Electron Spin-nuclear Spin Research Articles

Accurate hyperfine tensors for solid state quantum applications: case of the NV center in diamond

The decoherence of point defect qubits is often governed by the electron spin-nuclear spin hyperfine interaction that can be parameterized by using ab inito calculations in principle. So far most of the theoretical works have focused on the hyperfine interaction of the closest nuclear spins, while the accuracy of the predictions for distinct nuclear spins is barely discussed. Here we demonstrate for the case of the NV center in diamond that the absolute relative error of the computed hyperfine parameters can exceed 100% using an industry standards first-principles code. To overcome this issue, we implement an alternative method and report on significantly improved hyperfine values with O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{{{\\mathcal{O}}}}}}}}$$\\end{document}(1%) relative mean error at all distances. The provided accurate hyperfine data for the NV center enables high-precision simulation of NV quantum nodes for quantum information processing and positioning of nuclear spins by comparing experimental and theoretical hyperfine data.

Hyperfine and Zeeman interactions in ultracold collisions of molecular hydrogen with atomic lithium.

We present a rigorous quantum scattering study of the effects of hyperfine and Zeeman interactions on cold Li-H2 collisions in the presence of an external magnetic field using a recent abinitio potential energy surface. We find that the low-field-seeking states of H2 predominantly undergo elastic collisions: the ratio of elastic-to-inelastic cross sections exceeds 100 for collision energies below 100 mK. Furthermore, we demonstrate that most inelastic collisions conserve the space-fixed projection of the nuclear spin. We show that the anisotropic hyperfine interaction between the nuclear spin of H2 and the electron spin of Li can have a significant effect on inelastic scattering in the ultracold regime, as it mediates two processes: the electron spin relaxation in lithium and the nuclear spin-electron spin exchange. Given the predominance of elastic collisions and the propensity of inelastic collisions to retain H2 in its low-field-seeking states, our results open up the possibility of sympathetic cooling of molecular hydrogen by atomic lithium, paving the way for future exploration of ultracold collisions and high-precision spectroscopy of H2 molecules.

NMR of Paramagnetic Proteins: 13C Derived Paramagnetic Relaxation Enhancements Are an Additional Source of Structural Information in Solution

In paramagnetic metalloproteins, longitudinal relaxation rates of 13C′ and 13Cα nuclei can be measured using 13C detected experiments and converted into electron spin-nuclear spin distance restraints, also known as Paramagnetic Relaxation Enhancement (PRE) restraints. 13C are less sensitive to paramagnetism than 1H nuclei, therefore, 13C based PREs constitute an additional, non-redundant, structural information. We will discuss the complementarity of 13C PRE restraints with 1H PRE restraints in the case of the High Potential Iron Sulfur Protein (HiPIP) PioC, for which the NMR structure of PioC has been already solved by a combination of classical and paramagnetism-based restraints. We will show here that 13C R1 values can be measured also at very short distances from the paramagnetic center and that the obtained set of 13C based restraints can be added to 1H PREs and to other classical and paramagnetism based NMR restraints to improve quality and quantity of the NMR information.

A variational model for the hyperfine resolved spectrum of VO in its ground electronic state.

A variational model for the infra-red spectrum of vanadium monoxide (VO) is presented, which aims to accurately predict the hyperfine structure within the VO XΣ-4 electronic ground state. To give the correct electron spin splitting of the XΣ-4 state, electron spin dipolar interaction within the ground state and the spin-orbit coupling between XΣ-4 and two excited states, AΠ4 and 1Σ+2, are calculated ab initio alongside hyperfine interaction terms. Four hyperfine coupling terms are explicitly considered: Fermi-contact interaction, electron spin-nuclear spin dipolar interaction, nuclear spin-rotation interaction, and nuclear electric quadrupole interaction. These terms are included as part of a full variational solution of the nuclear-motion Schrödinger equation performed using program Duo, which is used to generate both hyperfine-resolved energy levels and spectra. To improve the accuracy of the model, ab initio curves are subject to small shifts. The energy levels generated by this model show good agreement with the recently derived empirical term values. This and other comparisons validate both our model and the recently developed hyperfine modules in Duo.

A Method for the Variational Calculation of Hyperfine-Resolved Rovibronic Spectra of Diatomic Molecules.

