Electron Spin Transitions Research Articles

Breaking the rotating wave approximation for a strongly driven dressed single-electron spin

We investigate the dynamics of a strongly driven microwave-dressed donor-bound electron spin qubit in silicon. A resonant oscillating magnetic field ${B}_{1}$ is used to dress the electron spin and create a new quantum system with a level splitting proportional to ${B}_{1}$. The dressed two-level system can then be driven by modulating the detuning $\mathrm{\ensuremath{\Delta}}\ensuremath{\nu}$ between the microwave source frequency ${\ensuremath{\nu}}_{\mathrm{MW}}$ and the electron spin transition frequency ${\ensuremath{\nu}}_{e}$ at the frequency of the level splitting. The resulting dressed qubit Rabi frequency ${\mathrm{\ensuremath{\Omega}}}_{R\ensuremath{\rho}}$ is defined by the modulation amplitude, which can be made comparable to the level splitting using frequency modulation on the microwave source. This allows us to investigate the regime where the rotating wave approximation breaks down without requiring microwave power levels that would be incompatible with a cryogenic environment. We observe clear deviations from normal Rabi oscillations and can numerically simulate the time evolution of the states in excellent agreement with the experimental data.

Wide-band nanoscale magnetic resonance spectroscopy using quantum relaxation of a single spin in diamond

We demonstrate a wide-band all-optical method of nanoscale magnetic resonance (MR) spectroscopy under ambient conditions. Our method relies on cross-relaxation between a probe spin, the electronic spin of a nitrogen-vacancy centre in diamond, and target spins as the two systems are tuned into resonance. By optically monitoring the spin relaxation time ($T_1$) of the probe spin while varying the amplitude of an applied static magnetic field, a frequency spectrum of the target spin resonances, a $T_1$-MR spectrum, is obtained. As a proof of concept, we measure $T_1$-MR spectra of a small ensemble of $^{14}$N impurities surrounding the probe spin within the diamond, with each impurity comprising an electron spin 1/2 and a nuclear spin 1. The intrinsically large bandwidth of the technique and probe properties allows us to detect both electron spin transitions -- in the GHz range -- and nuclear spin transitions -- in the MHz range -- of the $^{14}$N spin targets. The measured frequencies are found to be in excellent agreement with theoretical expectations, and allow us to infer the hyperfine, quadrupole and gyromagnetic constants of the target spins. Analysis of the strength of the resonances obtained in the $T_1$-MR spectrum reveals that the electron spin transitions are probed via dipole interactions, while the nuclear spin resonances are dramatically enhanced by hyperfine coupling and an electron-mediated process. Finally, we investigate theoretically the possibility of performing $T_1$-MR spectroscopy on nuclear spins without hyperfine interaction and predict single-proton sensitivity using current technology. This work establishes $T_1$-MR as a simple yet powerful technique for nanoscale MR spectroscopy, with broadband capability and a projected sensitivity down to the single nuclear spin level.

Multi-Frequency Pulsed Overhauser DNP at 1.2 Tesla

Abstract Dynamic nuclear polarization (DNP) is a methodology to increase the sensitivity of nuclear magnetic resonance (NMR) spectroscopy. It relies on the transfer of the electron spin polarization from a radical to coupled nuclear spins, driven by microwave excitation resonant with the electron spin transitions. In this work we explore the potential of pulsed multi-frequency microwave excitation in liquids. Here, the relevant DNP mechanism is the Overhauser effect. The experiments were performed with TEMPOL radicals in aqueous solution at room temperature using a Q-band frequency (1.2 T) electron paramagnetic resonance (EPR) spectrometer combined with a Minispec NMR spectrometer. A fast arbitrary waveform generator (AWG) enabled the generation of multi-frequency pulses used to either sequentially or simultaneously excite all three 14N-hyperfine lines of the nitroxide radical. The multi-frequency excitation resulted in a doubling of the observed DNP enhancements compared to single-frequency microwave excitation. Q-band free induction decay (FID) signals of TEMPOL were measured as a function of the excitation pulse length allowing the efficiency of the electron spin manipulation by the microwave pulses to be extracted. Based on this knowledge we could quantitatively model our pulsed DNP enhancements at 1.2 T by numerical solution of the Bloch equations, including electron spin relaxation and experimental parameters. Our results are in good agreement with theoretical predictions. Whereas for a narrow and homogeneous single EPR line continuous wave excitation leads to more efficient DNP enhancements compared to pulsed excitation for the same amount of averaged microwave power. The situation is different for radicals with several hyperfine lines or in the presence of inhomogeneous line broadening. In such cases pulsed single/multi-frequency excitation can lead to larger DNP enhancements.

