Spectral diffusion of electron spin polarization in glasses doped with radicals for DNP.

Spectral diffusion of electron spin polarization plays a key part in dynamic nuclear polarization (DNP). It determines the distribution of polarization across the electron spin resonance (ESR) line and consequently the polarization that is available for transfer to the nuclear spins. Various authors have studied it experimentally by means of electron-electron double resonance (ELDOR) and proposed and used macroscopic models to interpret these experiments. However, microscopic models predicting the rate of spectral diffusion are scarce. The present article is an attempt to fill this gap. It derives a spectral diffusion equation from first principles and uses Monte Carlo simulations to determine the parameters in this equation. The derivation given here builds on an observation made in a previous article on nuclear dipolar relaxation: spectral diffusion is also spatial diffusion and the random distribution of spins in space limits the former. This can be modelled assuming that rapid flip-flop transitions between a spin and its nearest neighbour do not contribute to diffusion of polarization across the ESR spectrum. The present article presents predictions of the spectral diffusion constant and shows that this limitation may lower the spectral diffusion constant by several orders of magnitude. As a check the constant is determined from first principles for a sample containing 40 mM TEMPOL. Including the limitation then results in a value that is close to that obtained from an analysis of previously reported ELDOR experiments.

Nuclear dipolar relaxation induced by interacting ground state electron spins.

In samples used for dynamic nuclear polarization (DNP), spin-lattice relaxation times are usefully increased by going to high magnetic field and low temperature, typically several tesla and below 1 K. But the relaxation times for dipolar components of the nuclear spin energy remain stubbornly shorter than those for the Zeeman energy: dipolar order decays faster than the polarization itself by a huge factor-up to four orders of magnitude or more in the materials studied thus far. Such fast nuclear dipolar relaxation poses experimental challenges, for instance, when transferring polarization between different nuclear spin species via intermediate nuclear order: a proven technique to polarize rare nuclear spins. The origin of this fast nuclear dipolar relaxation remained a mystery for a long time-existing theories of nuclear spin-lattice relaxation could at best predict about one order of magnitude difference between the nuclear dipolar and nuclear Zeeman relaxation rates-until it was recently discovered to be due to conversion of nuclear dipolar energy into super-hyperfine energy induced by nuclear flip-flop transitions. A previous article showed that the inclusion of this relaxation path enables a quantitative explanation of nuclear dipolar relaxation induced by photo-excited triplet states. This article extends the theory to nuclear dipolar relaxation induced by ground state electron spins and demonstrates that this new mechanism enables a precise quantitative prediction from first principles of the nuclear dipolar relaxation rate for Ca(OH)2 doped with O2- centres-in which DNP is caused by the solid effect (SE)-and LiF doped with F-centres-in which DNP is caused by thermal mixing (TM)-both at 5.5 T and 0.4 K. It is noticed that the proposed mechanism extends to other spin systems which has implications for e.g. TM and spectral diffusion.

Direct measurement of the triple spin flip rate in dynamic nuclear polarization.

A previous study of the effect of Gadolinium doping on the dynamic polarization (DNP) of 13C using trityls showed that the rate at which the polarization builds up is almost independent of the Gadolinium concentration, while the electron spin-lattice relaxation rate varies over an order of magnitude. In this paper we analyze the polarization build-up in detail and show that in this case DNP is due to the cross-effect (CE) and that the build-up rate can be quantitatively interpreted as the rate of the triple spin flips responsible for the CE. Thus this build-up rate presents a direct measurement of this triple spin flip rate.

Dynamic nuclear polarization via the cross effect and thermal mixing: B. Energy transport.

