Electron Spin-lattice Relaxation Research Articles

Electron Spin-Lattice Relaxation of Substitutional Nitrogen in Silicon: The Role of Disorder and Motional Effects.

In a previous investigation, the authors proposed nitrogen as a possible candidate for exploiting the donor spin in silicon quantum devices. This system is characterized by a ground state deeper than the other group V impurities in silicon, offering less stringent requirements on the device temperature necessary to access the unionized state. The nitrogen donor is slightly displaced from the substitutional site, and upon heating, the system undergoes a motional transition. In the present article, we show the results from our investigation on the spin-relaxation times in natSi and 28Si substrates and discuss the motional effects on relaxation. The stretched exponential relaxation observed is interpreted as a distribution of spin-lattice relaxation times, whose origin is also discussed. This information greatly contributes to the assessment of a nitrogen-doped silicon system as a potential candidate for quantum devices working at temperatures higher than those required for other group V donors in silicon.

Rate constants for saturation-recovery EPR and ELDOR of 14N-Spin labels

Saturation-recovery (SR)-EPR can determine electron spin–lattice relaxation rates in liquids over a wide range of effective viscosity, making it especially useful for biophysical and biomedical applications. Here, I develop exact solutions for the SR-EPR and SR-ELDOR rate constants of 14N-nitroxyl spin labels as a function of rotational correlation time and spectrometer operating frequency. Explicit mechanisms for electron spin–lattice relaxation are: rotational modulation of the N-hyperfine and electron-Zeeman anisotropies (specifically including cross terms), spin-rotation interaction, and residual frequency-independent vibrational contributions from Raman processes and local modes. Cross relaxation from mutual electron and nuclear spin flips, and direct nitrogen nuclear spin–lattice relaxation, also must be included. Both the latter are further contributions from rotational modulation of the electron-nuclear dipolar interaction (END). All the conventional liquid-state mechanisms are defined fully by the spin-Hamiltonian parameters; only the vibrational contributions contain fitting parameters. This analysis gives a firm basis for interpreting SR (and inversion recovery) results in terms of additional, less standard mechanisms.

Improving the molecular spin qubit performance in zirconium MOF composites by mechanochemical dilution and fullerene encapsulation.

Enlarging the quantum coherence times and gaining control over quantum effects in real systems are fundamental for developing quantum technologies. Molecular electron spin qubits are particularly promising candidates for realizing quantum information processing due to their modularity and tunability. Still, there is a constant search for tools to increase their quantum coherence times. Here we present how the mechanochemical introduction of active spin qubits in the form of 10% diluted copper(ii)-porphyrins in the diamagnetic PCN-223 and MOF-525 zirconium-MOF polymorph pair can be achieved. Furthermore, the encapsulation of fullerene during the MOF synthesis directs the process exclusively toward the rare PCN-223 framework with a controllable amount of fullerene in the framework channels. In addition to the templating role, the incorporation of fullerene increases the electron spin-lattice and phase-memory relaxation times, T1 and Tm. Besides decreasing the amount of nuclear spin-bearing solvent guests in the non-activated qubit frameworks, the observed improved relaxation times can be rationalized by modulating the phonon density of states upon fullerene encapsulation.

Electronic structure and spin-lattice relaxation in superconducting vortex states on the kagome lattice near van Hove filling

Starting from a tight-binding model on the kagome lattice near the van Hove filling, the superconducting (SC) properties are investigated self-consistently by using the Bogoliubov--de Gennes equations with the consideration of the inequivalent third-neighbor (TN) bonds. Near the van Hove filling, the most favorable SC pairings are found to derive from the electrons belonging to the same sublattice sites, including the on-site $s$-wave and the spin-singlet/spin-triplet TN pairings. The inequivalent TN bonds will result in multiple SC components with different orbital angular momenta for the TN SC pairings. Whereas the density of states and the temperature ($T$) dependence of the spin-lattice relaxation rate (${T}_{1}^{\ensuremath{-}1}$) exhibit distinct line shapes in the SC state for the three cases, a peak structure in the $T$ dependence of ${T}_{1}^{\ensuremath{-}1}$ can be found for all of them just below ${T}_{c}$ as a result of the van Hove singularity, even though the SC gap has nodes. The effects of magnetic vortices on the low-energy excitations and on the $T$ dependence of ${T}_{1}^{\ensuremath{-}1}$ with the implications of the results are also discussed for all the cases.

