Dynamic nuclear polarisation via the integrated solid effect I: theory

In the hyperpolarisation method known as dynamic nuclear polarisation (DNP), a small amount of unpaired electron spins is added to the sample containing the nuclear spins and the polarisation of these unpaired electron spins is transferred to the nuclear spins by means of a microwave field. Traditional DNP uses weak continuous wave (CW) microwave fields, so perturbation methods can be used to calculate the polarisation transfer. A much faster transfer of the electron spin polarisation is obtained with the integrated solid effect (ISE) which uses strong pulsed microwave fields. As in nuclear orientation via electron spin locking, the polarisation transfer is coherent, similar to the coherence transfer between nuclear spins. This paper presents a theoretical approach to calculate this polarisation transfer.

ISE is successfully used for a fast polarisation transfer from short-lived photo-excited triplet states to the surrounding nuclear spins in molecular crystals. These triplet states are strongly aligned in the photo-excitation process and do not require the low temperatures and strong magnetic fields needed to polarise the electron spins in traditional DNP. In the following paper, the theory is applied to the system naphthalene-h₈ doped with pentacene-d₁₄ which provides the photo-excited triplet states, and compared with experimental results.     

Dynamic nuclear polarisation via the integrated solid effect II: experiments on naphthalene-h8 doped with pentacene-d14

In dynamic nuclear polarisation (DNP), also called hyperpolarisation, a small amount of unpaired electron spins is added to the sample containing the nuclear spins, and the polarisation of these unpaired electron spins is transferred to the nuclear spins by means of a microwave field. Traditional DNP polarises the electron spin of stable paramagnetic centres by cooling down to low temperature and applying a strong magnetic field. Then weak continuous wave microwave fields are used to induce the polarisation transfer. Complicated cryogenic equipment and strong magnets can be avoided using short-lived photo-excited triplet states that are strongly aligned in the optical excitation process. However, a much faster transfer of the electron spin polarisation is needed and pulsed DNP methods like nuclear orientation via electron spin locking (NOVEL) and the integrated solid effect (ISE) are used.

To describe the polarisation transfer with the strong microwave fields in NOVEL and ISE, the usual perturbation methods cannot be used anymore. In the previous paper, we presented a theoretical approach to calculate the polarisation transfer in ISE. In the present paper, the theory is applied to the system naphthalene-h₈ doped with pentacene-d₁₄ yielding the photo-excited triplet states and compared with experimental results.     

High-Field Phenomena of Qubits

Electron and nuclear spins are very promising candidates to serve as quantum bits (qubits) for proposed quantum computers, as the spin degrees of freedom are relatively isolated from their surroundings and can be coherently manipulated, e.g., through pulsed electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR). For solid-state spin systems, impurities in crystals based on carbon and silicon in various forms have been suggested as qubits, and very long relaxation rates have been observed in such systems. We have investigated a variety of these systems at high magnetic fields in our multifrequency pulsed EPR/ENDOR (electron nuclear double resonance) spectrometer. A high magnetic field leads to large electron spin polarizations at helium temperatures, giving rise to various phenomena that are of interest with respect to quantum computing. For example, it allows the initialization of both the electron spin as well as hyperfine-coupled nuclear spins in a well-defined state by combining millimeter and radio-frequency radiation. It can increase the T ₂ relaxation times by eliminating decoherence due to dipolar interaction and lead to new mechanisms for the coherent electrical readout of electron spins. We will show some examples of these and other effects in Si:P, SiC:N and nitrogen-related centers in diamond.     

EPR and ENDOR Studies of Shallow Donors in SiC

Recent progress in the investigation of the electronic structure of the shallow nitrogen (N) and phosphorus (P) donors in 3C–, 4H– and 6H–SiC is reviewed with focus on the applications of magnetic resonance including electron paramagnetic resonance (EPR) and other pulsed methods such as electron spin echo, pulsed electron nuclear double resonance (ENDOR), electron spin-echo envelope modulation and two-dimensional EPR. EPR and ENDOR studies of the ²⁹Si and ¹³C hyperfine interactions of the shallow N donors and their spin localization in the lattice are discussed. The use of high-frequency EPR in combination with other pulsed magnetic resonance techniques for identification of low-temperature P-related centers in P-doped 3C–, 4H– and 6H–SiC and for determination of the valley–orbit splitting of the shallow N and P donors are presented and discussed.     

