Phase Memory Time Research Articles

Nitroxide Spin−Relaxation over the Entire Motional Range

Homogeneous line widths, characterized by the phase memory time, Tm, of a nitroxide spin-labeled peptide, were measured over the entire motional range (∼10-10−10-4 s at the spectrometer resonance frequency of 9.7 GHz) using spin−echo correlated spectroscopy (SECSY) ESR. Phase memory times as short as 20 ns could be determined by using schemes designed to minimize the effects of pulse ring-down. Experimental Tm versus temperature curve (from 192 to 310 K) clearly resolves the Tm minimum, which provides great sensitivity to the details of molecular dynamics.

Method of Extending Hyperfine Coherence Times inPr3+∶Y2SiO5

In this Letter, we present a method for increasing the coherence time of praseodymium hyperfine ground state transitions in Pr(3+):Y(2)SiO5 by the application of a specific external magnetic field. The magnitude and angle of the external field is applied such that the Zeeman splitting of a hyperfine transition is at a critical point in three dimensions, making the first order Zeeman shift vanishingly small for the transition. This reduces the influence of the magnetic interactions between the praseodymium ions and the spins in the host lattice on the transition frequency. Using this method a phase memory time of 82 ms was observed, a value 2 orders of magnitude greater than previously reported. It is shown that the residual dephasing is amenable to quantum error correction.

Temperature variation of the molecular structure of lithium hydrazinium sulphate—a one-dimensional proton conductor

The paper reports the results of detailed studies of the molecular structure of lithium hydrazinium sulphate single crystal in a wide temperature range with the aim to clarify previously reported anomalies in the molecular dynamics at ∼100 K. The crystal does not undergo any structural phase transition from 8 to 460 K however, the donor-acceptor distance, between the nitrogen atoms involved in the hydrogen bond along the c -orthorhombic axis, starts to increase from the temperature of ∼100 K. This results in an anomaly of the phase memory time observed in electron spin echo studies and anomalies of hydrazinium internal modes observed in Raman scattering. Moreover, the anisotropy of the SO 4 tetrahedra is maximal at ∼100 K and decreases at higher temperatures. The possible contribution of fast proton transport, described by the Grotthuss model, to the proton conductivity along the c -axis at the temperature above ∼400 K is discussed.

Electronic structure, Jahn–Teller dynamics and electron spin relaxation of two types of octahedral Cu(ii) complexes in cadmium formate dihydrate Cd(HCOO)2·2H2O. EPR and ESE studies

Cd(HCOO)2·2H2O single crystals weakly doped with Cu(II) ions have been studied by cw-EPR (4.2–300 K) and by electron spin echo – ESE (4.2–60 K). Copper(II) ions substitute Cd(II) in two different sites forming Cu(HCOO)6–Cuf and Cu(HCOO)2(H2O)4–Cuw octahedral complexes with strong preference to Cuf as shown by the intensity ratio of the EPR spectra (up to 20∶1). Despite different molecular structures both complexes have nearly identical EPR parameters at rigid lattice limit with gz=2.429, gy=2.092, gx=2.064, Az=120, Ay=32 and Ax=12×10−4 cm−1 for Cuf. This fact as well as strong axial deformation of the crystal field at Cu(II) sites indicate that the strong Jahn–Teller effect operates producing three wells in the potential surface with one having much lower energy than the others. In the Cuf complex the dynamic J–T-effect has been observed as a vibronic averaging of the two g and A parameters (along z and y axes). It indicates that only one of the higher energy wells is thermally accessible and the Silver–Getz model leads to the average energy difference between the two lowest energy wells δ12=500(60) cm−1. The δ12 is temperature dependent. For Cuw complex no vibronic effects were observed in EPR spectra indicating that higher energy wells are not populated up to 300 K. The spin–lattice relaxation time T1 and phase memory time TM were measured up to 60 K only, because for higher temperatures the ESE decay was too fast. Spin–lattice relaxation is governed by two-phonon Raman processes which allow one to determine the Debye temperature of the crystal as ΘD=193 K. The ESE decay was described as V(2τ)=V0exp(−τ/b−mτ2) indicating the contribution of the spectral diffusion (quadratic term). The ESE dephasing rate 1/TM is governed by spectral diffusion below 15 K. For higher temperatures the T1-processes and excitations to the higher vibronic levels of energy Δ=166 cm−1 give comparable contributions.