Ultra-slow electron spin-lattice relaxation in a low magnetic field enables massive optical spin polarization in the 4A2 ground state of Cr3+ in ruby* *This paper is dedicated to my late friend and mentor Dr Alex Szabo, the originator of transient spectral hole-burning and fluorescence line narrowing in the solid state, whose knowledge of the spectroscopy of ruby is unsurpassed.

Ruby (α-Al2O3 doped with Cr3+) has been an archetypal material in the development of optical spectroscopy of the solid state for the last 150 years and was the first material that was demonstrated to lase. Notwithstanding the vast literature on ruby, one effect was somehow missed: in a magnetic field B ∥c ∼ 235 mT, the spin-lattice relaxation time T 1 for the |+3/2⟩ level in the 4A2 ground state is massively lengthened to ∼12 s at 1.4 K as demonstrated in this study. This very long relaxation time enables optical pumping of the |+3/2⟩ level via the R 1(±1/2) lines and a considerable +3/2 spin polarization of ∼95% is readily achieved. The observed magnetic field dependence can be quantitatively described using the one-phonon relaxation process.

Анизотропное насыщение спектра ЭПР радикала DCO, стабилизированного в твердом CO при 4.2 K, и его ориентационное движение

Formyl radicals, DCO, were produced in solid CO matrix and studied by EPR using gas deposition technique on a cold substrate at 4.2 K. The radical electron spin-lattice relaxation was measured to be anisotropic. The anisotropy was found to originate from the anisotropic orientational motion of the radical with the most intensive librations performed around a z axis corresponding to the smallest moment of inertia of the molecule. It was shown that, in solid CO, the libration motion of small molecules is modeled by considering a particle rotating in the orientational potential box. A suggestion was substantiated about the complicated nature of the orientational motion of HCO in the solid CO matrix including the intensive librations and slow tunneling rotation of the molecule around the z axis.

Anisotropic saturation of the EPR spectrum of an DCO radical stabilized in solid CO at 4.2 K and its orientation motion

Formyl radicals, DCO, were produced in solid CO matrix and studied by EPR using gas deposition technique on a cold substrate at 4.2 K. The radical electron spin-lattice relaxation was measured to be anisotropic. The anisotropy was found to originate from the anisotropic orientational motion of the radical with the most intensive librations performed around a z axis corresponding to the smallest moment of inertia of the molecule. It was shown that, in solid CO, the libration motion of small molecules is modeled by considering a particle rotating in the orientational potential box. A suggestion was substantiated about the complicated nature of the orientational motion of HCO in the solid CO matrix including the intensive librations and slow tunneling rotation of the molecule around the z axis. Keywords: electron paramagnetic resonance, matrix isolation, formyl radical, anisotropy of the spin-lattice relaxation time, librations and tunneling rotation of molecules.

Relaxation of nuclear dipolar energy

Under typical conditions for dynamic nuclear polarization (DNP)—temperature about 1 K or below and magnetic field about 3 T or higher—the polarization agent causes nuclear dipolar order to relax up to four orders of magnitude faster than nuclear polarization. However, as far as we know, this ultra-fast dipolar relaxation has thus far not been explained in a satisfactory way.We report similar ultra-fast dipolar relaxation of proton spins in naphthalene due to the photo-excited triplet spin of pentacene and propose a three-step mechanism that explains such ultra-fast dipolar relaxation by ground state electron spins as well as by photo-excited triplet spins: nuclear spin diffusion transfers nuclear dipolar order—that is nuclear dipolar energy—spatially to near the electron spins. Flip-flop transitions between nuclear spins near the electron spins convert this dipolar energy into electron-nuclear interaction energy. Finally electron spin–lattice relaxation or decay of the triplet spin transfers the latter type of energy to the lattice. We will show that this mechanism quantitatively explains the observed dipolar relaxation rate.The proposed mechanism is expected to contribute to dipolar relaxation in any spin system containing more than one spin species. It tends to create a stationary state, in which all dipolar interactions are combined in a single energy reservoir described by a single spin temperature. As an example we suggest that the addition of a relaxation agent in samples used for DNP may significantly accelerate the relaxation of the dipolar energy of the polarization agent, and as a result could possibly reduce the contribution of thermal mixing (TM) to DNP.

