Singlet Order Research Articles

Cross-correlated relaxation in the NMR of near-equivalent spin pairs: Longitudinal relaxation and long-lived singlet order.

The evolution of nuclear spin state populations is investigated for the case of a 13C2-labeled triyne in solution, for which the near-equivalent coupled pairs of 13C nuclei experience cross-correlated relaxation mechanisms. Inversion-recovery experiments reveal different recovery curves for the main peak amplitudes, especially when the conversion of population imbalances to observable coherences is induced by a radio frequency pulse with a small flip angle. Measurements are performed over a range of magnetic fields by using a sample shuttle apparatus. In some cases, the time constant TS for decay of nuclear singlet order is more than 100 times larger than the time constant T1 for the equilibration of longitudinal magnetization. The results are interpreted by a theoretical model incorporating cross-correlated relaxation mechanisms, anisotropic rotational diffusion, and an external random magnetic field. A Lindbladian formalism is used to describe the dissipative dynamics of the spin system in an environment of finite temperature. Good agreement is achieved between theory and experiment.

NMR spectroscopy of a 18O-labeled rhodium paddlewheel complex: Isotope shifts, 103Rh-103Rh spin-spin coupling, and 103Rh singlet NMR.

Despite the importance of rhodium complexes in catalysis, and the favorable 100% natural abundance of the spin-1/2 103Rh nucleus, there are few reports of 103Rh nuclear magnetic resonance (NMR) parameters in the literature. In part, this is the consequence of the very low gyromagnetic ratio of 103Rh and its dismal NMR sensitivity. In a previous paper [Harbor-Collins et al., J. Chem. Phys. 159, 104 307 (2023)], we demonstrated an NMR methodology for 1H-enhanced 103Rh NMR and demonstrated an application to the 103Rh NMR of the dirhodium formate paddlewheel complex. In this paper, we employ selective 18O labeling to break the magnetic equivalence of the 103Rh spin pair of dirhodium formate. This allows the estimation of the 103Rh-103Rh spin-spin coupling and provides access to the 103Rh singlet state. We present the first measurement of a 18O-induced 103Rh secondary isotope shift as well as the first instance of singlet order generated in a 103Rh spin pair. The field-dependence of 103Rh singlet relaxation is measured by field-cycling NMR experiments.

Exploring weak ligand-protein interactions by relaxometry of long-lived spin order.

Relaxation times of nuclear spins often serve as a valuable source of information on the dynamics of various biochemical processes. Measuring relaxation as a function of the external magnetic field turned out to be extremely useful for the studies of weak ligand-protein interactions. We demonstrate that observing the relaxation of the long-lived spin order instead of longitudinal magnetization extends the capability of this approach. We studied the field-dependent relaxation of the longitudinal magnetization and the singlet order (SO) of methylene protons in alanine-glycine dipeptide and citrate in the presence of human serum albumin (HSA). As a result, SO relaxation proved to be more sensitive to ligand-protein interaction, providing higher relaxation contrast for various HSA concentrations. To assess the parameters of the binding process in more details, we utilized a simple analytical relaxation model to fit the experimental field dependences for both SO and T1 relaxation. We also tested the validity of our approach in the experiments with trimethylsilylpropanoic acid (TSP) used as a competitor in ligand binding with HSA.

Spectral properties of a mixed singlet-triplet Ising superconductor

Conventional two-dimensional superconductivity is destroyed when the critical in-plane magnetic field exceeds the so-called Pauli limit. Some monolayer transition-metal dichalcogenides lack inversion symmetry and the strong spin-orbit coupling leads to a valley-dependent Zeeman-like spin splitting. The resulting spin-valley locking lifts the valley degeneracy and results in a strong enhancement of the in-plane critical magnetic field. In these systems, it was predicted that the density of states in an in-plane field exhibits distinct mirage gaps at finite energies of about the spin-orbit coupling strength, which arise from a coupling of the electron and hole bands at energy larger than the superconducting gap. In this study, we investigate the impact of a triplet pairing channel on the spectral properties, primarily the mirage gap and the superconducting gap, in the clean limit. Notably, in the presence of the triplet pairing channel, the mirage-gap width is reduced for the low magnetic fields. Furthermore, when the temperature is lower than the triplet critical temperature, the mirage gaps survive even in the strong-field limit due to the finite singlet and triplet order parameters. Our work provides insights into controlling and understanding the properties of spin-triplet Cooper pairs.