The Electronic State of Flavoproteins: Investigations with Proton Electron–Nuclear Double Resonance

Electron–nuclear double resonance (ENDOR) spectroscopy provides useful information on hyperfine interactions between nuclear magnetic moments and the magnetic moment of an unpaired electron spin. Because the hyperfine coupling constant reacts quite sensitively to polarity changes in the direct vicinity of the nucleus under consideration, ENDOR spectroscopy can be favorably used for the detection of subtle protein–cofactor interactions. A number of pulsed ENDOR studies on flavoproteins have been published during the past few years; most of them were designed to characterize the flavin cofactor by means of its protonation state, or to detect individual protein–cofactor interactions. The aim of this study is to compare the pulsed ENDOR spectra from different flavoproteins in terms of variations of characteristic proton hyperfine values. The general concept is to observe limits of possible influences on the cofactor’s electronic state by surrounding amino acids. Furthermore, we compare ENDOR data obtained from in vivo experiments with in vitro data to emphasize the potential of the method for gaining molecular information in complex media.     

Magnetic field dependence of triplet-state ONP: theoretical analysis in terms of level anti-crossings

ABSTRACT

A theoretical approach to Optical Nuclear Polarisation (ONP) is described, which is based on the analysis of Level Anti-Crossings (LACs) in triplet states. Here we consider ONP formed in molecular crystals doped with suitable guest molecules and ONP generated in diamond crystals containing negatively charged nitrogen-vacancy (NV^–) centres. In both cases, electron spin polarisation of triplet states generated by light excitation is transferred to nuclei giving rise to ONP. Polarisation transfer is most efficient at LACs; for this reason, we consider in detail crossings of electron–nuclear energy levels and the role of different perturbation terms (coming from isotropic and anisotropic hyperfine coupling, zero-field splitting and sample orientation), which turn these crossings into LACs and give rise to ONP. Analytical results are supported by numerical calculations of the ONP field dependences. Thus, the outlined LAC analysis is a useful approach for interpreting the ONP magnetic field dependence.     

β-NMR

The β-NMR facility at ISAC is constructed specifically for experiments in condensed matter physics with radioactive ion beams. Using co-linear optical pumping, a ⁸Li^?+? ion beam having a large nuclear spin polarisation and low energy (nominally 30 keV) can be generated. When implanted into materials these ions penetrate to shallow depths comparable to length scales of interest in the physics of surfaces and interfaces between materials. Such low-energy ions can be decelerated with simple electrostatic optics to enable depth-resolved studies of near-surface phenomena over the range of about 2–200 nm. Since the β-NMR signal is extracted from the asymmetry intrinsic to beta-decay and therefore monitors the polarisation of the radioactive probe nuclear magnetic moments, this technique is fundamentally a probe of local magnetism. More generally though, any phenomena which affects the polarisation of the implanted spins by, for example, a change in resonance frequency, line width or relaxation rate can be studied. The β-NMR program at ISAC currently supports a number of experiments in magnetism and superconductivity as well as novel ultra-thin heterostructures exhibiting properties that cannot occur in bulk materials. The general purpose zero/low field and high field spectrometers are configured to perform CW and pulsed RF nuclear magnetic resonance and spin relaxation experiments over a range of temperatures (3–300 K) and magnetic fields (0–9 T).     

Dynamic Nuclear Polarization in III–V Semiconductors

We report on electron spin resonance, nuclear magnetic resonance and Overhauser shift experiments on two of the most commonly used III–V semiconductors, GaAs and InP. Localized electron centers in these semiconductors have extended wavefunctions and exhibit strong electron–nuclear hyperfine coupling with the nuclei in their vicinity. These interactions not only play a critical role in electron and nuclear spin relaxation mechanisms, but also result in transfer of spin polarization from the electron spin system to the nuclear spin system. This transfer of polarization, known as dynamic nuclear polarization (DNP), may result in an enhancement of the nuclear spin polarization by several orders of magnitude under suitable conditions. We determine the critical range of doping concentration and temperature conducive to DNP effects by studying these semiconductors with varying doping concentration in a wide temperature range. We show that the electron spin system in undoped InP exhibits electric current-induced spin polarization. This is consistent with model predictions in zinc-blende semiconductors with strong spin–orbit effects.     