EPR and optical studies of Ni(II) ions in Zn(4-chloropyrazole)6(ClO4)2 at 300 K: Probing the structure, bonding, and electron spin relaxation

CW EPR and optical absorption studies of Ni(II) ions doped in Zn(C3H3ClN2)6(ClO4)2 (Ni/ZCPC) were carried out at 300 K. The single crystal rotation along three orthogonal axes gave spin Hamiltonian parameters of gx = 2.1961, gy = 2.1679, and gz = 2.1234; Dx = 1014.3, Dy = 913.7, and Dz = −1928.0 G. A progressive CW power saturation study performed at 300 K was used to determine the product of the electron spin–lattice relaxation time and spin–spin relaxation time (T1 × T2) (3.51 × 10−14 s2) for transitions at 4085 and 5740 G. Interestingly, the result demonstrates that Ni/ZCPC is a rare system having the largest T1 × T2 value observed at 300 K compared to other Ni(II) systems reported to date. The optical and EPR data were used to obtain the bonding parameters. The EPR spin Hamiltonian parameters and deconvolution of the optical absorption spectrum reveal that the Ni(II) center has trigonal symmetry.

One-directional polarization transport in electron/nuclear spin chains with loss and gain

Understanding the joint dynamics of electron and nuclear spins is central to core concepts in solid-state magnetic resonance - such as spin-lattice relaxation and dynamic nuclear polarization - but a generalization that capitalizes on competing polarization loss and gain channels is still lacking. Here, we theoretically study the non-Hermitian dynamics of hybrid electron/nuclear spin systems in the simultaneous presence of electron spin pumping and spin-lattice relaxation. Focusing on periodic, one-dimensional chains, we find that by adjusting the electron spin pumping to a critical level, it is possible to steer the flow of nuclear polarization to create site-dependent distributions where either end of the array polarizes in opposite ways, irrespective of the initial state. By contrast, we show that ring-like patterns - where the limit nuclear polarization is uniform - exhibit a non-decaying, externally-driven nuclear spin current. Interestingly, cyclic magnetic field modulation can render these processes largely robust to defects in the chain, a response featuring some interesting similarities - and differences - with recent findings in other non-Hermitian physical platforms.

Direct measurement of the triple spin flip rate in dynamic nuclear polarization

A previous study of the effect of Gadolinium doping on the dynamic polarization (DNP) of 13C using trityls showed that the rate at which the polarization builds up is almost independent of the Gadolinium concentration, while the electron spin–lattice relaxation rate varies over an order of magnitude. In this paper we analyze the polarization build-up in detail and show that in this case DNP is due to the cross-effect (CE) and that the build-up rate can be quantitatively interpreted as the rate of the triple spin flips responsible for the CE. Thus this build-up rate presents a direct measurement of this triple spin flip rate.

Electron spin relaxation time of Ni(II) ion in hexapyrazole zinc(II) dinitrate at 300 K.

Understanding the electron spin relaxation properties of paramagnetic species is a fundamental requirement to use them as a probe to measure distances between sites in biomolecules by electron paramagnetic resonance (EPR) spectroscopy. Even though Ni(II) ion is an essential trace element for many species, relaxation properties are not well understood. Herein, the polycrystalline sample of Ni(II) ion magnetically diluted in Zn(Pyrazole)6 (NO3 )2 (Ni/ZPN) has been studied in detail by EPR spectroscopy to explore the electron spin relaxation time. Progressive continuous-wave (CW) EPR power saturation study on Ni/ZPN at 300 K yielded 907 mW as the P1/2 value. The cavity constant (KQ ) has been calculated using tempol in PVA-BA glass matrix and the product of electron spin-lattice relaxation time (T1 ) and spin-spin relaxation time (T2 ) for Ni/ZPN at 300 K has been reported for the first time.

