Single Nuclear Spin Research Articles

Electron and nuclear spin dynamics in antiferromagnetic molecular rings.

We study theoretically the spin dynamics of antiferromagnetic molecular rings, such as the ferric wheel Fe10. For a single nuclear or impurity spin coupled to one of the electron spins of the ring, we calculate nuclear and electronic spin correlation functions and show that nuclear magnetic resonance (NMR) and electron spin resonance (ESR) techniques can be used to detect coherent tunneling of the Néel vector in these rings. The location of the NMR/ESR resonances gives the tunnel splitting and its linewidth an upper bound on the decoherence rate of the electron spin dynamics. We illustrate the experimental feasibility of our proposal with estimates for Fe10 molecules.

Single-spin measurement using single-electron transistors to probe two-electron systems

We present a method for measuring single spins embedded in a solid by probing two electron systems with a single electron transistor (SET). Restrictions imposed by the Pauli Principle on allowed two electron states mean that the spin state of such systems has a profound impact on the orbital states (positions) of the electrons, a parameter which SET's are extremely well suited to measure. We focus on a particular system capable of being fabricated with current technology: a Te double donor in Si adjacent to a Si/SiO2 interface and lying directly beneath the SET island electrode, and we outline a measurement strategy capable of resolving single electron and nuclear spins in this system. We discuss the limitations of the measurement imposed by spin scattering arising from fluctuations emanating from the SET and from lattice phonons. We conclude that measurement of single spins, a necessary requirement for several proposed quantum computer architectures, is feasible in Si using this strategy.

Magnetic resonance of a single molecular spin

Magnetic-resonance spectroscopy on single molecules represents the ultimate limit in sensitivity of electron spin resonance: the detection of a single molecular spin. This is achieved by combining single molecule spectroscopy and optically detected magnetic resonance. Experimental results on pentacene in p-terphenyl both in zero-field and in the presence of a weak magnetic field demonstrate that magnetic-resonance spectroscopy on single molecules adds on to the specificity of single-molecule spectroscopy. It proved possible to identify single molecules which contain 13C nuclei in natural abundance and to observe the splitting of the electron spin resonance line resulting from the hyperfine intercation of a single molecular spin with a single 13C nuclear spin. From the Zeeman effect the orientation of the symmetry axes of individual molecules with respect to the direction of the external magnetic field is obtained. This allows to compare the orientation of individual molecules with their substitutional-site specific transition frequencies depending on the quality of the host crystal.

Direct optical enrichment of nuclear spin isomers of molecules

A novel enrichment method for nuclear spin isomers of polyatomic molecules is proposed. The method is based on the optical excitation of spin isomers to an upper vibrational or electronic state which is efficiently mixed by intramolecular interactions with different nuclear spin states. Under appropriate conditions, the proposed method allows the conversion of almost all molecules into a single nuclear spin state.

Ortho-para separation of molecules using optical orientation of atoms in hyperfine Zeeman states

Ortho-para separations of ${}^{7}{\mathrm{Li}}_{2}$ and ${}^{6}{\mathrm{Li}}_{2}$ molecules were achieved by using a monochromatic laser beam to align atoms into a single nuclear spin state. This approach is unlike the cryogenic cooling technique, which has been successful only on very light molecules (such as ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$), which have large energy gaps between the lowest rotational states. The atoms were ``pumped into'' a single hyperfine Zeeman state with defined electron and nuclear spin orientations. The well-resolved rotational structures of the lithium molecules, as shown by laser-induced fluorescence spectra, revealed the enrichment of ortho-components over para-components. Using laser radiation with a power density of $\ensuremath{\sim}10{\mathrm{m}\mathrm{W}/\mathrm{c}\mathrm{m}}^{2}$ can increase the amount of ortho-components by a factor of 2 for ${}^{7}{\mathrm{Li}}_{2}$ vapor and by a factor of 3 for ${}^{6}{\mathrm{Li}}_{2}$ vapor on a time scale of milliseconds. This paper proposes a model to account for the experimental observations. These increases in the concentrations of ortho-components to para-components are explained by a combined effect of (i) a decrease in molecular density due to the electron spin orientation and (ii) a transfer of nuclear spin momenta from oriented atoms to molecules. The exchange reaction, ${\mathrm{Li}}^{\ensuremath{'}}{+\mathrm{L}\mathrm{i}}_{2}{\ensuremath{\rightarrow}\mathrm{Li}}_{3}{\ensuremath{\rightarrow}\mathrm{Li}}^{\ensuremath{'}}\mathrm{L}\mathrm{i}+\mathrm{L}\mathrm{i},$ appears to transfer the spin orientation from atoms to molecules. A substantial number of ortho-para separations can be achieved through multiple exchange collisions. Applications of this technique to other homonuclear diatomic molecules and polyatomic molecules with nuclear exchange symmetry are predicted.

Single Molecule Electron Paramagnetic Resonance Spectroscopy: Hyperfine Splitting Owing to a Single Nucleus

Individual pentacene-d(14) molecules doped into a p-terphenyl-d(14) host crystal have been studied by optically detected electron paramagnetic resonance spectroscopy. The magnetic resonance transitions between the triplet sublevels of the pentacene molecule and the splitting of the resonance lines for a molecule that contains a carbon-13 nucleus have been observed in an external magnetic field. This splitting is caused by the hyperfine interaction of the triplet electron spin with the single carbon-13 nuclear spin.