An algorithm for the calculation of hyperfine structure and spectra of diatomic molecules based on the variational nuclear motion is presented. The hyperfine coupling terms considered are Fermi-contact, nuclear spin-electron spin dipole–dipole, nuclear spin–orbit, nuclear spin-rotation, and nuclear electric quadrupole interactions. Initial hyperfine-unresolved wave functions are obtained for a given set of potential energy curves and associated couplings by a variation solution of the nuclear-motion Schrödinger equation. Fully hyperfine-resolved parity-conserved rovibronic Hamiltonian matrices for a given final angular momentum, F, are constructed and then diagonalized to give hyperfine-resolved energies and wave functions. Electric transition dipole moment curves can then be used to generate a hyperfine-resolved line list by applying rigorous selection rules. The algorithm is implemented in Duo, which is a general program for calculating spectra of diatomic molecules. This approach is tested for NO and MgH, and the results are compared to experiment and shown to be consistent with those given by the well-used effective Hamiltonian code PGOPHER.

Overhauser Dynamic Nuclear Polarization: A Tool for Building Maps of Hydration Water

Coating the surface of every macromolecule or macromolecular assembly, one finds a hydration layer composed of water molecules that move typically between 3× and 10× slower than water molecules in bulk water. The interaction between the water molecules in the hydration layer and the macromolecules contributes to the structural stability and sometimes the function of, e.g., proteins and lipid bilayers. Overhauser Dynamic Nuclear Polarization (ODNP) is an emerging electron-spin nuclear-spin (EPR-NMR) double-resonance tool that has demonstrated a capability of measuring the translational dynamics of water in the hydration layer. Here we discuss our efforts on two fronts: First, we design a scheme for measuring the thickness of the hydration layer and the effect of confinement on translational dynamics, as measured by ODNP, with controlled, appropriately labeled reverse micelle systems. Second, we describe the development of an a priori technique for converting ODNP measurements into a 3D “map” of hydration layer properties in dynamic room temperature samples that explore an ensemble of structures. This latter effort focuses on transmembrane model systems and utilizes the modern structure-prediction tool Rosetta in a fashion analogous to successful efforts to predict NMR order parameters. Particular focus is given to improving the quality and automation of the ODNP measurement, as well as validating predicted ensemble structures against both continuous wave EPR and NMR Paramagnetic Relaxation Enhancement (PRE) data.

Laser-stimulated electric quadrupole transitions in the molecular hydrogen ion H2+

Molecular hydrogen ions are of metrological relevance due to the possibility of precise theoretical evaluation of their spectrum and of external-field-induced shifts. We report the results of the calculations of the rate of laser-induced electric quadrupole transitions between a large set of ro-vibrational states of ${\rm H_2^+}$. The hyperfine and Zeeman structure of the E2 transition spectrum and the effects of the laser polarization are treated in detail. We also present the nuclear spin-electron spin coupling constants, computed with a precision 10 times higher than previously.

Synthetic Approach To Determine the Effect of Nuclear Spin Distance on Electronic Spin Decoherence.

Nuclear-electronic interactions are a fundamental phenomenon which impacts fields from magnetic resonance imaging to quantum information processing (QIP). The realization of QIP would transform diverse areas of research including accurate simulation of quantum dynamics and cryptography. One promising candidate for the smallest unit of QIP, a qubit, is electronic spin. Electronic spins in molecules offer significant advantages with regard to QIP, and for the emerging field of quantum sensing. Yet relative to other qubit candidates, they possess shorter superposition lifetimes, known as coherence times or T2, due to interactions with nuclear spins in the local environment. Designing complexes with sufficiently long values of T2 requires an understanding of precisely how the position of nuclear spins relative to the electronic spin center affects decoherence. Herein, we report the first synthetic study of the relationship between nuclear spin-electron spin distance and decoherence. Through the synthesis of four vanadyl complexes, (Ph4P)2[VO(C3H6S2)2] (1), (Ph4P)2[VO(C5H6S4)2] (2), (Ph4P)2[VO(C7H6S6)2] (3), and (Ph4P)2[VO(C9H6S8)2] (4), we are able to synthetically place a spin-laden propyl moiety at well-defined distances from an electronic spin center by employing a spin-free carbon-sulfur scaffold. We interrogate this series of molecules with pulsed electron paramagnetic resonance (EPR) spectroscopy to determine their coherence times. Our studies demonstrate a sharp jump in T2 when the average V-H distance is decreased from 6.6(6) to 4.0(4) Å, indicating that spin-active nuclei sufficiently close to the electronic spin center do not contribute to decoherence. These results illustrate the power of synthetic chemistry in elucidating the fundamental mechanisms underlying electronic polarization transfer and provide vital principles for the rational design of long-coherence electronic qubits.