Transverse interference peaks in chirp FT-EPR correlated three-pulse ESEEM spectra

Fourier transform (FT) electron paramagnetic resonance (EPR) correlation spectroscopy usually requires broader excitation bandwidth than can be achieved by monochromatic rectangular pulses. Replacement of such pulses by frequency-swept pulses affords the correlation spectra, which, however, may not look the same as those that would be obtained with sufficiently broad-banded monochromatic rectangular pulses. This was recently observed for correlating nuclear frequencies to FT-EPR spectra by a three-pulse electron spin echo envelope modulation experiment. Here we analyze the origin of the additional cross peaks, whose position depends on the direction of the frequency sweep. We find that such peaks arise if coherence or polarization is transferred to an electron spin transition already before this transition is actually passed during the frequency sweep. This happens by excitation of a chain of transitions that connect levels of the source transition, where coherence resides before mixing, and the target transition, where it resides after mixing. The correlation spectra can be simplified by combining data from frequency up and down sweeps.

High-pressure behavior of the polymorphs of FeOOH

The high-pressure structural and electronic behavior of α-, β-, and γ-FeOOH were studied in situ using a combination of synchrotron X-ray diffraction (XRD) and X-ray emission spectroscopy (XES). We monitored α-FeOOH by XES as a function of pressure up to 85 GPa and observed an electronic spin transition that began at approximately 50 GPa, which is consistent with previous results. In the γ-FeOOH sample, we see the initiation of a spin transition at 35 GPa that remains incomplete up to 65 GPa. β-FeOOH does not show any indication of a spin transition up to 65 GPa. Analysis of the high-pressure XRD data shows that neither β-FeOOH nor γ-FeOOH transform to new crystal structures, and both amorphize above 20 GPa. Comparing our EOS results for the β and γ phases with recently published data on the α and e phases, we found that β-FeOOH exhibits distinct behavior from the other three polymorphs, as it is significantly less compressible and does not undergo a spin transition. A systematic examination of these iron hydroxide polymorphs as a function of pressure can provide insight into the relationship between electronic spin transitions and structural transitions in these OH- and Fe 3+ -bearing phases that may have implications on our understanding of the water content and oxidation state of the mantle.

PELDOR and RIDME Measurements on a High-Spin Manganese(II) Bisnitroxide Model Complex.

A homoleptic bisnitroxide complex of manganese(II) was synthesized as a model system for EPR spectroscopic distance determinations involving high-spin metal ions and more than one distance. The performance of the RIDME experiment is compared with that of the more frequently used PELDOR experiment. It is shown that the PELDOR experiment yields both distances, Mn(II)-nitroxide and nitroxide-nitroxide, and that they can be separated to a certain extent, whereas the RIDME experiment yields only the Mn(II)-nitroxide distance. Both pulse sequences yield artifacts, either due to multispin effects or higher electron-spin transitions. Orientation selection is mostly introduced by the nitroxide signal and can be averaged out by variation of the observer field in the RIDME experiment. Thus, both methods might be used complementarily to obtain a reliable picture of an unknown system.

Electron transfer and spin transition in metal-hexacyanoferrates driven by anatase TiO2: electronic and structural order effects

Pure LS Fe(ii) starting from a mix of LS Fe(ii) and Fe(iii) is obtained by synthetizing CoHCF in the presence of TiO2.

Fast room-temperature phase gate on a single nuclear spin in diamond.