Singlet-assisted diffusion-NMR (SAD-NMR): extending the scope of diffusion tensor imaging via singlet NMR.

In this study, long-lived nuclear singlet order methods are combined with diffusion tensor imaging with the purpose of characterizing the full diffusion tensor of molecules diffusing freely in large pores of up to a millimeter in size. Such sizes are out of reach in conventional diffusion tensor imaging because of the limitations imposed by the relaxation decay constant of the longitudinal magnetization. A singlet-assisted diffusion tensor imaging methodology able to circumvent such limitations is discussed, and the new possibilities that it offers are demonstrated through simulation and experiments on plastic phantoms containing cylindrical channels of 1 mm in diameter.

A dual-core NMR system for field-cycling singlet assisted diffusion NMR.

Long-lived singlet spin order offers the possibility to extend the spin memory by more than an order of magnitude. This enhancement can be used, among other applications, to assist NMR diffusion experiments in porous media where the extended lifetime of singlet spin order can be used to gain information about structural features of the medium as well as the dynamics of the imbibed phase. Other than offering the possibility to explore longer diffusion times of the order of many minutes that, for example, gives unprecedented access to tortuosity in structures with interconnected pores, singlet order has the important advantage to be immune to the internal field gradients generated by magnetic susceptibility inhomogeneities. These inhomogeneities, however, are responsible for very short T2 decay constants in high magnetic field and this precludes access to the singlet order in the first instance. To overcome this difficulty and take advantage of singlet order in diffusion experiments in porous media, we have here developed a dual-core system with radiofrequency and 3-axis pulsed field gradients facilities in low magnetic field, for preparation and manipulation of singlet order and a probe, in high magnetic field, for polarisation and detection. The system operates in field-cycling and can be used for a variety of NMR experiments including diffusion tensor imaging (both singlet assisted and not). In this paper we present and discuss the new hardware and its calibration, and demonstrate its capabilities through a variety of examples.

Classification of Yu-Shiba-Rusinov states of magnetic impurities on superconducting surfaces: A fully relativistic first-principles study

Magnetic adatoms at surfaces of superconductors may induce localized bound states within the superconducting energy gap referred to as Yu-Shiba-Rusinov (YSR) states. We solve the Kohn-Sham-Dirac Bogoliubov--de Gennes equations within the fully relativistic multiple scattering Green's function method to study the nature of the YSR states for $3d$ magnetic impurities (Cr, Mn, Fe, and Co) placed on a pristine Nb(110) surface, as well as capped by a monolayer of Bi, Re, or Ir. First, we perform self-consistent relativistic calculations in the normal state and determine the direction of the easy axis and the magnetic anisotropy energy. Then we study the relation between the electronic structure in the normal state and the YSR states. We show that the YSR states can be categorized according to the energy-resolved singlet and triplet order parameters as normal, superconducting singlet, or induced triplet states. Finally, we demonstrate that the rotation of the adatom magnetic moment shifts the energy of the YSR states as a consequence of the spin orbit coupling. During this rotation, some branches of the YSR states might cross the Fermi energy, implying that at certain paths in the configuration space a peak can be found at zero energy.

Selectively Probing the Magnetic Resonance Signals of γ-Aminobutyric Acid in Human Brains In Vivo.

Gamma-aminobutyric acid (GABA) is an inhibitory neurotransmitter in human brains, playing a role in the pathogenesis of various psychiatric disorders. Current methods have some non-neglectable shortcomings and noninvasive and accurate detection of GABA in human brains is long-term challenge. To develop a pulse sequence capable of selectively detecting and quantifying the 1 H signal of GABA in human brains based on optimal controlled spin singlet order. Prospective. A phantom of GABA (pH = 7.3 ± 0.1) and 11 healthy subjects (5 females and 6 males, body mass index: 21 ± 3 kg/m2 , age: 25 ± 4 years). 7 Tesla, 3 Tesla, GABA-targeted magnetic resonance spectroscopy (GABA-MRS-7 T, GABA-MRS-3 T), magnetization prepared two rapid acquisition gradient echoes sequence. By using the developed pulse sequences applied on the phantom and healthy subjects, the signals of GABA were successfully selectively probed. Quantification of the signals yields the concentration of GABA in the dorsal anterior cingulate cortex (dACC) in human brains. Frequency. The 1 H signals of GABA in the phantom and in the human brains of healthy subjects were successfully detected. The concentration of GABA in the dACC of human brains was 3.3 ± 1.5 mM. The developed pulse sequences can be used to selectively probe the 1 H MR signals of GABA in human brains in vivo. 1 TECHNICAL EFFICACY STAGE: 1.

