Nuclear Spin Dynamics Research Articles

Visualization of dynamics in coupled multi-spin systems.

Since the dawn of quantum mechanics, ways to visualize spins and their interactions have attracted the attention of researchers and philosophers of science. In this work we present a generalized measurement-based 3D-visualization approach for describing dynamics in strongly coupled spin ensembles. The approach brings together angular momentum probability surfaces (AMPS), Husimi functions, and DROPS (discrete representations of operators for spin systems) and finds particular utility when the total angular momentum basis is used for describing Hamiltonians. We show that, depending on the choice of a generalized measurement operator, the plotted surfaces either represent probabilities of finding the maximal projection of an angular momentum along any direction in space or represent measurable coherences between the states with different total angular momenta. Such effects are difficult to grasp by looking at (time-dependent) numerical values of density-matrix elements. The approach is complete in a sense that there is one-to-one correspondence between the plotted surfaces and the density matrix. Three examples of nuclear spin dynamics in two-spin systems are visualized: (i)a zero- to ultralow-field (ZULF) nuclear magnetic resonance (NMR) experiment in the presence of a magnetic field applied perpendicularly to the sensitive axis of the detector, (ii)interplay between chemical exchange and spin dynamics during high-field signal amplification by reversible exchange (SABRE), and (iii)a high-field spin-lock-induced crossing (SLIC) sequence, with the initial state being the singlet state between two spins. The presented visualization technique facilitates intuitive understanding of spin dynamics during complex experiments as exemplified here by the considered cases. Temporal sequences ("the movies") of such surfaces show phenomena like interconversion of spin order between the coupled spins and are particularly relevant in ZULF NMR.

Rapid characterization of crude oil by NMR relaxation using new user-friendly software

This study demonstrates the feasibility of using low-field nuclear magnetic resonance (LF-NMR) relaxometry for the identification and characterization of crude oils as an alternative and robust technique. In general, the NMR relaxometry is based on monitoring nuclear spin dynamics (molecular dynamics) and analyzing its dependencies on the physicochemical properties of samples. The approach reported in this study comprises the initial analysis of crude oils by several standard American Society for Testing and Materials (ASTM) methods followed by a series of routine LF-NMR measurements. The LF-NMR based method showed the following practical advantages: It is non-destructive, requires minimum sample preparation without hazardous solvents, which helps keeping analysis costs reasonably low. The NMR analysis itself is fast and takes a few seconds for a crude oil sample. The whole method workflow is simple and easy to perform in specially developed user-friendly software that was “trained” to determine physical properties including kinematic viscosity, density, oAPI gravity, sulfur content, total acid number, refractive index, specific gravity, asphaltene content, microcarbon residue of crude oils using empirical correlations between the oil properties and experimental NMR relaxation values.

Understanding the effect of an anionic side-chain on the nuclear spin dynamics of a polysaccharide

Understanding the effect of an anionic side-chain on the nuclear spin dynamics of a polysaccharide

Nuclear spin dynamics and noise in anisotropic large box model-=SUP=-*-=/SUP=-

We consider the central spin model in the box approximation taking into account external magnetic field and anisotropy of the hyperfine interaction. From the exact Hamiltonian diagonalization we obtain analytical expressions for the nuclear spin dynamics in the limit of many nuclear spins. We predict the nuclear spin precession in zero magnetic field for the case of anisotropic interaction between electron and nuclear spins. We calculate and describe the nuclear spin noise spectra in the thermodynamic equilibrium. The obtained results can be used for the analysis of the nuclear spin induced current fluctuations in organic semiconductors. Keywords: central spin model, box model, nuclear spin dynamics.

Ядерная спиновая динамика и флуктуации в анизотропной модели большого ящика

We consider the central spin model in the box approximation taking into account an external magnetic field and the anisotropy of the hyperfine interaction. From the exact Hamiltonian diagonalization we obtain analytical expressions for the nuclear spin dynamics in the limit of many nuclear spins. We predict the nuclear spin precession in zero magnetic field for the case of the anisotropic interaction between electron and nuclear spins. We calculate and describe the nuclear spin noise spectra in the thermodynamic equilibrium. The obtained results can be used for the analysis of the nuclear spin induced current fluctuations in organic semiconductors.

