Three-Pulse ELDOR Theory Revisited

The current theory of three-pulse electron double resonance (PELDOR) has been generalized to the case, when paramagnetic particles (spin labels) in pairs or groups have the electron paramagnetic resonance (EPR) spectra, which overlap essentially or coincide. The PELDOR signal modulation induced by the dipole–dipole interaction between paramagnetic spin ½ particles in pairs embedded in disordered systems has been analyzed comprehensively. It has been shown that the PELDOR signal contains additional terms in contrast to the situation considered in the current theory, when the EPR spectra of the spin labels in the pairs do not overlap. In disordered systems, the pairs of spin labels have the characteristic dipolar interaction frequency. According to the current theory for pairs of spin labels, the PELDOR signal reveals the modulation with this characteristic frequency. The additional terms, which are obtained in this work, do not change the modulation frequency of the PELDOR signal for pairs of spin labels. However, these additional terms should be taken into account when analyzing the amplitude of the PELDOR signal and the amplitude of the modulation of the PELDOR signal. The consistent approach to treating the PELDOR data for the groups containing three or more spin labels has been outlined on the basis of the results for pairs of spin labels. It has been also analyzed how the spin flips and molecular motion or molecular isomerization can affect the manifestation of the interaction between the spin labels in PELDOR experiments. PELDOR experiments for the stable biradicals (biradicals I containing 1-oxyl-2,2,5,5-tetramethylpyrroline-3-yl spin labels and biradicals II containing 3-imidazoline spin labels) have been performed. The results have been interpreted within the theory developed in this work.     

Effect of Pumping Pulse Duration on Echo Signal Amplitude in Four-Pulse PELDOR

The impact of pumping pulse duration on four-pulse pulsed electron?Celectron double resonance (PELDOR) data was experimentally studied. For biradicals with known distances between two spin labels, it is shown that refocused echo amplitude decreases with increasing the pumping pulse duration and decreasing the distance between spin labels. The effect becomes substantial when the pumping pulse duration is comparable or exceeds the inverse value of the dipole?Cdipole interaction between spin labels. This effect is essential for determination of distance distribution between labels in double-labeled molecules and for determination of the number of labels in clusters of spin-labeled molecules. PELDOR signal distortion was observed when the pumping pulse position in the time scale coincided with those of the detecting pulses. An approach of signal correction to eliminate this distortion is proposed.     

Pulsed electron double resonance (PELDOR) and its applications in free-radicals research

The papers related to the theoretical background and experimental investigations by pulsed electron double resonance (PELDOR) are reviewed. The main aim of this pulsed ESR application is to study the dipole-dipole spin interaction. In PELDOR the ESR spectrum is excited by two ESE pulses at frequencyω _a and additional pumping pulse atω _b. Decay functionV(T) of the ESE signal, when the time intervalT between the first ESE pulse and pumping pulse is varied, contains the information on dipole-dipole couplings in the spin system. The kinetics ofV(T) decay strongly depends upon distance, mutual orientation inside interacting spin pairs and space distribution of radicals throughout the sample. The distances between spins which were measured or estimated using PELDOR in the papers reviewed are in the range of 15 ÷ 130 Å. This pulsed ESR technique turns now to be a powerful supplement to conventional ESE in studying the free radicals space distribution..     

Membrane-peptide interaction studied by PELDOR and CW ESR: Peptide conformations and cholesterol effect on the spatial peptide distribution in the membrane

Pulsed electron-electron double resonance (PELDOR) combined with continuous-wave electron paramagnetic resonance was used to study inter- and intramolecular dipole-dipole interactions between spin labels for spin-labeled analogs of trichogin GA IV bound to multilamellar membranes of egg L-α-phosphatidylcholine (ePC) and in ePC membranes containing cholesterol. All samples were frozen to 77 K. For mono-labeled peptide concentrations in lipid over the range between 0.5 to 2.2 mol%, it is shown that in these membranes trichogin molecules are distributed homogeneously and are likely to be located on or near the inner and outer membrane surfaces. Addition of cholesterol to a final concentration of 16.5 mol% leads to an increase of the local concentration of trichogin molecules in the membranes. For the double-labeled trichogin, a distribution of the intramolecular distance between the two spin labels was observed. The distribution function is characterized by two main maxima located at distances of 1.3 and 1.8 nm. The distance of 1.3 nm is close to that expected for the α-helix structure of the peptide chain. The distance of 1.8 nm corresponds to a mixed structure in which a 3₁₀-helix is combined with a set of even more elongated conformations.     