Succinyl-DOTOPA: An effective triradical dopant for low-temperature dynamic nuclear polarization with high solubility in aqueous solvent mixtures at neutral pH

We report the synthesis of the nitroxide-based triradical compound succinyl-DOTOPA and the characterization of its performance as a dopant for dynamic nuclear polarization (DNP) experiments in frozen solutions at low temperatures. Compared with previously described DOTOPA derivatives, succinyl-DOTOPA has substantially greater solubility in glycerol/water mixtures with pH > 4 and therefore has wider applicability. Solid state nuclear magnetic resonance (ssNMR) measurements at 9.39 T and 25 K, with magic-angle spinning at 7.00 kHz, show that build-up times of DNP-enhanced, cross-polarized 13C ssNMR signals are shorter and that signal amplitudes are larger for glycerol/water solutions of L-proline containing succinyl-DOTOPA than for solutions containing the biradical AMUPol, with electron spin concentrations of 15 mM or 30 mM, resulting in greater net sensitivity gains from DNP. In similar measurements at 90 K, AMUPol yields greater net sensitivity, apparently due to its longer electron spin-lattice and spin-spin relaxation times. One- and two-dimensional 13C ssNMR measurements at 25 K on the complex of the 27-residue peptide M13 with the calcium-sensing protein calmodulin, in glycerol/water with 10 mM succinyl-DOTOPA, demonstrate the utility of this compound in DNP-enhanced ssNMR studies of biomolecular systems.

Magnetization dynamics of the material with spin triplet states under the action of a weak varying field and spin-lattice interaction in zero constant field

The anisotropic dynamics of spin triplet states (STS) of molecular single crystals in zero constant and weak varying magnetic fields (weakness means the absence of saturation at the steady state and of the nutation at the pulse EPR) directed along the molecular axes, is analytically investigated. The equations are derived for the free motion of the sample magnetization, describing its linear oscillations along that molecular axis, along which its nonzero initial value was created. The tensor of the steady-state dynamical susceptibility to the varying field is found. The result of the action of a short MW pulse on STS is analytically described, containing a periodic dependence on the pulse duration and its detuning. Abovementioned results can be applied also to I=1 NMR, what is important for nitrogen-containing explosives and narcotics monitoring. The anisotropic dynamics of electron spin-lattice relaxation (SLR) at its one-phonon mechanism is investigated without the high temperature approximation over the phonon temperature; the SLR rates of the separate transitions of STS are calculated; the corresponding SLR probabilities are written in the form, which supposes the fractal dimensionality d of a lattice; the results with d=4/3 agree well with the experimental data in STS of the buried tryptophan of ribonuclease T1.

Spin-lattice relaxation processes of transition metal ions in a heavily cobalt doped ZnO: Phonon heating effect

Inversion recovery with electron spin-echo detection has been used to study the electron spin-lattice relaxation rates 1/T1 for transition metal impurities in heavily cobalt-doped hydrothermally grown ZnO single crystals. The relaxation dynamics of Co2+ ions dominates the phonon bottleneck effect in the Orbach-Aminov process, which involves the modulation of the zero-field-splitting tensor. The relaxation mechanism may be treated in terms of phonon heating with fast rate of energy pump from Co2+ spins into the lattice phonon modes. The measurements reveal the cross-relaxation process in which the single Co2+ ions cross-relax to exchange-coupled clusters of cobalt ions. The higher temperature relaxation of Co2+ indicates an additional Orbach-Aminov process via a state of ∼226 cm−1 above the ground state Kramers doublet. It is shown that in this system Co2+ ions play a role of the rapidly relaxing centers, strongly mediating the spin-lattice relaxation of the other transition metal impurities, such as Mn2+ and Fe3+.

Engineering electronic structure to prolong relaxation times in molecular qubits by minimising orbital angular momentum

The proposal that paramagnetic transition metal complexes could be used as qubits for quantum information processing (QIP) requires that the molecules retain the spin information for a sufficient length of time to allow computation and error correction. Therefore, understanding how the electron spin-lattice relaxation time (T1) and phase memory time (Tm) relate to structure is important. Previous studies have focused on the ligand shell surrounding the paramagnetic centre, seeking to increase rigidity or remove elements with nuclear spins or both. Here we have studied a family of early 3d or 4f metals in the +2 oxidation states where the ground state is effectively a 2S state. This leads to a highly isotropic spin and hence makes the putative qubit insensitive to its environment. We have studied how this influences T1 and Tm and show unusually long relaxation times given that the ligand shell is rich in nuclear spins and non-rigid.