Study of the Variation of the Electronic Distribution and Motional Dynamics of Two Independent Molecules of an Asymmetric Unit of Atorvastatin Calcium by Solid-State NMR Measurements.

Significant changes in the spin-lattice time and chemical shift anisotropy (CSA) parameters are observed in two independent molecules of an asymmetric unit of atorvastatin calcium (ATC-I) (which is referred to as “a”- and “b”-type molecules by following Wang et al.). The longitudinal magnetization decay curve is fitted by two exponentials—one with longer relaxation time and another with shorter relaxation time for most of the carbon nuclei sites. The local correlation time also varies significantly. This is the experimental evidence of the coexistence of two different kinds of motional degrees of freedom within ATC-I molecule. The solubility and bioavailability of the drug molecule are enhanced due to the existence of two different kinds of dynamics. Hence, the macroscopic properties like solubility and bioavailability of a drug molecule are highly correlated with its microscopic properties. The motional degrees of freedom of “a”- and “b”-type molecules are also varied remarkably at certain carbon nuclei sites. This is the first time the change in the molecular dynamics of two independent molecules of an asymmetric unit of atorvastatin calcium is quantified using solid-state NMR methodology. These types of studies, in which the chemical shift anisotropy (CSA) parameters and spin-lattice relaxation time provide information about the change in electronic distribution and the spin dynamics at the various crystallographic location of the drug molecule, will enrich the field “NMR crystallography”. It will also help us to understand the electronic distribution around a nucleus and the nuclear spin dynamics at various parts of the molecule, which is essential to develop the strategies for the administration of the drug.

Study of the structure and dynamics at various parts of the antibacterial drug molecule cefpodoxime proxetil

The structure and dynamics of cefpodoxime proxetil are elucidated by measuring chemical shift anisotropy (CSA) tensor, spin-lattice relaxation time, and local correlation time at twenty-one crystallographically different 13C nuclei sites. The principal components of CSA tensor of cefpodoxime proxetil are extracted by the two-dimensional phase adjusted sinning sideband (2DPASS) cross-polarization magic angle spinning (CP-MAS) solid-state NMR experiment, and the spin-lattice relaxation time is measured by the method outlined by Torchia(T1CP). The local correlation time is calculated by bearing in mind that the spin-lattice relaxation mechanism of 13C nuclei is mainly governed by the CSA interaction and the heteronuclear dipole-dipole interaction. The aminothiazole ring, β-lactam ring, and dihydrothiazine ring provide stability to the drug molecule and increase the affinity of the drug to penicillin-binding proteins (PBPs) receptors. The principal components of CSA parameters, spin-lattice relaxation time, and local correlation time vary substantially for carbon nuclei residing on these three rings. These signify that not only the electronic environment, but the molecular conformation, and the local dynamics are also altered within the ring. The substitution of the acyl side chain, oxime group, and the aminothiazole ring at the C7 position of the β-lactam ring enhances the antibacterial activity and the binding affinity of the drug. A huge variation of the spin-lattice relaxation time and local correlation time is observed in those regions. The change in the electron charge distribution and nuclear spin dynamics at different parts of the drug molecule is clear by CSA and spin-lattice relaxation measurements, which will enrich the field “NMR crystallography”.

Radiofrequency to Microwave Coherent Manipulation of an Organometallic Electronic Spin Qubit Coupled to a Nuclear Qudit.

We report here a comprehensive characterization of a 3d organometallic complex, [V(Cp)2Cl2] (Cp = cyclopentadienyl), which can be considered as a prototypical multilevel nuclear qudit (nuclear spin I = 7/2) hyperfine coupled to an electronic qubit (electronic spin S = 1/2). By combining complementary magnetic resonant techniques, such as pulsed electron paramagnetic resonance (EPR) and broadband nuclear magnetic resonance (NMR), we extensively characterize its Spin Hamiltonian parameters and its electronic and nuclear spin dynamics. Moreover, we demonstrate the possibility to manipulate the qubit–qudit multilevel structure by resonant microwave and radiofrequency pulses, driving coherent Rabi oscillations between targeted electronuclear states. The obtained results demonstrate that this simple complex is a promising candidate for quantum computing applications.

Structure and dynamics of sodium alginate as elucidated by chemical shift anisotropy and site-specific spin-lattice relaxation time measurements.

