The matrix formalism for generalised gradients with time-varying orientation in diffusion NMR

Protein backbone 15N NMR spin relaxation rates are useful in characterizing the protein dynamics and structures. To observe the protein nuclear-spin resonances a pulse sequence has to include a water suppression scheme. There are two commonly employed methods, saturating or dephasing the water spins with pulse field gradients and keeping them unperturbed with flip-back pulses. Here different water suppression methods were incorporated into pulse sequences to measure 15N longitudinal T1 and transversal rotating-frame T1ρ spin relaxation. Unexpectedly the 15N T1 relaxation time constants varied significantly with the choice of water suppression method. For a 25-kDa Escherichiacoli. glutamine binding protein (GlnBP) the T1 values acquired with the pulse sequence containing a water dephasing gradient are on average 20% longer than the ones obtained using a pulse sequence containing the water flip-back pulse. In contrast the two T1ρ data sets are correlated without an apparent offset. The average T1 difference was reduced to 12% when the experimental recycle delay was doubled, while the average T1 values from the flip-back measurements were nearly unchanged. Analysis of spectral signal to noise ratios (s/n) showed the apparent slower 15N relaxation obtained with the water dephasing experiment originated from the differences in 1HN recovery for each relaxation time point. This in turn offset signal reduction from 15N relaxation decay. The artifact becomes noticeable when the measured 15N relaxation time constant is comparable to recycle delay, e.g., the 15N T1 of medium to large proteins. The 15N relaxation rates measured with either water suppression schemes yield reasonable fits to the structure. However, data from the saturated scheme results in significantly lower Model-Free order parameters (=0.81) than the non-saturated ones (=0.88), indicating such order parameters may be previously underestimated.     

Will spin-relaxation times in molecular magnets permit quantum information processing?

Using X-band pulsed electron-spin resonance, we report the intrinsic spin-lattice (T1) and phase-coherence (T2) relaxation times in molecular nanomagnets for the first time. In Cr7M heterometallic wheels, with M=Ni and Mn, phase-coherence relaxation is dominated by the coupling of the electron spin to protons within the molecule. In deuterated samples T2 reaches 3 micros at low temperatures, which is several orders of magnitude longer than the duration of spin manipulations, satisfying a prerequisite for the deployment of molecular nanomagnets in quantum information applications.     

Low-frequency spin fluctuations in Skyrmions confined by wires: measurements of local nuclear spin relaxation

We investigate low-frequency electron spin dynamics in a quantum Hall system with wire confinement by nuclear spin relaxation measurements. We developed a technique to measure the local nuclear spin relaxation rate T(1)(-1). T(1)(-1) is enhanced on both sides of the local filling factor ν(wire)=1, reflecting low-frequency fluctuations of electron spins associated with Skyrmions inside the wire. As the wire width is decreased, the fast nuclear spin relaxation is suppressed in a certain range of Skyrmion density. This suggests that the multi-Skyrmion state is modified and the low-frequency spin fluctuations are suppressed by the wire confinement.     

The effect of spin relaxation on ENDOR spectra recorded at high magnetic fields and low temperatures

A simple theoretical model that describes the pulsed Davies electron-nuclear double resonance (ENDOR) experiment for an electron spin S = (1/2) coupled to a nuclear spin I = (1/2) was developed to account for unusual W-band (95 GHz) ENDOR effects observed at low temperatures. This model takes into account the thermal polarization along with all internal relaxation processes in a four-level system represented by the electron- and nuclear-spin relaxation times T(1e) and T(1n), respectively, and the cross-relaxation time, T(1x). It is shown that under conditions of sufficiently high thermal spin polarization, nuclei can exhibit asymmetric ENDOR spectra in two cases: the first when t(mix) > T(1e) and T(1n), T(1x) > T(1e), where ENDOR signals from the alpha manifold are negative and those of the beta manifold positive, and the second when the cross- and/or nuclear-relaxation times are longer than the repetition time (t(mix) < T(1e) < t(R) and T(1n), T(1x) > t(R)). In that case the polarization of the ENDOR signals becomes opposite to the previous case, the lines in the alpha manifolds are positive, and those of the beta manifold are negative. This case is more likely to be encountered experimentally because it does not require a very long mixing time and is a consequence of the saturation of the nuclear transitions. Using this model the experimental t(mix) and t(R) dependencies of the W-band (1)H ENDOR amplitudes of [Cu(imidazole)(4)]Cl(2) were reproduced and the values of T(1e) and T(1x) > T(1e) were determined. The presence of asymmetry in the ENDOR spectrum is useful as it directly provides the sign of the hyperfine coupling. The presented model allows the experimentalist to adjust experimental parameters, such as t(mix) and t(R), in order to optimize the desired appearance of the spectrum.     

