Toward a theory of nuclear relaxation in dielectric glasses at ultralow temperatures

The temperature and frequency dependence of the nuclear relaxation rate in dielectric glasses is investigated. It is shown that at low and ultralow temperatures nuclear relaxation is due to an interaction between the nuclear quadrupole moment and fluctuations of the electric field created by dipole moments of two-level systems. Fluctuations of this field can be associated with the background relaxation or are due only to the dipole-dipole interaction between two-level systems. It is shown that at lower temperatures the second relaxation mechanism begins to dominate. Expressions are obtained for the temperature and frequency of crossover between different nuclear relaxation regimes. The possibility of experimental confirmation of our results is discussed. Zh. éksp. Teor. Fiz. 115, 2254–2262 (June 1999) Russian Scientific Center “Kurchatov Institute”     

Effect of surface magnetism of solid-state substrates on the NMR of liquid 3He

The results of investigations of the longitudinal relaxation rate of the nuclear spins of liquid helium-3 in contact with finely dispersed LiYF₄ dielectric powders with various degrees of filling of the microcracks on the crystal surface by water molecules are reported. It is found that exchange correlations appear between paramagnetic defect centers on the surface as a result of spin-density transfer via the molecular orbitals of oxygen in the water molecule. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 7, 503–509 (10 April 1999)     

The reverse shift of the EPR line of paramagnetic centers coupled to species with a fast paramagnetic relaxation

The EPR spectrum of the spin 1/2 paramagnetic centers with a relatively slow relaxation is considered in the case when they are coupled via the Heisenberg exchange interaction to partners which have short times of the longitudinal and transverse paramagnetic relaxation. Under these conditions only the EPR line of paramagnetic centers with a relatively slow relaxation is detectable in experiment. The shape of this line is analyzed by solving numerically kinetic equations for the spin density matrix for simple model systems. Depending on a ratio between the exchange integral and the paramagnetic relaxation rates of partner spins, the EPR line shifts in opposite directions. For moderate relaxation rates, as the relaxation rates decrease, the EPR line shifts toward the gravity center of the total EPR spectrum. In the case of extremely fast relaxation, as the relaxation rates decrease, the reverse shift of the EPR line is expected, the line shifts away from the gravity center of the total EPR spectrum. This type of the non-monotonous line shift was experimentally observed for the monocrystal of [CuNd₂(C₄O₄)₄(H₂O)₁₆] · 2H₂O when relaxation rates were changed by temperature variation.     

Temperature and frequency dependence of the spin-lattice relaxation times of E′1 centers in neutron-irradiated quartz glass

Results are reported for measurements of the spin-lattice relaxation times of E′₁ centers in quartz glass, produced by neutron irradiation, with the measurements made at two frequencies 9.25 and 24.0 GHz over a wide temperature interval 1.5–300 K. The experimental data are interpreted on the basis of interaction mechanisms of the spins with two-level systems with excitation energies ∼6, ∼26, and ∼420 cm⁻¹. A small modification of the existing theory allows us to explain a number of features of the observed temperature and frequency dependence of the relaxation rate. The results are compared with the data available in the literature on spin-lattice relaxation of irradiation centers in crystalline quartz and quartz glass. Fiz. Tverd. Tela (St. Petersburg) 39, 1335–1337 (August 1997)     

Influence of Reversible and Irreversible Relaxation on the Single-Pulse Echo Signal

An analytical expression for a signal of the single-pulse echo generated in nonresonant pulse excitation of an inhomogeneously broadened two-level quantum system has been obtained, with the reversible and irreversible relaxation taken into account. It is shown that the rate of decay of the single-pulse echo is determined by the rate of reversible and irreversible transverse relaxation. It has been established that the contribution of the reversible and irreversible relaxations to decay of the single-pulse echo depends on the ratio between the detuning of the pulse-carrying frequency from resonance to the Rabi frequency. The difference between the times of transverse irreversible relaxation measured in manganese ferrite MnFe₂O₄ by the methods of single and two-pulse echo of nuclear magnetic resonance has been explained within the framework of the theoretical expressions obtained.     