Nuclear spins support long lived quantum coherence due to weak coupling to the environment, but are difficult to rapidly control using nuclear magnetic resonance as a result of the small nuclear magnetic moment. We demonstrate a fast ∼500 ns nuclear spin phase gate on a (14)N nuclear spin qubit intrinsic to a nitrogen-vacancy center in diamond. The phase gate is enabled by the hyperfine interaction and off-resonance driving of electron spin transitions. Repeated applications of the phase gate bang-bang decouple the nuclear spin from the environment, locking the spin state for up to ∼140 μs.

Spin transition of Fe2+ in ringwoodite (Mg,Fe)2SiO4 at high pressures

Electronic spin transitions of iron in the Earth’s mantle minerals are of great interest to deep-Earth researchers because their effects on the physical and chemical properties of mantle minerals can significantly affect our understanding of the properties of the deep planet. Here we have studied the electronic spin states of iron in ringwoodite (Mg 0.75 Fe 0.25 ) 2 SiO 4 using synchrotron Mossbauer spectroscopy in a diamond-anvil cell up to 82 GPa. The starting samples were analyzed extensively using transmission and scanning electron microscopes to investigate nanoscale crystal chemistry and local iron distributions. Analyses of the synchrotron Mossbauer spectra at ambient conditions reveal two non-equivalent iron species, (Fe 2+ ) 1 and (Fe 2+ ) 2 , which can be attributed to octahedral and tetrahedral sites in the cubic spinel structure, respectively. High-pressure Mossbauer measurements show the disappearance of the hyperfine quadrupole splitting ( QS ) of the Fe 2+ ions in both sites at approximately 45–70 GPa, indicating an electronic high-spin (HS) to low-spin (LS) transition. The spin transition exhibits a continuous crossover nature over a pressure interval of ~25 GPa, and is reversible under decompression. Our results here provide the first experimental evidence for the occurrence of the spin transition in the spinel-structured ringwoodite, a mantle olivine polymorph, at high pressures.

Symmetrization driven spin transition in ε-FeOOH at high pressure

Structural and electronic spin transitions in high-pressure ε-FeOOH are studied using a combination of high pressure X-ray emission spectroscopy (XES), X-ray diffraction (XRD) and density functional theory (DFT) calculations. Using XES, a high- to low-spin transition in trivalent iron is found in ε-FeOOH on compression between 40 and 60 GPa. This is accompanied by a sudden discontinuity in unit cell volume at 53(±2) GPa, obtained from XRD data collected over the same compression range. These results are consistent with DFT calculations using an on-site Coulomb repulsion term (GGA+U), which predict a spin transition in ε-FeOOH at 64.8 GPa. A second order phase transition from P21nm to Pnnm is predicted from DFT at ∼43 GPa and evidenced in the XRD data from the anisotropic stiffening of the lattice parameters around the spin transition. In addition, the DFT results give evidence that the spin collapse is assisted by symmetrization of hydrogen bonds during the transition from P21nm to Pnnm. As the presence of hydrogen, even in small quantities, can affect phase relations, melting temperature, rheology, and other key properties of the Earthʼs mantle, our study unveils a connection between water (hydroxyl) content and the spin-transition pressure of Fe3+ in the Earthʼs mantle.

Spin readout and addressability of phosphorus-donor clusters in silicon

The spin states of an electron bound to a single phosphorus donor in silicon show remarkably long coherence and relaxation times, which makes them promising building blocks for the realization of a solid-state quantum computer. Here we demonstrate, by high-fidelity (93%) electrical spin readout, that a long relaxation time T1 of about 2 s, at B=1.2 T and T≈100 mK, is also characteristic of electronic spin states associated with a cluster of few phosphorus donors, suggesting their suitability as hosts for spin qubits. Owing to the difference in the hyperfine coupling, electronic spin transitions of such clusters can be sufficiently distinct from those of a single phosphorus donor. Our atomistic tight-binding calculations reveal that when neighbouring qubits are hosted by a single phosphorus atom and a cluster of two phosphorus donors, the difference in their electron spin resonance frequencies allows qubit rotations with error rates ≈10(-4). These results provide a new approach to achieving individual qubit addressability.