Geometric model-based fitting algorithm for orientation-selective PELDOR data

Pulsed electron–electron double resonance (PELDOR or DEER) spectroscopy is frequently used to determine distances between spin centres in biomacromolecular systems. Experiments where mutual orientations of the spin pair are selectively excited provide the so-called orientation-selective PELDOR data. This data is characterised by the orientation dependence of the modulation depth parameter and of the dipolar frequencies. This dependence has to be taken into account in the data analysis in order to extract distance distributions accurately from the experimental time traces. In this work, a fitting algorithm for such data analysis is discussed. The approach is tested on PELDOR data-sets from the literature and is compared with the previous results.     

Nonselective excitation of pulsed ELDOR using multi-frequency microwaves

The use of a polychromatic microwave pulse to expand the pumping bandwidth in pulsed electron-electron double resonance (PELDOR) was investigated. The pumping pulse was applied in resonance with the broad (～100 mT) electron paramagnetic resonance (EPR) signal of the manganese cluster of photosystem II in the S2 state. The observation pulses were in resonance with the narrow EPR signal of the tyrosine radical, YD·. It was found that in the case of the polychromatic pumping pulse containing five harmonics with the microwave frequencies between 8.5 and 10.5 GHz the PELDOR effect corresponding to the dipole interaction between the Mn cluster and YD· was about 2.9 times larger than that achieved with a monochromatic pulse. In addition to the dipolar modulation, the nuclear modulation effects were observed. The effects could be suppressed by averaging the PELDOR trace over the time interval between the observation microwave pulses. The polychromatic excitation technique described will be useful for improving the PELDOR sensitivity in the measurements of long distances in biological samples, where the pair consists of a radical with a narrow EPR spectrum and slow phase relaxation, and a metal center that has a broad EPR spectrum and a short phase relaxation time.     

High-frequency 263 GHz PELDOR

Pulsed electron–electron double resonance (PELDOR/DEER) at high frequencies can provide information on the relative orientation of paramagnetic centres or spin labels, if those are rigidly oriented in a host biomolecule and experiments are performed with sufficient orientation selectivity. We present the first comparative PELDOR study at 263 and 94 GHz on a model RNA system containing rigid nitroxides. We show that at 263 GHz still considerable modulation depth is observed and orientation selectivity is significant, particularly in g _x–g _y plane of the nitroxides.     

High-frequency 180 GHz PELDOR

For aromatic organic radicals, pulsed electron-electron double resonance (PELDOR) experiments at high magnetic fields offer the possibility to achieve orientation-selective pumping and detection that could allow one not only to determine the distance between paramagnetic species but also their relative orientation with respect to the interconnecting dipolar axis. We present a PELDOR two-frequency setup that was introduced into our homebuilt 180 GHz pulsed electron paramagnetic resonance (EPR) spectrometer and we discuss its technical and experimental features. The capability of 180 GHz PELDOR has been tested using the three-pulse ELDOR sequence on the protein RNR-R2 (ribonucleotide reductase) fromEscherichia coli, which contains two tyrosyl radicals at a distance of 3.3 nm. At 180 GHz, orientation selectivity is observed and the modulation frequency was found in good agreement with theoretical predictions, which take into account the relative orientation of the radicals from X-ray data.     

Effect of the nuclear hyperfine field on the 2D electron conductivity in the quantum Hall regime

The effect of the nuclear hyperfine interaction on the dc conductivity of 2D electrons under quantum Hall effect conditions at filling factor ν=1 is observed for the first time. The local hyperfine field enhanced by dynamic nuclear polarization is monitored via the Overhauser shift of the 2D conduction electron spin resonance in AlGaAs/GaAs multiquantum-well samples. The experimentally observed change in the dc conductivity resulting from dynamic nuclear polarization is in agreement with a thermal activation model incorporating the Zeeman energy change due to the hyperfine interaction. The relaxation decay time of the dc conductivity is, within experimental error, the same as the relaxation time of the nuclear spin polarization determined from the Overhauser shift. These findings unequivocally establish the nuclear spin origins of the observed conductivity change. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 1, 58–63 (10 January 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Conformational Properties of the Spin-Labeled Tylopeptin B and Heptaibin Peptaibiotics Based on PELDOR Spectroscopy Data