Pulsed EPR studies of shallow donor impurities in SiC

Spin-lattice relaxation time (T1) and phase memory time (TM) of shallow donors in 3C-, 4H- and 6H-SiC have been measured in time domain by using pulsed EPR technique. The temperature dependence of T1 suggests that the Orbach process should be frozen at relatively high temperatures. Shallow donors in SiC are promising in attaining a sufficiently long phase memory time at temperatures much higher than Si:P.

Shallow donor electron spins as qubits in Si and SiGe: a pulsed ESR study

X-band pulse electron spin resonance spectroscopy has been used to determine the characteristic phase memory time (TM) for phosphorous shallow donors in Si and Si1−xGex (x=0.052) which have been proposed as qubits in group IV based quantum computing devices. With fast intense microwave pulses, electron spin echoes, formally equivalent to single-qubit operations, can be detected providing the characteristic times as well as additional information on the coupling between the electron spin and its surroundings (other electron or nuclear spins). The electron spin echo envelope modulation due to the super-hyperfine interaction with 29Si and 73Ge, has been detected in the Si and Si1−xGex samples.

Long coherence times at 300 K for nitrogen-vacancy center spins in diamond grown by chemical vapor deposition

Electron-spin-echo experiments reveal phase-memory times as long as 58 μs at 300 K for nitrogen-vacancy centers in chemical vapor deposition (CVD) single crystals. The spins were optically polarized and optically detected. Two high-quality CVD samples were studied. From the current results, it is not clear whether these phase-memory times represent a fundamental limit or are limited by an external source of decoherence.

Spin-lattice and spin-spin relaxation times of 2,4,6-tri-tert-butyl phenoxyl and 2,6-di-tert-butyl-4-methyl phenoxyl in diamagnetic crystals: Relaxation mechanism and influence of molecular motions

The spin-lattice and phase-memory times were determined for 2,4,6-tri-tert-butyl phenoxyl and 2,6-di-tert-butyl-4-methyl phenoxyl dispersed in a diamagnetic matrix by use of primary and stimulated echoes. The temperature variations from room temperature and lower to liquid helium indicated interesting characteristics, albeit there were no echo signals between 150 and 100 K. It may be concluded that the relaxation times vary depending on the motional fluctuation of substituted molecular groups on the π-conjugated framework. In particular, the methyl rotational motion of thetert-butyl groups at theortho-positions or thepara-position is a dominant contribution, andtert-butyl rotation itself and additional methyl rotation at thepara-position are also responsible for the shortening, especially in the phase-memory times. The shortening of the relaxation times when approaching liquid helium temperature is probably due to the quantum mechanical tunneling effect of the methyl substituents.

A Novel Approach for Measuring Absolute Rate Constants by Pulsed Electron Spin Resonance: Addition of Phosphinoyl and 2-Hydroxy-2-propyl Radicals to Several Alkenes,

A time-resolved Fourier transform electron spin resonance (TR FT ESR) method for determining absolute rate constants of reactive, free radical reactions is described. The phase memory times TM of a family of reacting radicals were measured precisely by electron spin−echo (ESE) detection. In all cases the ESE signal decays show a simple pseudo-first-order behavior. Rate constants of the reactions were extracted from the linear relationship between the reciprocal of the TM values and the alkene concentrations. The validity of the method is demonstrated for the measurement of the rate constant for addition of different phosphinoyl and 2-hydroxy-2-propyl radicals to several acrylates, methyl methacrylate, and vinyl pivalate in organic solvents at room temperature. The results are in excellent agreement with those obtained by other kinetic investigations employing time-resolved steady-state electron spin resonance (TR CW ESR) and optical absorption spectroscopy. The technique is shown to be applicable to systems with rate constants between 104 and 108 M-1 s-1, a range covered by the alkenes examined.

Relaxation mechanism in γ-ray-irradiated L-alanine studied by transfer saturation EPR and pulse EPR

Stable paramagnetic centers in γ-ray-irradiated L-alanine dosimeters exhibit a maximum in relaxation rate in the vicinity of 190 K. The mechanism of this relaxation rate has been investigated on the first stable alanine radical center, SARI, by employing continuous-wave transfer saturation electron paramagnetic resonance and pulse electron paramagnetic resonance techniques. The detected in-phase and out-of-phase spectra as well as phase memory times,T M, indicate that besides the well-known τp of the CH3 group of SAR1 an additional correlation time, τl (ΔElk=2689±50 K and 0 τ10 = 0.15 ± 0.03 ps), is involved in the transverse relaxation process and effects the SAR1 center. For the SAR1 center this mechanism originates from the hindered motion of undamaged CH3 and NH 3 + groups in the lattice. The motion of these groups additionally effects the spectrum of the SAR1 center through averaging out of the anisotropic splitting.