Sub-Doppler infrared spectroscopy of propargyl radical (H2CCCH) in a slit supersonic expansion.

The acetylenic CH stretch mode (ν1) of propargyl (H2CCCH) radical has been studied at sub-Doppler resolution (∼60 MHz) via infrared laser absorption spectroscopy in a supersonic slit-jet discharge expansion, where low rotational temperatures (Trot = 13.5(4) K) and lack of spectral congestion permit improved determination of band origin and rotational constants for the excited state. For the lowest J states primarily populated in the slit jet cooled expansion, fine structure due to the unpaired electron spin is resolved completely, which permits accurate analysis of electron spin-rotation interactions in the vibrationally excited states (εaa = - 518.1(1.8), εbb = - 13.0(3), εcc = - 1.8(3) MHz). In addition, hyperfine broadening in substantial excess of the sub-Doppler experimental linewidths is observed due to nuclear spin-electron spin contributions at the methylenic (-CH2) and acetylenic (-CH) positions, which permits detailed modeling of the fine/hyperfine structure line contours. The results are consistent with a delocalized radical spin density extending over both methylenic and acetylenic C atoms, in excellent agreement with simple resonance structures as well as ab initio theoretical calculations.

Ortho–Para Mixing Hyperfine Interaction in the H2O+ Ion and Nuclear Spin Equilibration

The ortho to para conversion of water ion, H2O(+), due to the interaction between the magnetic moments of the unpaired electron and protons has been theoretically studied to calculate the spontaneous emission lifetime between the ortho- and para-levels. The electron spin-nuclear spin interaction term, Tab(SaΔIb + SbΔIa) mixes ortho (I = 1) and para (I = 0) levels to cause the "forbidden" ortho to para |ΔI| = 1 transition. The mixing term with Tab = 72.0 MHz is 4 orders of magnitude higher for H2O(+) than for its neutral counterpart H2O where the magnetic field interacting with proton spins is by molecular rotation rather than the free electron. The resultant 10(8) increase of ortho to para conversion rate possibly makes the effect of conversion in H2O(+) measurable in laboratories and possibly explains the anomalous ortho to para ratio recently reported by Herschel heterodyne instrument for the far-infrared (HIFI) observation. Results of our calculations show that the ortho ↔ para mixings involving near-degenerate ortho and para levels are high (∼10(-3)), but they tend to occur at high energy levels, ∼300 K. Because of the rapid spontaneous emission, such high levels are not populated in diffuse clouds unless the radiative temperature of the environment is very high. The low-lying 101 (para) and 111 (ortho) levels of H2O(+) are mixed by ∼10(-4) making the spontaneous emission lifetime for the para 101 → ortho 000 transition 520 years and 5200 years depending on the F value of the hyperfine structure. Thus the ortho ↔ para conversion due to the unpaired electron is not likely to seriously affect thermalization of interstellar H2O(+) unless either the radiative temperature is very high or number density of the cloud is very low.

Spin‐Labeled Heparins as Polarizing Agents for Dynamic Nuclear Polarization

A potentially biocompatible class of spin-labeled macromolecules, spin-labeled (SL) heparins, and their use as nuclear magnetic resonance (NMR) signal enhancers are introduced. The signal enhancement is achieved through Overhauser-type dynamic nuclear polarization (DNP). All presented SL-heparins show high (1)H DNP enhancement factors up to E=-110, which validates that effectively more than one hyperfine line can be saturated even for spin-labeled polarizing agents. The parameters for the Overhauser-type DNP are determined and discussed. A striking result is that for spin-labeled heparins, the off-resonant electron paramagnetic resonance (EPR) hyperfine lines contribute a non-negligible part to the total saturation, even in the absence of Heisenberg spin exchange (HSE) and electron spin-nuclear spin relaxation (T(1ne)). As a result, we conclude that one can optimize the use of, for example, biomacromolecules for DNP, for which only small sample amounts are available, by using heterogeneously distributed radicals attached to the molecule.

Hyperfine-induced valley mixing and the spin-valley blockade in carbon-based quantum dots

Hyperfine interaction (HFI) in carbon nanotube and graphene quantum dots is due to the presence of $^{13}\text{C}$ atoms. We theoretically show that in these structures the short-range nature of the HFI gives rise to a coupling between the valley degree of freedom of the electron and the nuclear spin, in addition to the usual electron spin-nuclear spin coupling. We predict that this property of the HFI affects the Pauli blockade transport in carbon-based double quantum dots. In particular, we show that transport is blocked only if both the spin and the valley degeneracies of the quantum dot levels are lifted, e.g., by an appropriately oriented magnetic field. The blockade is caused by four ``supertriplet'' states in the (1,1) charge configuration.