X-Band pulsed electron–electron double resonance (PELDOR) spectroscopy was used to investigate for the first time the magnetic dipole–dipole interaction between spin labels for frozen glassy methanol solutions at 77 K of double spin-labeled, medium-length peptaibiotics, namely, tylopeptin B and heptaibin. This study was conducted on tylopeptin labeled at positions 3 and 13 (T313) and heptaibin labeled at positions 2 and 14 (H214). PELDOR data analysis was carried out using the theory developed for short inter-spin distances. The distance distribution functions between spin labels for T313 (maximum at 1.76 nm, half-width of 0.07 nm) and H214 (maximum at 2.30 nm, half-width of 0.065 nm) were determined. It is found that the distance distribution function for peptide T313 has the Gaussian shape. The main part of the distance spectrum for H214 has Gaussian shape and additional less intensive broad lines are shifted to high distances range 2.5–3.5 nm. The upper limit of distance spectrum in this case corresponds approximately to the length of extended peptide molecule and the number of such configurations is low. Intramolecular distances between the labels at maxima observed allowed us to assign α-helical conformation to T313 and 3₁₀-helical structure to H214 in methanol solution.     

Pulsed EPR Analysis of the Photo-Induced Triplet Radical Pair in the BLUF Protein SyPixD: Determination of the Protein–Protein Distance and Orientation in the Oligomeric Protein

A photo-induced radical pair of FADH^· and Y8^· and in BLUF protein SyPixD was studied by pulsed electron paramagnetic resonance (EPR) spectroscopy. Blue light illumination at 150 K for 30 min followed by cooling to 50 K during illumination induced the stable radical pair. The EPR signal has been characterized by a Pake doublet signal with complete S = 1 spin state. The radical pair was utilized as a probe to analyze the oligomer of SyPixD. The relative arrangement of PixD proteins in the complex was investigated by pulsed electron–electron double resonance (PELDOR) with the orientation selection. Based on the decameric structure in the crystal, the possible structure for the PELDOR results was discussed.     

Superradiance by a system of highly polarized exchange-coupled nonequivalent spins

We propose a model of radiofrequency (rf) superradiance by a system of interacting nonequivalent spins in a point specimen. In contrast to the rf superradiance observed and described earlier, here spin-spin coupling acts as the interaction with the cavity. To be definite, we examine the spins of two isotopes of a metal that are coupled by the Ruderman-Kittel interaction. The analysis of such a system when the magnetization of one spin species is inverted shows that the system can have one resonance frequency and two different decay times, instead of two resonance frequencies and one decay time in the usual situation. When such “repulsion” of decay times occurs and the absolute values of the spin polarizations are large, transverse magnetization increases and exhibits features characteristic of superradiance. Finally, we calculate the parameters of this superradiance: the voltage across the terminals of an rf pickup coil, the pulse length, the delay time, and the superradiant intensity. Zh. éksp. Teor. Fiz. 112, 551–563 (August 1997)     

Effects in 94 GHz Orientation-Selected PELDOR on a Rigid Pair of Radicals with Non-Collinear Axes

For aromatic organic radicals, pulsed electron-electron double resonance (PELDOR) experiments at high magnetic fields provide information not only about the distance between the paramagnetic species but also about their relative orientation. However, the three-dimensional biradical structure is encoded in a complex pattern of orientation-selected PELDOR traces and the execution of the experiment is generally aggravated by constraints posed by the available hardware and the intrinsically low modulation depth observed. We present a 94 GHz PELDOR experiment performed with a commercial spectrometer and probe heads that permit separation of pump and detection frequencies up to 150 MHz. The setup is employed to examine the orientation selections on a general case of rigid biradicals with non-collinear g axes. The interacting radicals, a tyrosyl radical (Y₁₂₂·) located in the β2 subunit and an 3-aminotyrosyl radical (NH₂Y₇₃₁·) located in the α2 subunit, are generated by Escherichia coli ribonucleotide reductase with a 3-aminotyrosine (NH₂Y) site specifically incorporated into α2 in the presence of cytidine 5′-diphosphate and adenosine 5′-triphosphate. The experimental designs as well as some characteristic features of the observed modulation pattern are discussed.     