<Superscript>29</Superscript>Si nuclear spin relaxation in microcrystals of plastically deformed Si: B samples

Single crystals and microcrystals Si: B enriched with ²⁹Si isotopes have been studied using nuclear magnetic resonance and electron paramagnetic resonance (EPR) in the temperature range from 300 to 800 K. It has been found that an increase in the temperature from 300 to 500 K leads to a change in the kinetics of the relaxation of the saturated nuclear spin system. At 300 K, the relaxation kinetics corresponds to direct electron–nuclear interaction with inhomogeneously distributed paramagnetic centers introduced by the plastic deformation of the crystals. At 500 K, the spin relaxation occurs through the nuclear spin diffusion and electron–nuclear interaction with an acceptor impurity. It has been revealed that the plastic deformation affects the EPR spectra at 9 K.     

Two-photon nutation excited in a two-level spin system by microwave and RF fields

Two-photon transient nutation is observed in a two-level spin system (E′₁ centers in crystalline quartz) using a transverse microwave field and a linearly polarized rf field oriented along a static magnetic field in the electron paramagnetic resonance. Nutation is excited when the sum of the energies of a microwave photon and a rf photon is equal to the energy difference between two spin states. The two-photon nature of nutation is confirmed by measuring its frequency as a function of the amplitude and frequency of the rf field as well as the amplitude of the microwave field. The amplitude of the effective field of two-photon transitions is measured. It is shown that the decay rate of two-photon nutation is close to the decay rate for one-photon nutation and is determined by the spin-spin interaction between E′₁ centers.     

Nuclear magnetic resonance study of ultrananocrystalline diamonds

We report on a nuclear magnetic resonance (NMR) study of ultrananocrystalline diamond (UNCD) materials produced by detonation technique. Analysis of the ¹³C and ¹H NMR spectra, spin-spin and spin-lattice relaxation times in purified UNCD samples is presented. Our measurements show that UNCD particles consist of a diamond core that is partially covered by a sp ²-carbon fullerene-like shell. The uncovered part of outer diamond surface comprises a number of hydrocarbon groups that saturate the dangling bonds. Our findings are discussed along with recent calculations of the UNCD structure. Significant increase in the spin-lattice relaxation rate (in comparison with that of natural diamond), as well as stretched exponential character of the magnetization recovery, are attributed to the interaction of nuclear spins with paramagnetic centers which are likely fabrication-driven dangling bonds with unpaired electrons. We show that these centers are located mainly at the interface between the diamond core and shell.     

Electrical Mobility Magnetic Resonance Spectroscopy (EMMRS)

A method to determine electrical mobility of charge carriers containing paramagnetic elements is presented. The motion-induced phase shift of the transverse magnetization component is observed by magnetic (nuclear or electron) resonance (MR). In fluid media, this method can determine the type of carriers and respective motion, lifetimes distribution, thermal and frequency dispersion of the mobility, translational relaxation rate and activation energies of these processes.

     

Spin relaxation of quadrupole nuclei in paramagnetic and magnetically ordered insulators

The longitudinal and transverse spin relaxation through a (generally anisotropic) electron-nucleus interaction in paramagnetic and magnetically ordered insulators is theoretically studied for nuclei with a resolved quadrupole structure. Expressions are derived for the relaxation rates of both the transverse nuclear magnetization components when individual transitions are excited in the quadrupole structure and the total longitudinal nuclear magnetization component. These expressions are reduced to a form that contains the Fourier transforms of the time correlation functions only for the electron spins. Given the specific form of these correlation functions corresponding to different phase states of the electron spins and different origins of their fluctuations, the temperature dependences of the nuclear relaxation rates are ascertained in various cases, including those for dipole and isotropic hyperfine interactions. Calculations are performed for arbitrary electron and half-integer nuclear spins by taking into account the possible quadrupole splitting of the NMR spectrum without any restriction on the smallness of the ratio ?ω s/k_BT (ω_s is the resonance frequency of the electron spins). The derived expressions are compared with available experimental data on the longitudinal and transverse nuclear relaxation in colossal-magnetoresistance lanthanum manganites in the part of their phase diagram where the corresponding samples are either paramagnetic or magnetically ordered insulators and near the points of transition to an ordered state. Interpretations alternative to the existing ones are offered.     