Radio-Frequency Sweeps at Microtesla Fields for Parahydrogen-Induced Polarization of Biomolecules

Magnetic resonance imaging of 13C-labeled metabolites enhanced by parahydrogen-induced polarization (PHIP) enables real-time monitoring of processes within the body. We introduce a robust, easily implementable technique for transferring parahydrogen-derived singlet order into 13C magnetization using adiabatic radio frequency sweeps at microtesla fields. We experimentally demonstrate the applicability of this technique to several molecules, including some molecules relevant for metabolic imaging, where we show significant improvements in the achievable polarization, in some cases reaching above 60% nuclear spin polarization. Furthermore, we introduce a site-selective deuteration scheme, where deuterium is included in the coupling network of a pyruvate ester to enhance the efficiency of the polarization transfer. These improvements are enabled by the fact that the transfer protocol avoids relaxation induced by strongly coupled quadrupolar nuclei.

Distinguishing glutamate and glutamine in in vivo 1 HMRSbased on nuclear spin singlet order filtering.

The signals of glutamate (Glu) and glutamine (Gln) are often significantly overlapped in routine 1 H-MR spectra of human brain in vivo. Selectively probing the signals of Glu and Gln in vivo is very important for the study of the metabolisms in which Glu and Gln are involved. The Glu-/Gln- targeted pulse sequences are developed to selectively probe the signals of Glu and Gln. The core part of the Glu-/Gln- targeted pulse sequences lies on the preparation of the nuclear spin singlet orders (SSOs) of the five-spin systems of Glu and Gln. The optimal control method is used to prepare the SSOs of Glu and Gln with high efficiency. The Glu-/Gln- targeted pulse sequences have been applied on phantoms to selectively probe the signals of Glu and Gln. Moreover, in the in vivo experiments, the signals of Glu and Gln in human brains of healthy subjects have been successfully probed separately. The developed Glu-/Gln- targeted pulse sequences can be used to distinguish the 1 H-MR signals of Glu and Gln in human brains in vivo. The optimal control method provides an effective way to prepare the SSO of a specific spin system with high efficiency and in turn selectively probe the signals of a targeted molecule.

Symmetry-based singlet-triplet excitation in solution nuclear magnetic resonance.

Coupled pairs of spin-1/2 nuclei support one singlet state and three triplet states. In many circumstances, the nuclear singlet order, defined as the difference between the singlet population and the mean of the triplet populations, is a long-lived state that persists for a relatively long time in solution. Various methods have been proposed for generating singlet order, starting from nuclear magnetization. This requires the stimulation of singlet-to-triplet transitions by modulated radiofrequency fields. We show that a recently described pulse sequence, known as PulsePol [Schwartz et al., Sci. Adv., 4, eaat8978 (2018)], is an efficient technique for converting magnetization into long-lived singlet order. We show that the operation of this pulse sequence may be understood by adapting the theory of symmetry-based recoupling sequences in magic-angle-spinning solid-state nuclear magnetic resonance (NMR). The concept of riffling allows PulsePol to be interpreted by using the theory of symmetry-based pulse sequences and explains its robustness. This theory is used to derive a range of new pulse sequences for performing singlet-triplet excitation and conversion in solution NMR. Schemes for further enhancing the robustness of the transformations are demonstrated.

Singlet-triplet mixing in the order parameter of the noncentrosymmetric superconductor Ru7B3

One of the key effects which is predicted to arise in superconductors without a centre of inversion is the mixing of singlet and triplet order parameters, which are no longer good quantum numbers on their own due to parity. We have probed the gap structure in the noncentrosymmetric superconductor Ru$_7$B$_3$, through small-angle neutron diffraction from the vortex lattice, in order to search for the proposed mixed order parameter. We find that the measured temperature dependence of the vortex-lattice form factor is well characterised by a model constructed to describe the effects of broken inversion symmetry on the superconducting state, indicating the presence of a mixed singlet-triplet gap and confirming the theoretical predictions.

31P spin-lattice and singlet order relaxation mechanisms in pyrophosphate studied by isotopic substitution, field shuttling NMR, and molecular dynamics simulation.