Spin diffusion of dipolar energy in NQR

The theory of spin diffusion was extended to the case of nuclear dipolar order in solids containing paramagnetic impurities and nuclei with spin I > 1/2 having nuclear quadrupole moment. We show that spin diffusion process of dipolar order takes place in solids containing paramagnetic impurities. At the start of relaxation process, the direct relaxation regime is realized with non-exponential time dependence. Then the relaxation regime will be changed to diffusion-limited one. Using obtained expressions for the spin lattice relaxation times for these two relaxation regimes, the diffusion coefficient of the dipolar order in nuclear quadrupole resonance can be estimated from experimental data.     

Evidence for skyrmion crystallization from NMR relaxation experiments

A resistively detected NMR technique was used to probe the two-dimensional electron gas in a GaAs/AlGaAs quantum well. The spin-lattice relaxation rate (1/T(1)) was extracted at near complete filling of the first Landau level by electrons. The nuclear spin of (75)As is found to relax much more efficiently with T --> 0 and when a well developed quantum Hall state with R(xx) approximately 0 occurs. The data show a remarkable correlation between the nuclear spin relaxation and localization. This suggests that the magnetic ground state near complete filling of the first Landau level may contain a lattice of topological spin texture, i.e., a Skyrmion crystal.     

Temperature dependence of nuclear magnetization and relaxation

The temperature dependences of nuclear magnetization and relaxation rates are reviewed theoretically and experimentally in order to quantify the effects of temperature on NMR signals acquired by common imaging techniques. Using common sequences, the temperature dependences of the equilibrium nuclear magnetization and relaxation times must each be considered to fully understand the effects of temperature on NMR images. The temperature dependence of the equilibrium nuclear magnetization is negative because of Boltzmann's distribution for all substances at all temperatures, but the combined temperature dependences of the equilibrium magnetization and relaxation can be negative, weak or positive depending on the temperature (T), echo time (T(E)), repetition time (T(R)), and the temperature dependences of the relaxation times T(1)(T) and T(2)(T) in a pulse sequence. As a result, the magnitude of the NMR signal from a given substance can decrease, increase or stay somewhat constant with increasing temperature. Nuclear thermal coefficients are defined and predictions for spin echo and other simple sequences are verified experimentally using a number of substances representing various thermal and NMR properties.     

Direct observation of the electron spin relaxation induced by nuclei in quantum dots

We have studied the electron spin relaxation in semiconductor InAs/GaAs quantum dots by time-resolved optical spectroscopy. The average spin polarization of the electrons in an ensemble of p-doped quantum dots decays down to 1/3 of its initial value with a characteristic time T(Delta) approximately 500 ps, which is attributed to the hyperfine interaction with randomly oriented nuclear spins. We show that this efficient electron spin relaxation mechanism can be suppressed by an external magnetic field as small as 100 mT.     

Electron paramagnetic resonance study of the nuclear spin dynamics in an AlAs quantum well

The nuclear spin dynamics in an asymmetrically doped 16-nm AlAs quantum well grown along the [001] direction has been studied experimentally using the time decay of the Overhauser shift of paramagnetic resonance of conduction electrons. The nonzero spin polarization of nuclei causing the initial observed Overhauser shift is due the relaxation of the nonequilibrium spin polarization of electrons into the nuclear subsystem near electron paramagnetic resonance owing to the hyperfine interaction. The measured relaxation time of nuclear spins near the unity filling factor is (530 ± 30) min at the temperature T = 0.5 K. This value exceeds the characteristic spin relaxation times of nuclei in GaAs/AlGaAs heterostructures by more than an order of magnitude. This fact indicates the decrease in the strength of the hyperfine interaction in the AlAs quantum well in comparison with GaAs/AlGaAs heterostructures.     

Coulomb "Blockade" of nuclear spin relaxation in quantum dots

We study the mechanism of nuclear spin relaxation in quantum dots due to the electron exchange with the 2D gas. We show that the nuclear spin relaxation rate 1/T(1) is dramatically affected by the Coulomb blockade (CB) and can be controlled by gate voltage. In the case of strong spin-orbit (SO) coupling the relaxation rate is maximal in the CB valleys, whereas for the weak SO coupling the maximum of 1/T(1) is near the CB peaks.     