The biocompatible, biodegradable, linear copolymer sodium alginate is fabricated from [Formula: see text] linked [Formula: see text]-D-mannuronic acid (M block) and [Formula: see text]-L-guluronic acid (G-block). It has wide applications in drug delivery, cell encapsulation, and commercial application in the textile, cosmetics, paper, food, biomedical, and pharmaceutical industries. The structure and dynamics of sodium alginate were here investigated by measuring chemical shift anisotropy (CSA) parameters, spin-lattice relaxation time, and molecular correlation time. The principal components of the CSA tensor were determined by two-dimensional phase-adjusted spinning sideband (2DPASS) cross-polarization magic angle spinning (CP-MAS) SSNMR. The alternating M and G blocks of both equatorial and axial links are associated with greater overall flexibility. The molecular correlation time of the carboxyl carbon of both G and M blocks is faster than for the anomeric carbon and pyranose carbon. This is further experimental evidence of the coexistence of two different dynamics within the polysaccharide chains of sodium alginate, which was previously established by 1H-13C dipolar profile analysis. The relaxation time of the para-crystalline region of sodium alginate is comparable with that of chitosan, but it is much shorter than that of cellulose and chitin. The order of the molecular correlation time of sodium alginate and chitosan is also the same. Hence, it can be concluded that sodium alginate exhibits greater flexibility than cellulose and chitin. These types of investigation into the local electronic configuration and nuclear spin dynamics at various carbon nuclei sites of the biopolymer at atomic-scale resolution will help in the design of biomimetic materials.

One-directional polarization transport in electron/nuclear spin chains with loss and gain

Understanding the joint dynamics of electron and nuclear spins is central to core concepts in solid-state magnetic resonance - such as spin-lattice relaxation and dynamic nuclear polarization - but a generalization that capitalizes on competing polarization loss and gain channels is still lacking. Here, we theoretically study the non-Hermitian dynamics of hybrid electron/nuclear spin systems in the simultaneous presence of electron spin pumping and spin-lattice relaxation. Focusing on periodic, one-dimensional chains, we find that by adjusting the electron spin pumping to a critical level, it is possible to steer the flow of nuclear polarization to create site-dependent distributions where either end of the array polarizes in opposite ways, irrespective of the initial state. By contrast, we show that ring-like patterns - where the limit nuclear polarization is uniform - exhibit a non-decaying, externally-driven nuclear spin current. Interestingly, cyclic magnetic field modulation can render these processes largely robust to defects in the chain, a response featuring some interesting similarities - and differences - with recent findings in other non-Hermitian physical platforms.

Nuclear Spin Dynamics, Noise, Squeezing, and Entanglement in Box Model.

We obtain a compact analytical solution for the nonlinear equation for the nuclear spin dynamics in the central spin box model in the limit of many nuclear spins. The total nuclear spin component along the external magnetic field is conserved and the two perpendicular components precess or oscillate depending on the electron spin polarization, with the frequency, determined by the nuclear spin polarization. Asapplications of our solution, we calculate the nuclear spin noise spectrum and describe the effects of nuclear spin squeezing and many body entanglement in the absence of a system excitation.

NMR Spin Relaxation Theory of Biomolecules Undergoing Highly Asymmetric Exchange with Large Interaction Partners

The transient interactions of proteins and other molecules with much larger structures, such as synthetic or biological nanoparticles, lead to certain types of enhanced nuclear magnetic resonance (NMR) spin relaxation effects, which can be accurately measured by multidimensional solution NMR techniques. These relaxation effects provide new information about the nanostructures and the protein, their interactions, internal dynamics, and associated kinetic and thermodynamic parameters, such as exchange rates and populations. Although theoretical treatments exist that cover either the fast or slow exchange limits, a theoretical treatment that applies to all practically relevant exchange processes is still missing. A unified theoretical framework is presented for this purpose based on a stochastic Liouville equation (SLE). It covers nuclear spin dynamics, overall rotational diffusion of both the protein and the nanostructure, the exchange process between a free state and a bound state, and internal protein dynamics. Although the numerical implementation of the SLE typically involves large matrices, it is shown here that it is computationally still tractable for situations relevant in practice. Application of the theory demonstrates how transverse relaxation is substantially impacted by the kinetics of binding on a wide range of exchange timescales. It is further shown that when exchange occurs on the appropriate timescale, transverse relaxation is able to report on internal dynamics far slower than observable by traditional transverse relaxation experiments. The SLE will allow the realistic and quantitative interpretation of experimental NMR data reporting about transient protein-nanoparticle interactions, thereby providing a powerful tool for the characterization of protein dynamics modes on a vast range of timescales including motions that may be functionally relevant.