Optical nuclear spin polarization in quantum dots

Hyperfine interaction between electron spin and randomly oriented nuclear spins is a key issue of electron coherence for quantum information/computation. We propose an efficient way to establish high polarization of nuclear spins and reduce the intrinsic nuclear spin fluctuations. Here, we polarize the nuclear spins in semiconductor quantum dot(QD) by the coherent population trapping(CPT) and the electric dipole spin resonance(EDSR) induced by optical fields and ac electric fields. By tuning the optical fields, we can obtain a powerful cooling background based on CPT for nuclear spin polarization. The EDSR can enhance the spin flip–flop rate which may increase the cooling efficiency. With the help of CPT and EDSR, an enhancement of 1300 times of the electron coherence time can be obtained after a 10-ns preparation time.     

The exchange interaction effect in the scanning tunneling spectroscopy of a two-orbital Anderson impurity on metallic surface

We investigate the scanning tunneling spectroscopy (STS) of a two-orbital Anderson impurity adsorbed on a metallic surface by using the numerical renormalization group (NRG) method. The density of state of magnetic impurity and the local conduction electron are calculated. We obtain the Fano resonance line shape in the STM conductance at zero temperature. For the impurity atom with antiferromagnetic inter-orbital exchange interaction and a spin singlet ground state, we show that a dip in the STM spectra around zero bias voltage regime and side peaks of spin excitation can be observed. The spin excitation energy is proportional to the exchange interaction strength. As the exchange interaction is ferromagnetic, the underscreened Kondo effect dominates the low energy properties of this system, and it gives rise to drastically different STM spectra as compared with the spin singlet case.     

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.     

Spin effects in a quantum ring

Recent experiments that are reviewed explore the spin states of a ring-shaped many-electron quantum dot. Coulomb-blockade spectroscopy is used to access the spin degree of freedom. The Zeeman effect observed for states with successive electron number allows to select possible sequences of spin ground states of the ring. Spin-paired orbital levels can be identified by probing their response to magnetic fields normal to the plane of the ring and electric fields caused by suitable gate voltages. This narrows down the choice of ground-state spin sequences. A gate-controlled singlet–triplet transition is identified and the size of the exchange interaction matrix element is determined.     

Complete description of the interactions of a quadrupolar nucleus with a radiofrequency field. Implications for data fitting

We present a theory, with experimental tests, that treats exactly the effect of radiofrequency (RF) fields on quadrupolar nuclei, yet retains the symbolic expressions as much as possible. This provides a mathematical model of these interactions that can be easily connected to state-of-the-art optimization methods, so that chemically-important parameters can be extracted from fits to experimental data. Nuclei with spins >1/2 typically experience a Zeeman interaction with the (possibly anisotropic) local static field, a quadrupole interaction and are manipulated with RF fields. Since RF fields are limited by hardware, they seldom dominate the other interactions of these nuclei and so the spectra show unusual dependence on the pulse width used. The theory is tested with ²³Na NMR nutation spectra of a single crystal of sodium nitrate, in which the RF is comparable with the quadrupole coupling and is not necessarily on resonance with any of the transitions. Both the intensity and phase of all three transitions are followed as a function of flip angle. This provides a more rigorous trial than a powder sample where many of the details are averaged out. The formalism is based on a symbolic approach which encompasses all the published results, yet is easily implemented numerically, since no explicit spin operators or their commutators are needed. The classic perturbation results are also easily derived. There are no restrictions or assumptions on the spin of the nucleus or the relative sizes of the interactions, so the results are completely general, going beyond the standard first-order treatments in the literature.     

Five-level k · p model for conduction electrons in GaAs. Description of cyclotron resonance experiments

Five-level k·p model for the conduction electrons in GaAs in the presence of a quantising magnetic field is developed and used to describe spin splittings of the cyclotron resonance and the donor-shifted cyclotron resonance peaks, observed in this material up to fields of 22.5 T. It is shown that the spin splittings are insensitive to polaron effects and that their values can be very well described by the model.Required band parameters correctly account for the rate of electron spin relaxation in GaAs due to inversion asymmetry, as determined by other authors.