Hyperfine-Coupling-Programming of Current through Coupled Quantum Dots with Multiple-Sweep Bias Voltage Waveforms

Fine features in the leakage current within the two-electron spin blockade region in a weakly coupled vertical double dot device induced on application of a moderate out-of-dot-plane magnetic field (up to 2.5 T) are studied. The nature of these features is consistent with an electron-spin nuclear-spin (hyperfine) interaction origin, and furthermore, their appearance depends strongly on the bias voltage sweep direction through the spin blockade region. Applying multi-part 10 mHz bias voltage waveforms, we can program the total current response via the hyperfine interaction. We demonstrate the operation of shifting a down- (up-) bias sweep through three up- (down-) bias sweeps which leads to a unique outcome in the measured current.

Comparison of different methods for calculating the paramagnetic relaxation enhancement of nuclear spins as a function of the magnetic field

The enhancement of the spin-lattice relaxation rate for nuclear spins in a ligand bound to a paramagnetic metal ion [known as the paramagnetic relaxation enhancement (PRE)] arises primarily through the dipole-dipole (DD) interaction between the nuclear spins and the electron spins. In solution, the DD interaction is modulated mostly by reorientation of the nuclear spin-electron spin axis and by electron spin relaxation. Calculations of the PRE are in general complicated, mainly because the electron spin interacts so strongly with the other degrees of freedom that its relaxation cannot be described by second-order perturbation theory or the Redfield theory. Three approaches to resolve this problem exist in the literature: The so-called slow-motion theory, originating from Swedish groups [Benetis et al., Mol. Phys. 48, 329 (1983); Kowalewski et al., Adv. Inorg. Chem. 57, (2005); Larsson et al., J. Chem. Phys. 101, 1116 (1994); T. Nilsson et al., J. Magn. Reson. 154, 269 (2002)] and two different methods based on simulations of the dynamics of electron spin in time domain, developed in Grenoble [Fries and Belorizky, J. Chem. Phys. 126, 204503 (2007); Rast et al., ibid. 115, 7554 (2001)] and Ann Arbor [Abernathy and Sharp, J. Chem. Phys. 106, 9032 (1997); Schaefle and Sharp, ibid. 121, 5387 (2004); Schaefle and Sharp, J. Magn. Reson. 176, 160 (2005)], respectively. In this paper, we report a numerical comparison of the three methods for a large variety of parameter sets, meant to correspond to large and small complexes of gadolinium(III) and of nickel(II). It is found that the agreement between the Swedish and the Grenoble approaches is very good for practically all parameter sets, while the predictions of the Ann Arbor model are similar in a number of the calculations but deviate significantly in others, reflecting in part differences in the treatment of electron spin relaxation. The origins of the discrepancies are discussed briefly.

Microwave spectra of O2–HF and O2–DF: Hyperfine interactions and global fitting with infrared data

Spectra of the open shell complexes O(2)-HF and O(2)-DF were recorded using Fourier transform microwave spectroscopy. A complete analysis of the hyperfine structure and a global fit including microwave and infrared frequencies [W. M. Fawzy, C. M. Lovejoy, D. J. Nesbitt, and J. T. Hougen, J. Chem. Phys. 117, 693 (2002)] are reported. The Fermi contact interaction between the electron and nuclear spins, the electron spin-nuclear spin dipolar interaction, the nuclear spin-nuclear spin dipolar interaction, and the nuclear electric quadrupole interaction (for O(2)-DF) were considered in the analysis. The correspondence between the magnetic hyperfine constants and the two nuclei of the H(D)F is unambiguously established. In both O(2)-HF and O(2)-DF, the Fermi contact parameter is larger for the fluorine than for the hydrogen, while for the nuclear spin-electron spin dipolar hyperfine constants, the reverse is true. The effective angle between the HF bond and the a axis of the complex, determined from the nuclear spin-nuclear spin interaction constant, is 38(4) degrees. The same angle for the DF complex, derived from the deuterium nuclear quadrupole coupling constant, is 31(4) degrees.