NV-Diamond Magnetometer Using Electron Irradiation

ABSTRACTNitrogen-vacancy (NV) center in diamond is an emerging system for quantum-logic device and sensor applications. The key feature of the NV center is the ability of spin manipulation at room temperature. We apply a wide range of electron irradiation to generate the NV centers in nitrogen-rich diamond for creating best sensitivity. The NV0 and NV─ concentrations in electron irradiated diamond are determined from optical spectra. Additionally, electron spin resonance (ESR) has also proven to be an effective method for probing the electron spin transition between |ms=±1> and |ms=0> states of the NV centers. A study of ESR frequency shift and signal broadening and magnetometer sensitivity as a function of electron irradiation dose has been conducted. The research presented herein is a demonstration of minimum detectable magnetic field tailoring required for future-generation high-sensitivity diamond magnetometry.

Current-induced nuclear spin depolarization at Landau level filling factorν=1/2

Hyperfine interactions between electron and nuclear spins in the quantum Hall regime provide powerful means for manipulation and detection of nuclear spins. In this work we demonstrate that significant changes in nuclear spin polarization can be created by applying an electric current in a 2-dimensional electron system at Landau level filling factor nu=1/2. Electron spin transitions at nu= 2/3 and 1/2 are utilized for the measurement of the nuclear spin polarization. Consistent results are obtained from these two different methods of nuclear magnetometry. The finite thickness of the electron wavefunction is found to be important even for a narrow quantum well. The current induced effect on nuclear spins can be attributed to electron heating and the efficient coupling between the nuclear and electron spin systems at nu=1/2. The electron temperature, elevated by the current, can be measured with a thermometer based on the measurement of the nuclear spin relaxation rate. The nuclear spin polarization follows a Curie law dependence on the electron temperature. This work also allows us to evaluate the electron g-factor in high magnetic fields as well as the polarization mass of composite fermions.

A Synthetic Two‐Spin Quantum Bit: g‐Engineered Exchange‐Coupled Biradical Designed for Controlled‐NOT Gate Operations

A quantum gate: A system of two coupled electron spins that is useful for simple quantum computing operations has been prepared by synthesis of a biradical 1 and co-crystallization with an isomorphous host molecule. The two weakly exchange-coupled quantum bits (target qubit blue and control qubit red) span four electron spin states. The electron spin transition is denoted by two black arrows.

Relaxation and modulation interference effects in two-pulse electron spin echo envelope modulation (ESEEM)

Two-pulse electron spin echo envelope modulation (ESEEM) line widths are influenced by transverse electron spin relaxation, which is in turn induced by local field fluctuations. Simultaneous analysis of the decays of the unmodulated and modulated parts of the ESEEM signal provides deeper insight into the relaxation of a spin system consisting of an electron spin 1/2 coupled to NI nuclei with spin 1/2. Standard two-pulse ESEEM formulas either do not account for relaxation or assume uniform relaxation for all lines. In general, the relaxation rates on allowed and forbidden transitions may not be the same. Experimental results obtained on a single crystal of Cu(II)-doped l-histidine suggest that such a difference exists. Theoretical considerations show that in such a case the product rule for two-pulse ESEEM does not extend to expressions including relaxation. Product rules in general do not properly account for relaxation in three-pulse ESEEM and HYSCORE experiments. Decay of the apparently non-oscillatory part of the two-pulse echo may be strongly affected by modulation interference. Such interference of difference frequencies of matrix nuclei may cause a rather flat initial feature, which was previously attributed solely to non-exponential phase relaxation of electron spin transitions due to spin diffusion of the matrix nuclei. In addition, the sometimes observed drastic initial decay of the time domain signal is related to modulation interference of multiple-quantum coherences that arise from a strong cross-suppression effect.