Frequency-swept pulses for ultrafast spatially encoded NMR

Ultrafast NMR based on spatial encoding yields arbitrary multidimensional spectra in a single scan. The dramatic acceleration afforded by spatial parallelisation makes it possible to capture transient species and processes, and has notably been applied to the monitoring of reactions and the analysis of hyperpolarised species. At the heart of ultrafast NMR lies the spatially sequential manipulation of nuclear spins. This is virtually always achieved by combining a swept radio-frequency pulse with a magnetic field gradient pulse. The dynamics of nuclear spins during these pulse sequence elements is key to understand and design ultrafast NMR experiments, and can often be described by surprisingly simple models. This article describes the spatial encoding of relaxation, chemical shift and diffusion in a common framework and discusses directions for future developments.

Ligand Control of 59Co Nuclear Spin Relaxation Thermometry.

Studying the correlation between temperature-driven molecular structure and nuclear spin dynamics is essential to understanding fundamental design principles for thermometric nuclear magnetic resonance spin-based probes. Herein, we study the impact of progressively encapsulating ligands on temperature-dependent 59Co T1 (spin–lattice) and T2 (spin–spin) relaxation times in a set of Co(III) complexes: K3[Co(CN)6] (1); [Co(NH3)6]Cl3 (2); [Co(en)3]Cl3 (3), en = ethylenediamine); [Co(tn)3]Cl3 (4), tn = trimethylenediamine); [Co(tame)2]Cl3 (5), tame = triaminomethylethane); and [Co(dinosar)]Cl3 (6), dinosar = dinitrosarcophagine). Measurements indicate that 59Co T1 and T2 increase with temperature for 1–6 between 10 and 60 °C, with the greatest ΔT1/ΔT and ΔT2/ΔT temperature sensitivities found for 4 and 3, 5.3(3)%T1/°C and 6(1)%T2/°C, respectively. Temperature-dependent T2* (dephasing time) analyses were also made, revealing the highest ΔT2*/ΔT sensitivities in structures of greatest encapsulation, as high as 4.64%T2*/°C for 6. Calculations of the temperature-dependent quadrupolar coupling parameter, Δe2qQ/ΔT, enable insight into the origins of the relative ΔT1/ΔT values. These results suggest tunable quadrupolar coupling interactions as novel design principles for enhancing temperature sensitivity in nuclear spin-based probes.

Polarization transfer in a spin-exchange optical-pumping experiment

Spin-exchange optical pumping (SEOP) enables hyperpolarization of magnetic noble gas nuclei and allows enormously enhanced signal in nuclear magnetic resonance studies in materials, biosciences, and medicine. We model the dynamics of the SEOP process taking place in a $\mathrm{Rb}\ensuremath{-}^{129}\mathrm{Xe}$ gas mixture and shed light on how the different microscopic processes influence the macroscopic polarization transfer. For each Rb-Xe collision taking place in simulated molecular dynamics trajectory, we sample a time series of quantum-chemically preparametrized Hamiltonians. Combined electron and nuclear spin dynamics of each event is propagated by solving the corresponding Liouville--von Neumann equation. The rarely occurring, long-lived van der Waals molecules are seen to give the most significant contribution to polarization transfer under the simulated conditions ($T=300$ K, $p=2.4$ bar), in agreement with earlier findings. Besides the lifetime of the collision complex, the average and minimum Rb-Xe interatomic distances characterize the efficiency of the polarization transfer events. We obtain insight into magnetization transfer in both individual binary collisions and van der Waals complexes and demonstrate a stepwise buildup of $^{129}\mathrm{Xe}$ spin polarization upon bond-length oscillations in the latter.

Programmable Nuclear-Spin Dynamics in Ti(IV) Coordination Complexes.