Nuclear spin relaxation mechanisms are often difficult to isolate and identify, especially in molecules with internal flexibility. Here we combine experimental work with computation in order to determine the major mechanisms responsible for 31P spin-lattice and singlet order (SO) relaxation in pyrophosphate, a physiologically relevant molecule. Using field-shuttling relaxation measurements (from 2 μT to 9.4 T) and rates calculated from molecular dynamics (MD) trajectories, we identified chemical shift anisotropy (CSA) and spin-rotation as the major mechanisms, with minor contributions from intra- and intermolecular coupling. The significant spin-rotation interaction is a consequence of the relatively rapid rotation of the -PO32- entities around the bridging P-O bonds, and is treated by a combination of MD simulations and quantum chemistry calculations. Spin-lattice relaxation was predicted well without adjustable parameters, and for SO relaxation one parameter was extracted from the comparison between experiment and computation (a correlation coefficient between the rotational motion of the groups).

Interplay between singlet and triplet pairings in multiband two-dimensional oxide superconductors

We theoretically study the superconducting properties of multi-band two-dimensional transition metal oxide superconductors by analyzing not only the role played by conventional singlet pairings, but also by the triplet order parameters, favored by the spin-orbit couplings present in these ma- terials. In particular, we focus on the two-dimensional electron gas at the (001) interface between LaAlO3 and SrTiO3 band insulators where the low electron densities and the sizeable spin-orbit couplings affect the superconducting features. Our theoretical study is based on an extended su- perconducting mean-field analysis of the typical multi-band tight-binding Hamiltonian, as well as on a parallel analysis of the effective electronic bands in the low-momentum limit, including static on-site and inter-site intra-band attractive potentials under applied magnetic fields. The presence of triplet pairings is able to strongly reduce the singlet order parameters which, as a result, are no longer a monotonic function of the charge density. The interplay between the singlet and the triplet pairings affects the dispersion of quasi-particle excitations in the Brillouin zone and also induces anisotropy in the superconducting behavior under the action of an in-plane and of an out- of-plane magnetic fields. Finally, non-trivial topological superconducting states become stable as a function of the charge density, as well as of the magnitude and of the orientation of the magnetic field. In addition to the chiral, time-reversal breaking, topological superconducting phase, favored by the linear Rashba couplings and by the on-site attractive potentials in the presence of an out- of-plane magnetic field, we find that a time-reversal invariant topological helical superconducting phase is promoted by not-linear spin-orbit couplings and by the inter-site attractive interactions in the absence of magnetic field.

Nuclear singlet relaxation by chemical exchange.

The population imbalance between nuclear singlet states and triplet states of strongly coupled spin-1/2 pairs, also known as nuclear singlet order, is well protected against several common relaxation mechanisms. We study the nuclear singlet relaxation of 13C pairs in aqueous solutions of 1,2-13C2 squarate over a range of pH values. The 13C singlet order is accessed by introducing 18O nuclei in order to break the chemical equivalence. The squarate dianion is in chemical equilibrium with hydrogen-squarate (SqH-) and squaric acid (SqH2) characterized by the dissociation constants pK1 = 1.5 and pK2 = 3.4. Surprisingly, we observe a striking increase in the singlet decay time constants TS when the pH of the solution exceeds ∼10, which is far above the acid-base equilibrium points. We derive general rate expressions for chemical-exchange-induced nuclear singlet relaxation and provide a qualitative explanation of the TS behavior of the squarate dianion. We identify a kinetic contribution to the singlet relaxation rate constant, which explicitly depends on kinetic rate constants. Qualitative agreement is achieved between the theory and the experimental data. This study shows that infrequent chemical events may have a strong effect on the relaxation of nuclear singlet order.

Hyperpolarization of cis-15 N2 -Azobenzene by Parahydrogen at Ultralow Magnetic Fields*.

The development of nuclear spins hyperpolarization, and the search for molecules that can be efficiently hyperpolarized is an active area in nuclear magnetic resonance. In this work we present a detailed study of SABRE SHEATH (signal amplification by reversible exchange in shield enabled alignment transfer to heteronuclei) experiments on 15N2‐azobenzene. In SABRE SHEATH experiments the nuclear spins of the target are hyperpolarized through transfer of spin polarization from parahydrogen at ultralow fields during a reversible chemical process. Azobenzene exists in two isomers, trans and cis. We show that all nuclear spins in cis‐azobenzene can be efficiently hyperpolarized by SABRE at suitable magnetic fields. Enhancement factors (relative to 9.4 T) reach up to 3000 for 15N spins and up to 30 for the 1H spins. We compare two approaches to observe either hyperpolarized magnetization of 15N/1H spins, or hyperpolarized singlet order of the 15N spin pair. The results presented here will be useful for further experiments in which hyperpolarized cis‐15N2‐azobenzene is switched by light to trans‐15N2‐azobenzene for storing the produced hyperpolarization in the long‐lived spin state of the 15N pair of trans‐15N2‐azobenzene.