Spin relaxation and decoherence of holes in quantum dots

We investigate heavy-hole spin relaxation and decoherence in quantum dots in perpendicular magnetic fields. We show that at low temperatures the spin decoherence time is 2 times longer than the spin relaxation time. We find that the spin relaxation time for heavy holes can be comparable to or even longer than that for electrons in strongly two-dimensional quantum dots. We discuss the difference in the magnetic-field dependence of the spin relaxation rate due to Rashba or Dresselhaus spin-orbit coupling for systems with positive (i.e., GaAs quantum dots) or negative (i.e., InAs quantum dots) g factor.     

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.     

Foreign gas broadening of an IR absorption line of formaldehyde

The theory of nuclear spin state relaxation of symmetrical molecules like formaldehyde contains a collision time t_c that is interpreted as time between rotationally inelastic molecular collisions. This time traditionally is determined from measurements of pressure broadening of spectral lines. In order to test whether these collision times, which determine spin relaxation rate constants and line broadening coefficients, respectively, are the same or at least related to another, we have performed systematic measurements of the broadening of an IR line of formaldehyde by other gases of different pressures.     

Electrical control of spin relaxation in a quantum dot

We demonstrate electrical control of the spin relaxation time T1 between Zeeman-split spin states of a single electron in a lateral quantum dot. We find that relaxation is mediated by the spin-orbit interaction, and by manipulating the orbital states of the dot using gate voltages we vary the relaxation rate W identical withT1(-1) by over an order of magnitude. The dependence of W on orbital confinement agrees with theoretical predictions, and from these data we extract the spin-orbit length. We also measure the dependence of W on the magnetic field and demonstrate that spin-orbit mediated coupling to phonons is the dominant relaxation mechanism down to 1 T, where T1 exceeds 1 s.     

Comparison of electron spin relaxation times measured by Carr-Purcell-Meiboom-Gill and two-pulse spin-echo sequences

Electron spin relaxation times obtained by two-pulse spin-echo and Carr-Purcell-Meiboom-Gill (CPMG) experiments were compared for samples with: (i) low concentrations of nuclear spins, (ii) higher concentrations of nuclear spins and low concentrations of unpaired electrons, (iii) higher concentrations of nuclear spins and of electron spins, and (iv) dynamic averaging of inequivalent hyperfine couplings on the EPR timescale. In each case, the CPMG time constant decreased as the time between the refocusing pulses increased. For the samples with low concentrations of nuclear spins (the E' center in irradiated amorphous SiO2) the limiting value of the CPMG time constant at short interpulse spacings was similar to the Tm obtained by two-pulse spin echo at small turning angle. For the other samples, the time constants obtained by CPMG at short interpulse spacings were systematically longer than Tm obtained by two-pulse spin echo. For most of the samples, the CPMG time constant decreased with increasing electron spin concentration, which is consistent with the expectation that the CPMG sequence does not refocus dephasing due to electron-electron dipolar interaction between resonant spins. Dynamic processes that average inequivalent hyperfine couplings contributed less to the CPMG time constant than to the spin-echo decay time constant. The impact of nuclear echo envelope modulation on CPMG time constants also was examined. For a Nycomed trityl radical in glassy D2O:glycerol-d8 solution, the CPMG time constant was up to 20 times longer when the time between pulses was approximately equal to integer multiples of the reciprocal of the deuterium Larmor frequency than when the time between pulses was an odd multiple of half the reciprocal of the deuterium Larmor frequency.     

Electron spin relaxation of radicals in γ-irradiated malonic acid and methyl malonic acid

Radicals generated by γ-irradiation of malonic acid and methyl malonic acid were studied as a function of temperature by inversion recovery, echo-detected saturation recovery and electron-electron double resonance (ELDOR) at X-band, and by continuous-wave saturation recovery at X-band and S-band. ELDOR reductions for malonic acid radical in polycrystalline and single-crystal samples indicate that nuclear spin relaxation is faster than both electron spin relaxation and cross relaxation between 93 and 233 K. Deuteration of the carboxylate protons caused the maximum ELDOR reduction to shift from about 110 to 150 K, consistent with the assignment of the rapid nuclear spin relaxation to hydrogen-bonded proton dynamics. ELDOR enhancements for both radicals formed in methyl malonic acid indicate that cross relaxation is faster than both electron spin relaxation and nuclear spin relaxation between 77 and 220 K. Enhanced cross relaxation and electron spin relaxation are attributed to the rotation of methyl groups at a rate comparable to the electron Larmor frequency. The temperature dependence of the enhancement of 1/T _1e was analyzed to determine the activation energies for methyl rotation. The same radical is formed in irradiated methyl malonic acid and L-alanine, but the barrier to rotation of the α-methyl is 500 K in the methyl malonic acid host and 1500 K in the L-alanine host, which indicates a large impact of the lattice on the barrier to rotation.     