Interstitial patterning of nuclear spins is a nascent design principle for controlling electron spin superposition lifetimes in open-shell complexes and solid-state defects. Herein we report the first test of the impact of the patterning principle on ligand-based nuclear spin dynamics. We test how substitutional patterning of 1H and 79/81Br nuclear spins on ligands modulates proton nuclear spin dynamics in the ligand shell of metal complexes. To do so, we studied the 1H nuclear magnetic resonance relaxation times (T1 and T2) of a series of eight polybrominated catechol ligands and six complexes formed by coordination of the ligands to a Ti(IV) ion. These studies reveal that 1H T1 values can be enhanced in the individual ligands by a factor of 4 (from 10.8(3) to 43(5) s) as a function of substitution pattern, reaching the maximum value for 3,4,6-tribromocatechol. The T2 for 1H is also enhanced by a factor of 4, varying by ∼14 s across the series. When complexed, the impact of the patterning design strategy on nuclear spin dynamics is amplified and 1H T1 and T2 values vary by over an order of magnitude. Importantly, the general trends observed in the ligands also match those when complexed. Hence, these results demonstrate a new design principle to control 1H spin dynamics in metal complexes through pattern-based design strategies in the ligand shell.

Stabilization of an optical transition energy via nuclear Zeno dynamics in quantum-dot–cavity systems

We investigate the effect of nuclear spins on the phase shift and polarisation rotation of photons scattered off a quantum dot-cavity system. We show that as the phase shift depends strongly on the resonance energy of an electronic transition in the quantum dot, it can provide a sensitive probe of the quantum state of nuclear spins that broaden this transition energy. By including the electron-nuclear spin coupling at a Hamiltonian level within an extended input-output formalism, we show how a photon scattering event acts as a nuclear spin measurement, which when rapidly applied leads to an inhibition of the nuclear spin dynamics via the quantum Zeno effect, and a corresponding stabilisation of the optical resonance. We show how such an effect manifests in the intensity autocorrelation $g^{(2)}(\tau)$ of scattered photons, whose long-time bunching behaviour changes from quadratic decay for low photon scattering rates (weak laser intensities), to ever slower exponential decay for increasing laser intensities as optical measurements impede the nuclear spin evolution.

Quantum information processing using frozen core Y3+ spins in Eu3+:Y2SiO5

In this paper, we present a method to investigate and control the dynamics of the nearby host nuclear spins (the ‘frozen core’) about a rare-earth ion doped in a crystal. Optically detected, double quantum magnetic resonance measurements were conducted on Eu3+ Y2SiO5. The distinct magnetic resonant frequencies of nearby Y3+ spins were measured along with the lifetime and coherence time of an individual Y3+ spin. We demonstrate an entangling gate between the Eu3+ spins and a Y3+ spin associated with a particular position. Further, we propose a method to initialize the Y3+ spin states, enabling the Y3+ spins to be used as a quantum resource for quantum information applications.

Classical spin simulations with a quantum two-spin correction

Classical simulations of high-temperature nuclear spin dynamics in solids are known to accurately predict relaxation for spin 1/2 lattices with a large number of interacting neighbors. Once the number of interacting neighbors becomes four or smaller, classical simulations lead to noticeable discrepancies. Here we attempt to improve the performance of the classical simulations by adding a term representing two-spin quantum correlations. The method is tested for a spin-1/2 chain. It exhibits good performance at shorter times, but, at longer times, it is hampered by a singular behavior of the resulting equations of motion.

Nuclear spin dynamics influenced and detected by electron spin polarization in CdTe/(Cd,Mg)Te quantum wells

Nuclear spin coherence and relaxation dynamics of all constituent isotopes of an n-doped CdTe/(Cd,Mg)Te quantum well structure are studied employing optically detected nuclear magnetic resonance. Using time-resolved pump-probe Faraday ellipticity, we generate and detect the coherent spin dynamics of the resident electrons. The photogenerated electron spin polarization is transferred into the nuclear spin system, which becomes polarized and acts back on the electron spins as the Overhauser field. Under the influence of resonant radio frequency pulses, we trace the coherent spin dynamics of the nuclear isotopes $^{111}$Cd, $^{113}$Cd, and $^{125}$Te. We measure nuclear Rabi oscillations, the inhomogeneous dephasing time $T_2^*$, the spin coherence time $T_2$, and the longitudinal relaxation time $T_1$. Furthermore, we investigate the influence of the laser excitation and the corresponding electron spin polarization on the nuclear spin relaxation time and find a weak extension of this time induced by interaction with the electron spins.