Optimal control in NMR spectroscopy: Numerical implementation in SIMPSON

We present the implementation of optimal control into the open source simulation package SIMPSON for development and optimization of nuclear magnetic resonance experiments for a wide range of applications, including liquid- and solid-state NMR, magnetic resonance imaging, quantum computation, and combinations between NMR and other spectroscopies. Optimal control enables efficient optimization of NMR experiments in terms of amplitudes, phases, offsets etc. for hundreds-to-thousands of pulses to fully exploit the experimentally available high degree of freedom in pulse sequences to combat variations/limitations in experimental or spin system parameters or design experiments with specific properties typically not covered as easily by standard design procedures. This facilitates straightforward optimization of experiments under consideration of rf and static field inhomogeneities, limitations in available or desired rf field strengths (e.g., for reduction of sample heating), spread in resonance offsets or coupling parameters, variations in spin systems etc. to meet the actual experimental conditions as close as possible. The paper provides a brief account on the relevant theory and in particular the computational interface relevant for optimization of state-to-state transfer (on the density operator level) and the effective Hamiltonian on the level of propagators along with several representative examples within liquid- and solid-state NMR spectroscopy.     

Defects in Nanodiamonds: Application of High-Frequency cw and Pulse EPR,ODMR

Different aspects of applications of electron paramagnetic resonance (EPR) based techniques including high frequency (HF) electron spin echo (ESE), electron-nuclear double resonance (ENDOR) and optically detected magnetic resonance (ODMR) approaches to study diamond nanostructures are examined.     

Spin dynamic simulations of solid effect DNP: the role of the relaxation superoperator

Relaxation plays a crucial role in the spin dynamics of dynamic nuclear polarisation. We review here two different strategies that have recently been used to incorporate relaxation in models to predict the spin dynamics of solid effect dynamic nuclear polarisation. A detailed explanation is provided on how the Lindblad–Kossakowski form of the master equation can be used to describe relaxation in a spin system. Fluctuations of the spin interactions with the environment as a cause of relaxation are discussed and it is demonstrated how the relaxation superoperator acting in Liouville space on the density operator can be derived in the Lindblad–Kossakowski form by averaging out non-secular terms in an appropriate interaction frame. Furthermore we provide a formalism for the derivation of the relaxation superoperator starting with a choice of a basis set in Hilbert space. We show that the differences in the prediction of the nuclear polarisation dynamics that are found for certain parameter choices arise from the use of different interaction frames in the two different strategies. In addition, we provide a summary of different relaxation mechanisms that need to be considered to obtain more realistic spin dynamic simulations of solid effect dynamic nuclear polarisation.     

Electrical detection of coherent nuclear spin oscillations in phosphorus-doped silicon using pulsed ENDOR

We demonstrate the electrical detection of pulsed X-band electron nuclear double resonance (ENDOR) in phosphorus-doped silicon at 5 K. A pulse sequence analogous to Davies ENDOR in conventional electron spin resonance is used to measure the nuclear spin transition frequencies of the (31)P nuclear spins, where the (31)P electron spins are detected electrically via spin-dependent transitions through Si/SiO(2) interface states, thus not relying on a polarization of the electron spin system. In addition, the electrical detection of coherent nuclear spin oscillations is shown, demonstrating the feasibility to electrically read out the spin states of possible nuclear spin qubits.     

Numerical simulation of NQR/NMR: Applications in quantum computing

A numerical simulation program able to simulate nuclear quadrupole resonance (NQR) as well as nuclear magnetic resonance (NMR) experiments is presented, written using the Mathematica package, aiming especially applications in quantum computing. The program makes use of the interaction picture to compute the effect of the relevant nuclear spin interactions, without any assumption about the relative size of each interaction. This makes the program flexible and versatile, being useful in a wide range of experimental situations, going from NQR (at zero or under small applied magnetic field) to high-field NMR experiments. Some conditions specifically required for quantum computing applications are implemented in the program, such as the possibility of use of elliptically polarized radiofrequency and the inclusion of first- and second-order terms in the average Hamiltonian expansion. A number of examples dealing with simple NQR and quadrupole-perturbed NMR experiments are presented, along with the proposal of experiments to create quantum pseudopure states and logic gates using NQR. The program and the various application examples are freely available through the link http://www.profanderson.net/files/nmr_nqr.php.     

