) Padé approximant. The general formula for R(1rho) obtained by this approach is substantially simpler than existing expressions and is equally or slightly more accurate, in most cases. In addition, particular solutions for the R(1rho) rate constant are presented for two special cases: equal populations of the two exchanging sites, or placement of the radiofrequency carrier at the average resonance frequency of the two sites. The solutions are exact when the R1 and R2 relaxation rate constants are identical, and nearly exact under realistic experimental conditions.     

1H relaxation and dynamics of triphenylbismuth in deuterated solvents

ABSTRACT

¹H spin–lattice relaxation experiments have been performed for triphenylbismuth dissolved in fully deuterated glycerol and tetrahydrofuran. The experiments have been carried out in a broad frequency range, from 10?kHz to 40?MHz, versus temperature. The data have been analysed in terms of a relaxation model including two relaxation pathways: ¹H-¹H dipole–dipole interactions between intrinsic protons of triphenylbismuth molecule and ¹H-²H dipole–dipole interactions between the solvent and solute molecules. As a result of the analysis, rotational correlation times of triphenylbismuth molecules in the solutions and relative translational diffusion coefficient between the solvent and solute molecules have been determined. Moreover, the role of the intramolecular ¹H-¹H relaxation contribution has been revealed, depending on the motional parameters, as a result of decomposing the overall relaxation dispersion profile into contributions associated with the ¹H-¹H and ¹H-²H relaxation pathways. The possibility of accessing the contribution of the relaxation of the intrinsic protons is important from the perspective of exploiting Quadrupole Relaxation Enhancement effects as possible contrast mechanisms for Magnetic Resonance Imaging.     

Slow-motion theory of nuclear spin relaxation in paramagnetic low-symmetry complexes: A generalization to high electron spin

The slow-motion theory of nuclear spin relaxation in paramagnetic low-symmetry complexes is generalized to comprise arbitrary values of S. We describe the effects of rhombic symmetry in the static zero-field splitting (ZFS) and allow the principal axis system of the static ZFS tensor to deviate from the molecule-fixed frame of the nuclear-electron dipole–dipole tensor. We show nuclear magnetic relaxation dispersion (NMRD) profiles for different illustrative cases, ranging from within the Redfield limit into the slow-motion regime with respect to the electron spin dynamics. We focus on S = 3/2 and compare the effects of symmetry-breaking properties on the paramagnetic relaxation enhancement (PRE) in this case with that of S = 1, which we have treated in a previous paper. We also discuss cases of S = 2, 5/2, 3, and 7/2. One of the main objectives of this investigation, together with the previous papers, is to provide a set of standard calculations using the general slow-motion theory, against which simplified models may be tested.     

Field-dependent nuclear relaxation of spins 1/2 induced by dipole-dipole couplings to quadrupole spins: LaF3 crystals as an example

A general theory of spin-lattice nuclear relaxation of spins I=1/2 caused by dipole-dipole couplings to quadrupole spins S1, characterized by a non-zero averaged (static) quadrupole coupling, is presented. In multispin systems containing quadrupolar and dipolar nuclei, transitions of spins 1/2 leading to their relaxation are associated through dipole-dipole couplings with certain transitions of quadrupole spins. The averaged quadrupole coupling attributes to the energy level structure of the quadrupole spin and influences in this manner relaxation processes of the spin 1/2. Typically, quadrupole spins exhibit also a complex multiexponential relaxation sensed by the dipolar spin as an additional modulation of the mutual dipole-dipole coupling. The proposed model includes both effects and is valid for an arbitrary magnetic field and an arbitrary quadrupole spin quantum number. The theory is applied to interpret fluorine relaxation profiles in LaF3 ionic crystals. The obtained results are compared with predictions of the 'classical' Solomon relaxation theory.