Photochemically Induced Dynamic Nuclear Polarization of Heteronuclear Singlet Order.

Photochemically induced dynamic nuclear polarization (photo-CIDNP) is a method to hyperpolarize nuclear spins using light. In most cases, CIDNP experiments are performed in high magnetic fields and the sample is irradiated by light inside a nuclear magnetic resonance (NMR) spectrometer. Here we demonstrate photo-CIDNP hyperpolarization generated in the Earth's magnetic field and under zero- to ultralow-field (ZULF) conditions. Irradiating a sample containing tetraphenylporphyrin and para-benzoquinone for several seconds with light-emitting diodes produces strong hyperpolarization of 1H and 13C nuclear spins, enhancing the NMR signals more than 200 times. The hyperpolarized spin states at the Earth's field and in ZULF are different. In the latter case, the state corresponds to the singlet order between scalar-coupled 1H-13C nuclear spins. This state has a longer lifetime than the state hyperpolarized at Earth's field. The method is simple and cost-efficient and should be applicable to many molecular systems known to exhibit photo-CIDNP, including amino acids and nucleotides.

Nuclear Spin Relaxation of Longitudinal and Singlet Order in Liquid-CO2 Solutions.

Hyperpolarization techniques can enormously enhance the NMR signal thus allowing the exploitation of hyperpolarized substrates for in-vivo MRI applications. The short lifetime of hyperpolarized spin order poses significant limitations in such applications. Spin order storage can be prolonged through the use of long-lived spin states. Additionally, the storage of spin polarization–either in the form of longitudinal or singlet order–can be prolonged in low viscosity solutions. Here, we report the use of low viscosity liquid-CO2 solutions to store nuclear spin polarization in the form of longitudinal and singlet order for extended periods. Our results demonstrate that this storage time can be considerably sustained in liquid-CO2 solutions in comparison to other low viscosity solvents, opening up the possibility of new, exciting storage experiments in the future.

Constant-adiabaticity pulse schemes for manipulating singlet order in 3-spin systems with weak magnetic non-equivalence

Parahydrogen-induced polarization (PHIP) is a source of nuclear spin hyperpolarization, and this technique allows for the preparation of biomolecules for in vivo metabolic imaging. PHIP delivers hyperpolarization in the form of proton singlet order to a molecule, but most applications require that a heteronuclear (e.g. 13C or 15N) spin in the molecule is hyperpolarized. Here we present high field pulse methods to manipulate proton singlet order in the [1-13C]fumarate, and in particular to transfer the proton singlet order into 13C magnetization. We exploit adiabatic pulses, i.e., pulses with slowly ramped amplitude, and use constant-adiabaticity variants: the spin Hamiltonian is varied in such a way that the generalized adiabaticity parameter is time-independent. This allows for faster polarization transfer, and we achieve 96.2% transfer efficiency in thermal equilibrium experiments. We demonstrate this in experiments using hyperpolarization, and obtain 6.8% 13C polarization. This work paves the way for efficient hyperpolarization of nuclear spins in a variety of biomolecules, since the high-field pulse sequences allow individual spins to be addressed.

Singlet-Contrast Magnetic Resonance Imaging: Unlocking Hyperpolarization with Metabolism*.

Hyperpolarization‐enhanced magnetic resonance imaging can be used to study biomolecular processes in the body, but typically requires nuclei such as 13C, 15N, or 129Xe due to their long spin‐polarization lifetimes and the absence of a proton‐background signal from water and fat in the images. Here we present a novel type of 1H imaging, in which hyperpolarized spin order is locked in a nonmagnetic long‐lived correlated (singlet) state, and is only liberated for imaging by a specific biochemical reaction. In this work we produce hyperpolarized fumarate via chemical reaction of a precursor molecule with para‐enriched hydrogen gas, and the proton singlet order in fumarate is released as antiphase NMR signals by enzymatic conversion to malate in D2O. Using this model system we show two pulse sequences to rephase the NMR signals for imaging and suppress the background signals from water. The hyperpolarization‐enhanced 1H‐imaging modality presented here can allow for hyperpolarized imaging without the need for low‐abundance, low‐sensitivity heteronuclei.