Decay of dipolar order in diamagnetic and paramagnetic proteins and protein gels

Magnetic relaxation in solids may be complicated by the creation and loss of dipolar order at finite rates. In tissues the molecular and spin dynamics may be significantly different because of the relatively high concentration of water. We have applied a modified Jeneer-Broekaert pulse sequence to measure dipolar relaxation rates in both dry and hydrated protein systems that may serve as magnetic models for tissue. In lyophilized and dry serum albumin, the dipolar relaxation time, T(1D) is on the order of 1 ms and is consistent with earlier reports. When hydrated by deuterium oxide, the dipolar relaxation times measured were on the order of tens of microseconds. When paramagnetic centers are included in the protein, the Jeneer-Broekaert echo decay times became the order of the decay time for transverse magnetization, i.e., the order of 10 micros or less. In the hydrated or paramagnetic systems, the dipolar relaxation times are too short to require inclusion in the quantitative analysis of magnetization transfer experiments.     

Relaxation mechanism in γ-ray-irradiated L-alanine studied by transfer saturation EPR and pulse EPR

Stable paramagnetic centers in γ-ray-irradiated L-alanine dosimeters exhibit a maximum in relaxation rate in the vicinity of 190 K. The mechanism of this relaxation rate has been investigated on the first stable alanine radical center, SARI, by employing continuous-wave transfer saturation electron paramagnetic resonance and pulse electron paramagnetic resonance techniques. The detected in-phase and out-of-phase spectra as well as phase memory times,T _M, indicate that besides the well-known τ_p of the CH₃ group of SAR1 an additional correlation time, τ_l (ΔElk=2689±50 K and 0 τ₁₀ = 0.15 ± 0.03 ps), is involved in the transverse relaxation process and effects the SAR1 center. For the SAR1 center this mechanism originates from the hindered motion of undamaged CH₃ and NH ₃ ⁺ groups in the lattice. The motion of these groups additionally effects the spectrum of the SAR1 center through averaging out of the anisotropic splitting.     

Modulation of the distance dependence of paramagnetic relaxation enhancements by CSA × DSA cross-correlation

Paramagnetic metal ions with fast-relaxing electronic spin and anisotropic susceptibility tensor provide a rich source of structural information that can be derived from pseudo-contact shifts, residual dipolar couplings, dipole-dipole Curie spin cross-correlation, and paramagnetic relaxation enhancements. The present study draws attention to a cross-correlation effect between nuclear relaxation due to anisotropic chemical shielding (CSA) and due to the anisotropic dipolar shielding (DSA) caused by the electronic Curie spin. This CSA x DSA cross-correlation contribution seems to have been overlooked in previous interpretations of paramagnetic relaxation enhancements. It is shown to be sufficiently large to compromise the 1/r6 distance dependence usually assumed. The effect cannot experimentally be separated from auto-correlated DSA relaxation. It can increase or decrease the observed paramagnetic relaxation enhancement. Under certain conditions, the effect can dominate the entire paramagnetic relaxation, resulting in nuclear resonances narrower than in the absence of the paramagnetic center. CSAxDSA cross-correlation becomes important when paramagnetic relaxation is predominantly due to the Curie rather than the Solomon mechanism. Therefore the effect is most pronounced for relaxation by metal ions with large magnetic susceptibility and fast-relaxing electron spin. It most strongly affects paramagnetic enhancements of transverse relaxation in macromolecules and of longitudinal relaxation in small molecules.     

Modulation of the distance dependence of paramagnetic relaxation enhancements by CSA x DSA cross-correlation

Paramagnetic metal ions with fast-relaxing electronic spin and anisotropic susceptibility tensor provide a rich source of structural information that can be derived from pseudo-contact shifts, residual dipolar couplings, dipole-dipole Curie spin cross-correlation, and paramagnetic relaxation enhancements. The present study draws attention to a cross-correlation effect between nuclear relaxation due to anisotropic chemical shielding (CSA) and due to the anisotropic dipolar shielding (DSA) caused by the electronic Curie spin. This CSA x DSA cross-correlation contribution seems to have been overlooked in previous interpretations of paramagnetic relaxation enhancements. It is shown to be sufficiently large to compromise the 1/r6 distance dependence usually assumed. The effect cannot experimentally be separated from auto-correlated DSA relaxation. It can increase or decrease the observed paramagnetic relaxation enhancement. Under certain conditions, the effect can dominate the entire paramagnetic relaxation, resulting in nuclear resonances narrower than in the absence of the paramagnetic center. CSAxDSA cross-correlation becomes important when paramagnetic relaxation is predominantly due to the Curie rather than the Solomon mechanism. Therefore the effect is most pronounced for relaxation by metal ions with large magnetic susceptibility and fast-relaxing electron spin. It most strongly affects paramagnetic enhancements of transverse relaxation in macromolecules and of longitudinal relaxation in small molecules.     