Understanding Overhauser Dynamic Nuclear Polarisation through NMR relaxometry

Overhauser dynamic nuclear polarisation (DNP) represents a potentially outstanding tool to increase the sensitivity of solution and solid state NMR experiments, as well as of magnetic resonance imaging. DNP signal enhancements are strongly linked to the spin relaxation properties of the system under investigation, which must contain a paramagnetic molecule used as DNP polariser. In turn, nuclear spin relaxation can be monitored through NMR relaxometry, which reports on the field dependence of the nuclear relaxation rates, opening a route to understand the physical processes at the origin of the Overhauser DNP in solution. The contributions of dipole–dipole and Fermi-contact interactions to paramagnetic relaxation are here described and shown to be responsible to both the relaxometry profiles and the DNP enhancements, so that the experimental access to the former can allow for predictions of the latter.     

Quantitative estimation of SPINOE enhancement in solid state

A theoretical approach to quantitatively estimate the spin polarization enhancement via spin polarization-induced nuclear Overhauser effect (SPINOE) in solid state is presented. We show that theoretical estimates from the model are in good agreement with published experimental results. This method provides a straightforward way to predict the enhanced factor of nuclear magnetic resonance signals in solid state experiments.     

Dynamic nuclear polarization in pulsed ENDOR experiments

Properly prepared pulse sequences of microwave and radio frequency have been employed to investigate the effect of polarization transfer from the polarized photo excited triplet state of pentacene in p-terphenyl crystals to the surrounding protons in pulsed ENDOR experiments. The ENDOR signal, measured as the change of electron spin echo (ESE) amplitude, is affected by the mode of RF pulses. When B0 parallelx (the long molecular axis), the ESE amplitude of the high-field transition of the triplet state changes from the maximum positive to zero with a pi RF pulse, and to the maximum negative with a 2pi pulse, while that of the low-field transition changes from nearly zero to the maximum negative as the RF pulse width increases. The effect is attributed to the strong electron spin polarization produced in the creation of the photoexcited triplet state and the subsequent efficient electron- nuclear polarization transfer process.     

Multiplet-to-net CIDEP conversion by MW-pulses with adiabatically ramped amplitude

ABSTRACT

A method is proposed to manipulate electron spin order of spin-correlated radical pairs. As radical pairs are often born in a well-defined spin state, e.g. in the singlet state, they acquire Chemically Induced Dynamic Electron Polarisation (CIDEP). In the case of singlet-state preparation CIDEP is of the multiplet (or anti-phase) type resulting in reduction of EPR (electron paramagnetic resonance) signals due to overlap of absorptive and emissive lines in the spectrum. Here we propose to convert the singlet spin order into net magnetisation of the radical pair by applying a microwave field, with its amplitude slowly (adiabatically) reduced to zero. We demonstrate that by properly choosing the microwave frequency one can completely convert the singlet order into net polarisation of the radical pair with significant enhancement of the signal as compared to multiplet CIDEP. Calculations show that the technique is operative for both weakly coupled and strongly coupled spin pairs. Potential applications of the method are discussed.     

Spin evolution in a radio frequency field studied through muon spin resonance

The application of composite inversion pulses to a novel area of magnetic resonance, namely muon spin resonance, is demonstrated. Results confirm that efficient spin inversion can readily be achieved using this technique, despite the challenging experimental setup required for beamline measurements and the short lifetime (≈2.2μs) associated with the positive muon probe. Intriguingly, because the muon spin polarisation is detected by positron emission, the muon magnetisation can be monitored during the radio-frequency (RF) pulse to provide a unique insight into the effect of the RF field on the spin polarisation. This technique is used to explore the application of RF inversion sequences under the non-ideal conditions typically encountered when setting up pulsed muon resonance experiments.