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.     

13C spin-lattice relaxation in natural diamond: Zeeman relaxation in fields of 500 to 5000 G at 300 K due to fixed paramagnetic nitrogen defects

¹³C Spin–lattice relaxation (SLR) times in the laboratory frame have been measured at room temperature as a function of field in the range of 500 to 5000 G on two natural type Ib and Ia diamonds after dynamic nuclear polarization. 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. Three different nuclear SLR paths, namely that due to electron SLR and two types of three spin processes, are discussed. The one three-spin process (TSP) (type 1) involves a simultaneous transition of two electron spins belonging to the same hyperfine EPR line and a ¹³C spin while the other process (type 2) 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 decreases with an increase in field intensity, thus forming a bottleneck in the ¹³C relaxation path due to the type 1 TSP. The contribution of TSP of type 1 dominates that due to electron SLR and the type 2 TSP in relaxing the ¹³C nuclei in type Ib diamond from about 1200 to 5000 G, while for type Ia diamond it dominates from 500 up to about 2200 G. In type Ia diamond over the range 2200 to 5000 G it seems that the type 2 TSP, which involves electrons of neighboring P2 hyperfine lines, dominates that of electron spin–lattice and the type 1 TSP. Over the range 500 to about 1200 G, a field-dependent electron SLR mechanism associated with N3 centers appears to dominate the ¹³C SLR.     

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 nuclear quadruple resonance for assignment of overlapping spectra

Multiple resonance methods are important tools in EPR for revealing the network of hyperfine levels of free radicals and paramagnetic centers. The variations of electron nuclear double resonance (ENDOR) or electron spin-echo envelope modulation (ESEEM) techniques help to correlate nuclear frequencies with each other. These methods have limited utility when there is extensive overlap or suspected overlap in the EPR spectrum between different species or different orientations. In the ENDOR spectrum, overlap and second-order shifts of lines also leads to ambiguity in assignment and interpretation. A new electron nuclear multiple resonance method is presented here that is based on population transfer ENDOR. It is a quadruple resonance method that correlates ENDOR lines and reveals the network of hyperfine levels in samples with unoriented paramagnetic species and in samples with overlapping EPR or ENDOR lines.     

Recent advances in positive muon spin rotation; muonium as a probe of fullerenes

In non-metallic solids the positive muon often forms paramagnetic muonium centers which are characterized by the hyperfine interactions of the unpaired electron with the positive muon and with the surrounding nuclear spins. The static and fluctuating components of these hyperfine interactions provide information on local molecular dynamics and local electronic structure. Some recent results on C₆₀ and related compounds are presented to illustrate this.     

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.     

Electric field induced nuclear spin resonance mediated by oscillating electron spin domains in GaAs-based semiconductors

We demonstrate an alternative nuclear spin resonance using a radio frequency (rf) electric field [nuclear electric resonance (NER)] instead of a magnetic field. The NER is based on the electronic control of electron spins forming a domain structure. The rf electric field applied to a gate excites spatial oscillations of the domain walls and thus temporal oscillations of the hyperfine field to nuclear spins. The rf power and burst duration dependence of the NER spectrum provides insight into the interplay between nuclear spins and the oscillating domain walls.     

Optical pumping of quantum-dot nuclear spins

Hyperfine interactions with randomly oriented nuclear spins present a fundamental decoherence mechanism for electron spin in a quantum dot, that can be suppressed by polarizing the nuclear spins. Here, we analyze an all-optical scheme that uses hyperfine interactions to implement laser cooling of quantum-dot nuclear spins. The limitation imposed on spin cooling by the dark states for collective spin relaxation can be overcome by modulating the electron wave function.     