Fluorescence detection of single molecule magnetic resonance for pentacene in p-terphenyl. The hyperfine interaction of a single triplet spin with a single 13C nuclear spin

We report the observation of the broadening of a magnetic-resonance transition between triplet sublevels of a single pentacene molecule owing to the interaction of the triplet electron spin with a single 13C nuclear spin. Analysis of this broadening allows the assignment of particular features in the fluorescence—excitation spectrum to pentacene molecules containing 13C isotopes in specific positions.

Slow-motional ESR spectra for vanadyl complexes and their model dependence

The slow-motional ESR analysis appropriate for vanadyl(1V) ions is developed with an accurate treatment of the nonsecular contributions. This results in good agreement between theory and experiments on VO(acac2(pm)) in toluene with axially symmetric magnetic parameters over the whole motional range when a Brownian motion model is used. It is also found that a slightly modified motional narrowing theory based upon the stochastic Liouville equation leads to improved agreement between theory and experiment for VO(a~ac)~ in toluene which also obeys a Brownian motion model. It is shown that vanadyl slow-tumbling spectra are very sensitive to model (even more so than nitroxides). In particular, experiments on VO(H20),2+ in aqueous solution are approximately fit by a model of moderate jump, while those on VO(NCS)t- could only be crudely fit by temperature-dependent variations in model. The theory given here is appropriate for any S = 1/2 radical with a single nuclear spin I provided only the high-field approximation is valid, so that nonsecular terms may be treated by a perturbation approach. The effects of (1) angular-dependent transition probabilities and (2) field- vs. frequency-swept spectra upon the slow-motional theory are also discussed.

Theory of chemically-induced dynamic spin polarization. IV. Low-field effects

The Pedersen–Freed theory of chemically-induced dynamic spin polarization is extended to low field cases where the T±→S transitions must be included. The solutions of the stochastic-Liouville equation are again obtained by numerical finite-difference (FD) methods, but order of magnitude reductions in the size of the matrices to be inverted are realized by introduction of a simple modification of the FD expressions. The simplest case of a single nuclear spin of I=1/2 on one radical is treated in detail. The results show unequivocally the significant dependence of both CIDNP and CIDEP signals on both the magnitude and the range of the exchange interaction. Also, significant polarizations which should be observable are predicted for both types of experiment under appropriate low field conditions. All the computed results are consistent with a simple qualitative model involving two primary regions in r space: in the outer region the hyperfine terms induce T±→S transitions and J (r) =0, while in the inner region J (r) modulates the effectiveness of these transitions. Consideration is also given to magnetic-field effects on chemical reactivity as well as T±→S contributions in high field but viscous CIDEP.

Transformation of spin coordinates and the solution of the spin Hamiltonian for an orthorhombic paramagnetic center in a rigid lattice

The analysis of many spin problems is greatly simplified by the use of coordinate transformations prior to quantization of the spin operators. To illustrate the use of these transformations, the eigenvalues and eigenvectors are obtained for the spin Hamiltonian describing an electron spin [Formula: see text] interacting with a single nuclear spin I in an orthorhombic magnetic environment.

Impurities and Nuclear Spin Relaxation in Aluminum

Both positive- and negative-temperature nuclear spin distributions are used to study the nuclear spin-lattice relaxation in zero external field at liquid helium temperatures in aluminum with controlled impurity content. The relaxation shows considerable deviation from previous theoretical predictions, which were based on the assumption of a single nuclear spin temperature. Most of the deviation is removed by introducing strong impurity effects at zero field, which result in cross relaxation within the nuclear spin system. In addition, the magnetic-field dependence of the relaxation is measured, and the results are compared to theoretical predictions.

Energy Transfer within a Spin System

The nature of the transfer, within a single nuclear spin system, of energy absorbed from an external source of radio-frequency magnetic field has been investigated by a double-irradiation technique. Energy from a high-power oscillator running at fixed frequency is absorbed by the nuclear spin system. The frequency of a second, low-level oscillator is then swept through the nuclear resonance, sampling the line shape existing in the presence of the strong rf field from the fixed-frequency oscillator. Particular spin systems investigated were the proton system in single crystalline CaS${\mathrm{O}}_{4}$\ifmmode\cdot\else\textperiodcentered\fi{}2${\mathrm{H}}_{2}$O, and the ${\mathrm{Al}}^{27}$ system in aluminum metal. In aluminum, the technique gives direct experimental verification of a completely homogeneous saturation behavior, a behavior expected from elementary considerations. It also gives further verification of the Redfield saturation theory. In CaS${\mathrm{O}}_{4}$\ifmmode\cdot\else\textperiodcentered\fi{}2${\mathrm{H}}_{2}$O, an enhancement effect is observed which allows one to determine the importance of double-flip spin-lattice relaxation processes. The technique could be usefully applied to many spin systems to determine the degree of inhomogeneity in the resonance line broadening.