Gadolinium Effect at High-Magnetic-Field DNP: 70% 13C Polarization of [U-13C] Glucose Using Trityl.

We show that the trityl electron spin resonance (ESR) features, crucial for an efficient dynamic nuclear polarization (DNP) process, are sample-composition-dependent. Working at 6.7 T and 1.1 K with a generally applicable DNP sample solvent mixture such as water/glycerol plus trityl, the addition of Gd3+ leads to a dramatic increase in [U-13C] glucose polarization from 37 ± 4% to 69 ± 3%. This is the highest value reported to date and is comparable to what can be achieved on pyruvic acid. Moreover, performing ESR measurements under actual DNP conditions, we provide experimental evidence that gadolinium doping not only shortens the trityl electron spin-lattice relaxation time but also modifies the radical g-tensor. The latter yielded a considerable narrowing of the ESR spectrum line width. Finally, in the frame of the spin temperature theory, we discuss how these two phenomenaaffect the DNP performance.

Initialization and Readout of Nuclear Spins via a Negatively Charged Silicon-Vacancy Center in Diamond.

In this Letter, we demonstrate initialization and readout of nuclear spins via a negatively charged silicon-vacancy (SiV) electron spin qubit. Under Hartmann-Hahn conditions the electron spin polarization is coherently transferred to the nuclear spin. The readout of the nuclear polarization is observed via the fluorescence of the SiV. We also show that the coherence time of the nuclear spin (6ms) is limited by the electron spin-lattice relaxation due to the hyperfine coupling to the electron spin. This Letter paves the way toward realization of building blocks of quantum hardware with an efficient spin-photon interface based on the SiV color center coupled to a long lasting nuclear memory.

An x-band continuous wave saturation recovery electron paramagnetic resonance spectrometer based on an arbitrary waveform generator.

An X-band (ca. 9-10 GHz) continuous wave saturation recovery spectrometer to measure electron spin-lattice relaxation (T1) was designed around an arbitrary waveform generator (AWG). The AWG is the microwave source and is used for timing of microwave pulses, generation of control signals, and digitizer triggering. Use of the AWG substantially simplifies the hardware in the bridge relative to that in conventional spectrometers and decreases the footprint. The bridge includes selectable paths with different power amplifications to permit experiments requiring hundreds of milliwatts to fractions of nanowatts for the pump and observe periods. The signal is detected with either a single or quadrature-output double balanced mixer. The system can operate with reflection or crossed-loop resonators. The source noise from the AWG was decreased by addition of a Wenzel high-stability clock. The source is sufficiently stable that automatic frequency control is not needed. The spectrometer was tested with samples that contained 1 × 1015 to 8 × 1017 spins and have T1 between a few hundred ns and hundreds of μs. Excellent signal-to-noise ratio was obtained with acquisition times of 2-90 s. Signal-to-noise performance is similar to that of a conventional saturation recovery spectrometer with a solid-state source. The stability and data reproducibility are better than with conventional sources. With replacement of frequency-sensitive components, this spectrometer can be used to perform saturation recovery measurements at any frequency within the range of the AWG.

Anisotropy of the electron spin–lattice relaxation. PO32− radical in glycinium phosphite gly·H3PO3 crystal

Electron spin–lattice relaxation has been measured for PO32− radical in glycinium phosphite gly·H3PO3 crystal and its deuterated analogue in temperature range 40–300 K. Angular dependence of the relaxation rate was measured in three crystal planes at room temperature. The Debye cut-off temperature has been calculated as ΘD = 97 K, which indicates that the temperature dependence of 1/T1 is governed by radical local vibrations localized in optical phonon modes range. Theories of possible 1/T1 angular dependence are reviewed. The anisotropy of spin–lattice relaxation rate in our crystal is assumed to be a result of local magnetic field fluctuations due to electron–proton dipolar coupling. Theoretical evaluation of 1/T1 were performed for coupling with protons at distances up to 0.46 nm. Not perfect agreement was found with motion correlation time τc = 2·10−9 s.