Long-lived memory for electronic spin in a quantum dot: Numerical analysis

Techniques for coherent control of electron spin-nuclear spin interactions in quantum dots can be directly applied in spintronics and in quantum information processing. In this work we study numerically the interaction of electron and nuclear spins in the context of storing the spin state of an electron in a collective state of nuclear spins. We take into account the errors inherent in a realistic system: the incomplete polarization of the bath of nuclear spins and the different hyperfine interactions between the electron and individual nuclei in the quantum dot. Although these imperfections deteriorate the fidelity of the quantum information retrieval, we find reasonable fidelities are achievable for modest bath polarizations.

Quantum-size-effect-enhanced dynamic magnetic interactions among doped spins in Cd1−xMnxSe nanocrystals

Dynamic magnetic properties of spins from Mn ions doped in semiconductor nanocrystals (Cd1−xMnxSe) have been studied using an electron paramagnetic resonance method based on two different crystalline sizes and a series of Mn concentrations. By decreasing the size of the quantum dots, the electron spin-nuclear spin interactions are reduced due to enhanced magnetic interactions between Mn ions. A linewidth analysis was also carried out, showing longer spin relaxation times and supporting the enhancement of spin coherence. We suggest that the enhancement of Mn–Mn interactions results from the quantized electrons which have longer coherence length in quantum dots. Quantum size effects may benefit to control and manipulation of spins in a semiconductor nanocrystalline system in which the magnetic ions are incorporated.

Magnetic properties of nanocrystalline Pb/sub 1-X/Mn/sub X/Se

Mn-doped diluted magnetic semiconductors are important semiconductor materials and have received much attention due to their application in magnetooptics, spintronics, displays, and lasers. The authors present the magnetic properties of Mn-doped PbSe nanocrystals (NCs) based on electron paramagnetic resonance and superconducting quantum interference device measurements, demonstrating that the electron spin-nuclear spin interactions, hyperfine interactions, in NCs are enhanced due to the quantum confinement effects.

A strategy for the NMR characterization of type II copper(II) proteins: the case of the copper trafficking protein CopC from Pseudomonas Syringae.

CopC from Pseudomonas syringae was found to be a protein capable of binding both Cu(I) and Cu(II) at two different sites. The solution structure of the apo protein is available, and structural information has been obtained on the Cu(I) bound form. We attempt here to set the limits for the determination of the solution structure of a Cu(II) protein, such as the Cu(II) bound form of CopC, in which the Cu(II) ion takes a type II coordination. The electron relaxation time is estimated from NMRD measurements to be 3 ns which leads to a correlation time for the nuclear spin-electron spin dipolar interaction of 2 ns. This information allowed us to tailor the NMR experiments and to fully exploit purely heteronuclear spectroscopy to assign as many signals as possible. In this way, 37 (13)C and 11 (15)N signals that completely escape detection with conventional approaches were assigned. Paramagnetic based structural constraints were obtained by measuring paramagnetic longitudinal relaxation enhancements (rho(para)) which allowed us to precisely locate the copper ion within the protein frame. Pseudocontact shifts (pcs's) were also used as constraints for 83 (1)H and 18 (13)C nuclei. With them, together with other standard structural constraints, a structure is obtained (and submitted to PDB) where information is only missing in a sphere with a 6 A radius from the copper ion. If we borrow information from EXAFS data, which show evidence of two copper coordinated histidines, then His 1 and His 91 are unambiguously identified as copper ligands. EXAFS data indicate two more light donor atoms (O/N) which could be from Asp 27 and Glu 89, whereas the NMRD data indicate the presence of a semicoordinated water molecule at 2.8 A (Cu-O distance) roughly orthogonal to the plane identified by the other four ligands. This represents the most extensively characterized structure of a type II Cu(II) protein obtained employing the most advanced NMR methods and with the aid of EXAFS data. The knowledge of the location of the Cu(II) in the protein is important for the copper transfer mechanism.

Hyperfine coupling and pseudorotational motion interaction in Na3

Hyperfine patterns calculations are carried out for the Na3 cluster with a view towards understanding the microwave measurements which were performed for three rotational transitions belonging to the ground X̃ electronic state. The calculations take simultaneously into account the pseudorotational motion, the spin-rotation coupling, and the magnetic electron spin-nuclear spin hyperfine coupling. Matching calculated and observed patterns suggests that the cluster is characterized by small pseudorotational tunneling and spin-rotation splittings, some amount of Fermi contact interaction at the two terminal nuclei, and significant dipolar spin-nuclear spin coupling for the central atom.