Electronic spin transitions in finite-size graphene

Density Functional Theory study on graphene ribbons with various shapes and sizes shows that as ribbon increases in length and width, its orbital energy gap decreases and prefers a higher spin state. Such a transition occurs when the energy gap between the highest doubly occupied and the lowest unoccupied molecular orbitals of the ground state is about 1.13eV. Our results suggest that high-spin states are stable, and graphene ribbons have ferromagnetic properties. The results are consistent with recent observations where bulk graphene possesses both ferromagnetic and antiferromagnetic properties as in phase-separated systems. The open-shell singlet state was suggested previously for the antiferromagnetic property of graphene ribbons.

Effects of spin transitions degeneracy in pulsed EPR of the fullerene C 70 triplet state produced by continuous light illumination

X-band echo-detected electron paramagnetic resonance (ED EPR) spectra of triplet state of fullerene C 70 generated by continuous light illumination were found to correspond below 30 K to a non-equilibrium electron spin polarization. Above 30 K spectra are characteristic of Boltzmann equilibrium. Spectra were simulated fairly well with zero-field splitting parameters D = 153 MHz and E and distributed within the range of 6–42 MHz. The origin of E distribution is attributed to the Jahn–Teller effect, which in glassy matrix is expected to depend on the local surrounding of a fullerene molecule (a so-called E-strain). In the center of ED EPR spectra a narrow hole was observed. With increase of the microwave pulse turning angle this hole transforms into a single narrow absorptive line. Numerical simulations by density matrix formalism confirm that central hole originates from a simultaneous excitation of both allowed electron spin transitions of the triplet ( T 0 ↔ T + and T 0 ↔ T −), because of their degeneracy at this spectral position. Also explanations are given why this hole has not been observed in the previously reported experiments on continuous wave EPR and on ED EPR under laser pulse excitation.

Alkali-metal electron spin density shift induced by a helium nanodroplet

Helium (He) nanodroplets provide a cold and virtually unperturbing environment for the study of weakly bound molecules and van der Waals aggregates. High resolution microwave spectroscopy and the detection of electron spin transitions in doped He droplets have recently become possible. Measurements of hyperfine-resolved electron spin resonance in potassium (39K) and rubidium (85Rb) atoms on the surface of He droplets show small line shifts relative to the bare atoms. These shifts were recorded for all 2I + 1 components (I is the nuclear spin) of a transition at high accuracy for He droplets ranging in size from 1000 to 15,000 He atoms. Evaluation of the spectra yields the influence of the He environment on the electron spin density at the alkali-metal nucleus. A semi-empirical model is presented that shows good qualitative agreement with the measured droplet size dependent increase of Fermi contact interaction at the nuclei of dopant K and Rb.

Hole burning—EIT studies of the NV centre in diamond

The negative nitrogen-vacancy centre in diamond is used to illustrate electromagnetically induced transparency features within a coherent hole. A hole is created in an inhomogeneously broadened electron spin transition and its spectrum modified by driving hyperfine transitions. The modified spectrum is discussed in terms of dressed states of the system, and the spectrum is shown to be in good correspondence with numerical solutions of the density matrix for the doubly driven system.

1H and 13C Dynamic Nuclear Polarization in Aqueous Solution with a Two-Field (0.35 T/14 T) Shuttle DNP Spectrometer

Dynamic nuclear polarization (DNP) permits increasing the NMR signal of nuclei by pumping the electronic spin transitions of paramagnetic centers nearby. This method is emerging as a powerful tool to increase the inherent sensitivity of NMR in structural biology aiming at detection of macromolecules. In aqueous solution, additional technical issues associated with the penetration of microwaves in water and heating effects aggravate the performance of the experiment. To examine the feasibility of low-field (9.7 GHz/0.35 T) DNP in high resolution NMR, we have constructed the prototype of a two-field shuttle DNP spectrometer that polarizes nuclei at 9.7 GHz/0.35 T and detects the NMR spectrum at 14 T. We report our first (1)H and (13)C DNP enhancements with this spectrometer. Effective enhancements up to 15 were observed for small molecules at (1)H 600 MHz/14 T as compared to the Boltzmann signal. The results provide a proof of principle for the feasibility of a shuttle DNP experiment and open up perspectives for the application potential of this method in solution NMR.