Anisotropic hyperfine structure in the EPR spectrum of impurity ions in single crystals

Expressions are obtained for the hyperfine splitting in EPR spectra of impurity ions with electron spin 1/2 and arbitrary nuclear spin for arbitrary anisotropy of the g-factor and hyperfine structure constants. These results generalize the previously obtained results of Weil for the case of weakly anisotropic g-factors and hyperfine structure constants. Fiz. Tverd. Tela (St. Petersburg) 41, 1026–1027 (June 1999)     

Measurement of a heavy-hole hyperfine interaction in InGaAs quantum dots using resonance fluorescence

We measure the strength and the sign of hyperfine interaction of a heavy hole with nuclear spins in single self-assembled quantum dots. Our experiments utilize the locking of a quantum dot resonance to an incident laser frequency to generate nuclear spin polarization. By monitoring the resulting Overhauser shift of optical transitions that are split either by electron or exciton Zeeman energy with respect to the locked transition using resonance fluorescence, we find that the ratio of the heavy-hole and electron hyperfine interactions is -0.09 ± 0.02 in three quantum dots. Since hyperfine interactions constitute the principal decoherence source for spin qubits, we expect our results to be important for efforts aimed at using heavy-hole spins in quantum information processing.     

Stark tuning of donor electron spins in silicon

We report Stark shift measurements for 121Sb donor electron spins in silicon using pulsed electron spin resonance. Interdigitated metal gates on a Sb-implanted 28Si epilayer are used to apply the electric fields. Two quadratic Stark effects are resolved: a decrease of the hyperfine coupling between electron and nuclear spins of the donor and a decrease in electron Zeeman g factor. The hyperfine term prevails at magnetic fields of 0.35 T, while the g factor term is expected to dominate at higher magnetic fields. We discuss the results in the context of the Kane model quantum computer.     

Direct measurement of the hole-nuclear spin interaction in single InP/GaInP quantum dots using photoluminescence spectroscopy

We measure the hyperfine interaction of the valence band hole with nuclear spins in single InP/GaInP semiconductor quantum dots. Detection of photoluminescence (PL) of both "bright" and "dark" excitons enables direct measurement of the Overhauser shift of states with the same electron but opposite hole spin projections. We find that the hole hyperfine constant is ≈11% of that of the electron and has the opposite sign. By measuring the degree of circular polarization of the PL, an upper limit to the contribution of the heavy-light hole mixing to the measured value of the hole hyperfine constant is deduced. Our results imply that environment-independent hole spins are not realizable in III-V semiconductor, a result important for solid-state quantum information processing using hole spin qubits.     

Electroelastic hyperfine tuning of phosphorus donors in silicon

We demonstrate an electroelastic control of the hyperfine interaction between nuclear and electronic spins opening an alternative way to address and couple spin-based qubits. The hyperfine interaction is measured by electrically detected magnetic resonance in phosphorus-doped silicon epitaxial layers employing a hybrid structure consisting of a silicon-germanium virtual substrate and a piezoelectric actuator. By applying a voltage to the actuator, the hyperfine interaction is changed by up to 0.9 MHz, which would be enough to shift the phosphorus donor electron spin out of resonance by more than one linewidth in isotopically purified 28Si.     