The fundamental process of dynamic nuclear polarization (DNP) via the cross effect (CE) and thermal mixing (TM) is a triple spin flip, in which two interacting electron spins and a nuclear spin interacting with one of these electron spins flip together. In the previous article (Wenckebach, 2018) these triple spin flips were treated by first determining the eigenstates of the two interacting electron spins exactly and next investigating transitions involving these exact eigenstates and the nuclear spin states. It was found that two previously developed approaches-the scrambled states approach and the fluctuating field approach-are just two distinct limiting cases of this more general approach. It was also shown that triple spin flips constitute a single process causing two flows of energy: a flow originating in the electron Zeeman energy and a flow originating in the mutual interactions between the electron spins. In order to render their definitions more precise, the former flow was denoted as the CE and the latter as TM. In this article the treatment is extended to a glass containing NI equivalent nuclear spins I=12 and NS randomly distributed and oriented electron spins S=12. Rate equations are derived for the two flows of energy to the nuclear spins. The flow originating in the electron Zeeman energy-i.e. the CE-is found to lead to the same stationary state as was previously predicted by the scrambled states approach, though the rate may be smaller due to limitations imposed by conservation of energy. The flow originating in the mutual interactions between the electron spins-i.e. TM-is found to involve the full spectrum of the mutual interactions between the electron spins, while the fluctuating field approach only accounts for the component of this spectrum at the nuclear magnetic resonance (NMR) frequency. Still, TM is found to induce equal spin temperature for different nuclear spin species during nuclear spin-lattice relaxation and, at least in some cases also during polarization. It is also confirmed that TM couples local nuclear spins near the electron spins so strongly to the mutual interactions between electron spins, that they may constitute a single energy reservoir (Cox et al., 1973). Hence such local nuclear spins may have to be included in treatments of the dynamics of the electron spins.

Dynamic nuclear polarization via the cross effect and thermal mixing: A. The role of triple spin flips.

In dynamic nuclear polarization (DNP) via the cross effect (CE) and thermal mixing (TM) a microwave field first reduces the polarization of some electron spins, so the electron spin system deviates from thermal equilibrium with the lattice. Next, the mutual interactions combine with their interaction with the nuclear spins to transform this deviation into nuclear spin polarization. Two approaches were introduced to describe the latter process. The fluctuating field approach considers the electron spins to fluctuate between their up and down states due to their mutual interactions. This results in a classical fluctuating field at the position of the nuclear spins, and the component of this field at the NMR frequency induces flips of the nuclear spins. The scrambled states approach considers the electron and nuclear spin states to be mixed by the hyperfine and super-hyperfine interaction. Next the mutual interaction between the electron spins induces transitions between these mixed states and thus flips nuclear spins. Some authors considered the fluctuating field approach and the scrambled states approach to be just two equivalent methods to describe exactly the same process. Other authors considered the two approaches to describe two separate processes, the former exchanging electron interaction energy, the latter transferring differences of electron spin polarization to the nuclear spins. The present work introduces a generalized approach that first calculates the mixing of electron spin states exactly. Next it considers the hyperfine or super-hyperfine interaction to induce transitions involving these mixed states and the nuclear spin states. It is found that the scrambled states approach and the fluctuating field approach are neither fully equivalent, nor completely independent processes, but rather represent two distinct limits of a single process. The former corresponding to very weak mutual interactions between electron spins and the latter to very strong mutual interactions. It extends the treatment to the whole range of mutual interactions and shows that this single process simultaneously exchanges electron Zeeman energy and electron interaction energy with the nuclear spins. Expressions for these two flows as a function of the strength of the mutual interaction are derived.

Spectral diffusion and dynamic nuclear polarization: Beyond the high temperature approximation.

Dynamic Nuclear Polarization (DNP) has proven itself most powerful for the orientation of nuclear spins in polarized targets and for hyperpolarization in magnetic resonance imaging (MRI). Unfortunately, the theoretical description of some of the processes involved in DNP invokes the high temperature approximation, in which Boltzmann factors are expanded up to first order, while the high electron and nuclear spin polarization required for many applications do not justify such an approximation. A previous article extended the description of one of the mechanisms of DNP-thermal mixing-beyond the high temperature approximation (Wenckebach, 2017). But that extension is still limited: it assumes that fast spectral diffusion creates a local equilibrium in the electron spin system. Provotorov's theory of cross-relaxation enables a consistent further extension to slower spectral diffusion, but also invokes the high temperature approximation. The present article extends the theory of cross-relaxation to low temperature and applies it to spectral diffusion in glasses doped with paramagnetic centres with anisotropic g-tensors. The formalism is used to describe DNP via the mechanism of the cross effect. In the limit of fast spectral diffusion the results converge to those obtained in Wenckebach (2017) for thermal mixing. In the limit of slow spectral diffusion a hole is burnt in the electron spin resonance (ESR) signal, just as predicted by more simple models. The theory is applied to DNP of proton and 13C spins in samples doped with the radical TEMPO.