Theory of the electron and nuclear spin coherence times of shallow donor spin qubits in isotopically and chemically purified zinc oxide

In this article, I present a theoretical study of the electron and nuclear spin coherence times of shallow donor spin qubits in zinc oxide (ZnO) at low temperature. The influence of different spin-phonon processes as well as different spin-spin processes on the spin coherence time of shallow donors in ZnO is considered, both in the case of an electron spin qubit and in the case of a nuclear spin qubit encoded on a shallow donor. It is estimated that the electron spin coherence time of an isolated indium shallow donor in natural quasi-intrinsic ZnO is on the order of hundreds of microseconds, limited by the nuclear spectral diffusion process. The electron spin coherence time of an isolated indium shallow donor can be extended to few milliseconds in isotopically and chemically purified quasi-intrinsic ZnO. In this optimal case, the electron spin coherence time of an isolated indium shallow donor is only limited by a spin-lattice decoherence process. It is also estimated that the nuclear spin coherence time of an isolated indium shallow donor in natural quasi-intrinsic ZnO is on the order of hundreds of milliseconds, limited by the nuclear spectral diffusion process. The nuclear spin coherence time of an isolated indium shallow donor can be extended to few seconds in isotopically and chemically purified quasi-intrinsic ZnO. In this optimal case, the nuclear spin coherence time of an isolated indium shallow donor is only limited by the cross relaxation decoherence process. This study thus shows the great potential of electron and nuclear spin qubits encoded on shallow donors in isotopically and chemically purified quasi-intrinsic ZnO for the implementation of quantum processor and/or quantum memories.     

Electrically detected electron spin resonance in a high-mobility silicon quantum well

The resistivity change due to electron spin resonance (ESR) absorption is investigated in a high-mobility two-dimensional electron system formed in a Si/SiGe heterostructure. Results for a specific Landau level configuration demonstrate that the primary cause of the ESR signal is a reduction of the spin polarization, not the effect of electron heating. The longitudinal spin relaxation time T1 is obtained to be of the order of 1 ms in an in-plane magnetic field of 3.55 T. The suppression of the effect of the Rashba fields due to high-frequency spin precession explains the very long T1.     

Spectral densities and nuclear spin relaxation in solids

We investigate the properties of ten spectral densities relevant for nuclear spin relaxation studies in solids. This is preceded by a brief review of nuclear spin relaxation in solids which includes a discussion of the appropriate spin-dependent interactions and the various relaxation rates which can be measured. Also, the link between nuclear spin relaxation and dielectric relaxation is discussed. Where possible and/or appropriate each of the spectral densities is expressed as a continuous distribution of Bloembergen-Purcell-Pound (or Debye) spectral densities 2ξ /(1 + ξ² ω²) for nuclear Larmor angular frequency ω and correlation time ξ. The spectral densities are named after their originators or the shape of the distributions of correlation times or both and are (1) Bloembergen-Purcell-Pound or δ-function, (2) Havriliak-Negami, (3) Cole-Cole, (4) Davidson-Cole, (5) Fang, (6) Fuoss-Kirkwood, (7) Bryn Mawr, (8) Wagner or log-Gaussian, (9) log-Lorentzian, and (10) Fröhlich or energy box. The Havriliak-Negami spectral density is related to the Dissado-Hill theory for dielectric relaxation. The spectral densities are expressed in a way which makes them easy to compare with each other and with experimental data. Many plots of the distributions of correlation times and of the spectral densities vs. various correlation times characterizing the distributions are given.     

Metamagnetic quantum criticality revealed by 17O-NMR in the itinerant metamagnet Sr3Ru2O7

We have investigated the spin dynamics using 17O-NMR in the bilayered perovskite Sr3Ru2O7, which sits close to a metamagnetic quantum critical point. The nuclear spin-lattice relaxation rate divided by temperature 1/T1T is enhanced on approaching the metamagnetic critical field of approximately 7.9 T, and at the critical field 1/T1T continues to increase and does not show Fermi-liquid behavior down to 0.3 K. The temperature dependence of T1T in this region suggests the critical temperature Theta to be approximately 0 K, which is strong evidence that the spin dynamics possesses a quantum critical character. Comparison between uniform susceptibility and 1/T1T reveals that antiferromagnetic fluctuations instead of two-dimensional ferromagnetic fluctuations dominate the spin fluctuation spectrum at the critical field, which is unexpected for itinerant metamagnetism.