High-Frequency EPR and ENDOR Spectroscopy on Semiconductor Quantum Dots

It is shown that high-frequency electron paramagnetic resonance (EPR) and electron-nuclear double resonance (ENDOR) spectroscopy are excellent tools for the investigation of the electronic properties of semiconductor quantum dots (QDs). The great attractions of these techniques are that, in contrast to optical methods, they allow the identification of the dopants and provide information about the spatial distribution of the electronic wave function. This latter aspect is particularly attractive because it allows for a quantitative measurement of the effect of confinement on the shape and properties of the wave function. In this contribution EPR and ENDOR results are presented on doped ZnO QDs. Shallow donors (SDs), related to interstitial Li and Na and substitutional Al atoms, have been identified in this material by pulsed high-frequency EPR and ENDOR spectroscopy. The shallow character of the wave function of the donors is evidenced by the multitude of ENDOR transitions of the ⁶⁷Zn nuclear spins and by the hyperfine interaction of the ⁷Li, ²³Na and ²⁷Al nuclear spins that are much smaller than for atomic lithium, sodium and aluminium. The EPR signal of an exchange-coupled pair consisting of a shallow donor and a deep Na-related acceptor has been identified in ZnO nanocrystals with radii smaller than 1.5 nm. From ENDOR experiments it is concluded that the deep Na-related acceptor is located at the interface of the ZnO core and the Zn(OH)₂ capping layer, while the shallow donor is in the ZnO core. The spatial distribution of the electronic wave function of a shallow donor in ZnO semiconductor QDs has been determined in the regime of quantum confinement by using the nuclear spins as probes. Hyperfine interactions as monitored by ENDOR spectroscopy quantitatively reveal the transition from semiconductor to molecular properties upon reduction of the size of the nanoparticles. In addition, the effect of confinement on the g-factor of SDs in ZnO as well as in CdS QDs is observed. Finally, it is shown that an almost complete dynamic nuclear polarization (DNP) of the ⁶⁷Zn nuclear spins in the core of ZnO QDs and of the ¹H nuclear spins in the Zn(OH)₂ capping layer can be obtained. This DNP is achieved by saturating the EPR transition of SDs present in the QDs with resonant high-frequency microwaves at low temperatures. This nuclear polarization manifests itself as a hole and an antihole in the EPR absorption line of the SD in the QDs and a shift of the hole (antihole). The enhancement of the nuclear polarization opens the possibility to study semiconductor nanostructures with nuclear magnetic resonance techniques.     

EasySpin, a comprehensive software package for spectral simulation and analysis in EPR

EasySpin, a computational package for spectral simulation and analysis in EPR, is described. It is based on Matlab, a commercial technical computation software. EasySpin provides extensive EPR-related functionality, ranging from elementary spin physics to data analysis. In addition, it provides routines for the simulation of liquid- and solid-state EPR and ENDOR spectra. These simulation functions are built on a series of novel algorithms that enhance scope, speed and accuracy of spectral simulations. Spin systems with an arbitrary number of electron and nuclear spins are supported. The structure of the toolbox as well as the theoretical background underlying its simulation functionality are presented, and some illustrative examples are given.     

The theory of nuclear orientation via electron spin locking (NOVEL)

Nuclear orientation via electron spin locking (NOVEL) is a technique to orient nuclear spins embedded in a solid. Like other methods of dynamic nuclear polarization (DNP) it employs a small amount of unpaired electron spins and uses a microwave field to transfer the polarization of these unpaired electron spins to the nuclear spins. Traditional DNP uses CW microwave fields, but NOVEL uses pulsed electron spin resonance (ESR) techniques: a 90 degree pulse–90 degree phase shift–locking pulse sequence is applied and during the locking pulse the polarization transfer is assured by satisfying the Hartmann–Hahn condition. The transfer is coherent and similar to coherence transfer between nuclear spins. However, NOVEL requires an extension of the existing theory to many, inequivalent nuclear spins and to arbitrary, i.e. high electron and nuclear spin polarization. In this paper both extensions are presented. The theory is applied to the system naphthalene doped with pentacene, where the proton spins are polarized using the photo-excited triplet states of the pentacene molecules and found to show excellent agreement with the experimentally observed evolution of the polarization transfer during the locking pulse.     

Time-resolved electron paramagnetic resonance of radical pair intermediates in cryptochromes

Electron transfer plays a key role in many biological systems, including core complexes of photosynthesis and respiration. As this involves unpaired electron spins, electron paramagnetic resonance (EPR) is the method of choice to investigate such processes. Systems that show photo-induced charge separation and electron transfer are of particular interest, as here the processes can easily be synchronised to the experiment and therefore followed directly over its time course. One particular class of proteins, the cryptochromes, showing charge separation and in turn spin-correlated radical pairs upon excitation with blue light, have been investigated by time-resolved EPR spectroscopy in great detail and the results obtained so far are summarised in this contribution. Highlights include the first observation of spin-correlated radical pairs in these proteins, a fact with great impact on the proposed role as key part of a magnetic compass of migratory birds, as well as the assignment of the radical-pair partners and the unravelling of alternative and unexpected electron transfer pathways in these proteins, giving new insights into aspects of biological electron transfer itself.