Dynamic nuclear polarization via thermal mixing: Beyond the high temperature approximation.

Dynamic Nuclear Polarization (DNP) via the mechanism of thermal mixing has proven itself most powerful for the orientation of nuclear spins in polarized targets and hyperpolarization for magnetic resonance imaging (MRI). Unfortunately, theoretical descriptions of this mechanism have been limited to using-at least partially-the high temperature approximation, in which Boltzmann factors are expanded linearly. However, the high nuclear spin polarization required and obtained for these applications does not justify such approximations. This article extends the description of thermal mixing beyond the high temperature approximation, so Boltzmann factors are not expanded. It applies for DNP in samples doped with paramagnetic centres, for which the electron spin resonance spectrum is mainly inhomogeneously broadened by g-value anisotropy. It verifies Provotorov's hypothesis that fast spectral diffusion leads to a density matrix containing two inverse spin temperatures: the inverse electron Zeeman temperature and the inverse electron non-Zeeman temperature, while thermal mixing equalizes the nuclear Zeeman temperature and the electron non-Zeeman temperature. Equations are derived for the evolution of these temperatures and the energy flows between the spins and the lattice. Solutions are given for DNP of proton spins in samples doped with the radical TEMPO.

An apparatus for pulsed ESR and DNP experiments using optically excited triplet states down to liquid helium temperatures.

In standard Dynamic Nuclear Polarization (DNP) electron spins are polarized at low temperatures in a strong magnetic field and this polarization is transferred to the nuclear spins by means of a microwave field. To obtain high nuclear polarizations cryogenic equipment reaching temperatures of 1 K or below and superconducting magnets delivering several Tesla are required. This equipment strongly limits applications in nuclear and particle physics where beams of particles interact with the polarized nuclei, as well as in neutron scattering science. The problem can be solved using short-lived optically excited triplet states delivering the electron spin. The spin is polarized in the optical excitation process and both the cryogenic equipment and magnet can be simplified significantly. A versatile apparatus is described that allows to perform pulsed dynamic nuclear polarization experiments at X-band using short-lived optically excited triplet sates. The efficient (4)He flow cryostat that cools the sample to temperatures between 4 K and 300 K has an optical access with a coupling stage for a fiber transporting the light from a dedicated laser system. It is further designed to be operated on a neutron beam. A combined pulse ESR/DNP spectrometer has been developed to observe and characterize the triplet states and to perform pulse DNP experiments. The ESR probe is based on a dielectric ring resonator of 7 mm inner diameter that can accommodate cubic samples of 5mm length needed for neutron experiments. NMR measurements can be performed during DNP with a coil integrated in the cavity. With the presented apparatus a proton polarization of 0.5 has been achieved at 0.3 T.

A terahertz system using semi-large emitters: noise and performance characteristics.

We have built a relatively simple, highly efficient, terahertz (THz) emission and detection system centred around a 15 fs Ti:sapphire laser. In the system, 200 mW of laser power is focused on a 120 microm diameter spot between two silverpaint electrodes on the surface of a semi-insulating GaAs crystal, kept at a temperature near 300 K, biased with a 50 kHz, +/- 400 V square wave. Using rapid delay scanning and lock-in detection at 50 kHz, we obtain probe laser quantum-noise limited signals using a standard electro-optic detection scheme with a 1 mm thick (110) oriented ZnTe crystal. The maximum THz-induced differential signal that we observe is deltaP/P = 7 x 10(-3), corresponding to a THz peak amplitude of 95 V cm(-1). The THz average power was measured to be about 40 microW, to our knowledge the highest power reported so far generated with Ti:sapphire oscillators as a pump source. The system uses off-the-shelf electronics and requires no microfabrication techniques.