Defects and impurities in nanodiamonds: EPR, NMR and TEM study

EPR, ¹³C NMR and TEM study of ultradisperse diamond (UDD) samples is reported. The compounds show a high concentration of paramagnetic centers (up to 10²⁰ spin/g), which are due to structural defects (dangling C-C bonds) on the diamond cluster surface. The anomalous reduction in the spin-lattice relaxation time of ¹³C (from several hours in natural diamond to ∼150 ms in UDD clusters) is attributed to the interaction between the unpaired electrons of the paramagnetic centers and nuclear spins. ¹³C NMR line-width reflects the fact that the structure of the UDD surface is distorted in comparison to the ‘bulk’ diamond structure.     

Longitudinal muon spin relaxation in muonium-like systems

Nuclear spin-lattice relaxation in paramagnetic systems is treated using the classic expression for transition probability between the coupled electron and nuclear spin states. The rate equations governing the incoherent occupancies of these states are solved analytically (where possible) and numerically (where not) to construct the relaxation function for the nuclear spin. The method is illustrated for muonium, and the muonium-substituted molecular radicals, for the case of perturbation due to fluctuation of the local field,i.e. modulation of the interaction with a third spin. A slight departure from single exponential behaviour is demonstrated for slow fluctuations.     

The Effect of Curing Temperature on Early Hydration of Gray Cement Via Fast Field Cycling-NMR Relaxometry

In the present work, we use fast field cycling (FFC) nuclear magnetic resonance relaxometry to evaluate the influence introduced by the curing temperature on the hydration process of gray cement. The main advantage of FFC relaxometry as compared with other relaxation studies performed at a specific frequency is that it is sensitive to a wider range of molecular motions and better separates the surface and bulk contributions from the global measured relaxation rate. In the case of cement hydration, the relaxation process is dominated by the interaction of water protons with the paramagnetic centers located on the surface of cement grains. This allows us in the frame of a two-phase exchange model to monitor the temperature dependence of the transverse diffusional correlation time at the surface of cement grains. An increase of the surface diffusion coefficient of water molecules with the temperature was revealed. Another outcome is that the surface-to-volume ratio of capillary pores continuously increases during the early hydration and this process is strongly enhanced by rising the temperature.     

13C spin-lattice relaxation in natural diamond: Zeeman relaxation at 4.7 T and 300 K due to fixed paramagnetic nitrogen defects

13C spin-lattice relaxation times in the laboratory frame, ranging from 1.4 to 36 h, have been measured on a suite of five natural type Ia and Ib diamonds at 4.7 T and 300 K. 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. Spin-lattice relaxation behavior of 13C in diamonds containing paramagnetic P1, P2, N2. and N3 centers are discussed. Depending on the paramagnetic impurity types and concentrations present in each diamond, three different nuclear spin-lattice relaxation (SLR) paths exist, namely that due to electron SLR mechanisms and two types of three-spin processes (TSPs). The one three-spin process (TSP1) involves a simultaneous transition of two electron spins belonging to the same hyperfine EPR line and a flip of a 13C spin, while the other process (TSP2) 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 is field dependent, thus forming a bottleneck in the 13C relaxation path due to TSP1 at high magnetic fields.     

Anomalous nuclear spin–lattice relaxation of <Superscript>3</Superscript>Не in contact with ordered Al<Subscript>2</Subscript>O<Subscript>3</Subscript> aerogel

Spin–lattice relaxation of ³Не in contact with the ordered Al₂O₃ fiber aerogel has been studied at the temperature of 1.6 K in fields of 0.1–0.5 T by the pulsed nuclear magnetic resonance (NMR) method. An additional mechanism of the relaxation of ³Не in aerogels is found and it is shown that this relaxation mechanism is not associated with the adsorbed layer. A hypothesis about the influence of intrinsic paramagnetic centers on the relaxation of gaseous ³Не is proposed.     

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.