Single-Qubit Operations with the Nitrogen-Vacancy Center in Diamond

A concept combining optics and microwave pulses with the negative charge-state of the nitrogen-vacancy (NV-) center in diamond is demonstrated through experiments that are equivalent to single-qubit gates, and decoherencefor this qubit is examined. The spin levels of the ground state provide the two-level system. Optical excitation provides polarization of these states. The polarized state is operated coherently by 35 GHz microwave pulses. The final state is read out through the photoluminescence intensity. Decoherence arises from different sources for different samples. For high-pressure, high-temperature synthetic diamonds, the high concentration of substitutional N limits the phase-memory to a few μs. In a single-crystal CVD diamond, the phase memory time is at least 32 μs at 100 K. 1 4 N is tightly coupled to the electronic spin and produces modulation of the electron-spin echo decay under certain conditions. A two-qubit gate is proposed using this nuclear spin. This demonstration provides a great deal of insight into quantum devices in the solid state with some possibility for real application.

Spin soliton in aπ-conjugated ladder polydiacetylene

The electronic structure and the spin dynamics of a spin soliton observed in a polydiacetylene have been investigated using multifrequency pulsed and continuous-wave (cw) electron paramagnetic resonance (EPR), electron spin echo (ESE) spectroscopy, electron-nuclear double resonance (ENDOR), and electron-nuclear-nuclear triple resonance (TRIPLE). The undoped ladder polymer in which two polydiacetylene wires are linked by bridges consisting of two triple bonds exhibits a strong EPR signal. In contrast, no EPR signal is observed in the ladder-structured polydiacetylene, where the bridges consist of single bonds. The observed bridge effect on the probability of formation of paramagnetic centers is interpreted in terms of a quasidegenerate ground state due to the π-conjugated ladder structure that creates a π-bond kink corresponding to a spin soliton. High-frequency and high-field EPR reveals a small anisotropy of the g tensor (principal values g 1 =2.0037, g 2 =2.0028, and g 3 =2.0023) for the spin soliton. By nutation spectroscopy, the spin multiplicity was confirmed to be S=½. The hyperfine pattern attributed to the β protons was detected by ENDOR and TRIPLE methods, providing evidence for both the positive and negative spin densities of the soliton wave function. These experimental results led to the conclusion that the unpaired electron of the spin soliton was substantially delocalized over the two polydiacetylenes through the π-conjugation. At temperatures (T) below 50 K, the width of the EPR spectrum narrows by about 45% with increasing temperature and the width remains nearly constant for T>50 K. The pronounced change in the line width for T<50 K suggests the presence of a mobile spin soliton in the ladder-structured polydiacetylene. A temperature dependence of the electron spin system's phase memory time T M for T<50 K was also observed by ESE spectroscopy. The decay of the ESE exhibits a nonexponential behavior, with T M increasing monotonically with rising temperature These findings represent clear experimental evidence for motional narrowing phenomena. Based on a one-dimensional random-walk model for the unpaired electron spin along the ladder polymer, the soliton's diffusion rate constant was estimated from an analysis of the ESE dephasing process. An Arrhenius plot of the diffusion rate was asymptotic to 8×10 7 s - 1 at very low temperature, which is two orders of magnitude slower than that of the soliton in trans-polyacetylene.

Electron spin relaxation in solids-an application to spontaneously occurring radical centre in phenol-formaldehyde resins

An outline of electron spin-relaxation is briefly presented with mechanisms and processes of spin-lattice relaxation in ionic and amorphous solids. Electron spin resonance (EPR) and pulsed EPR measurements were performed in the temperature range 4-300 K on a radical occurring in a dried resol phenol-formaldehyde resin. The radical appears in a small concentration of about 1/spl times/10/sup 16/ radicals/g in 30/spl deg/C dried samples and the number of the radicals increases continuously with time up to 2/spl times/10/sup 17/ radicals/g after 100 days. Computer simulations of the EPR spectrum show that breaking of the dimethylene ether linkage probably forms the radical during synthesis reactions. Electron spin-lattice relaxation rate increases relatively slowly on heating and at <80 K is determined by interactions with two-level tunnelling systems in the polymer structure. For higher temperatures the relaxation is governed by interactions with centres having energy levels split by 298 cm/sup -1/. Phase relaxation is described by the phase memory time with rigid lattice limit T/sub M//sup 0/=2 /spl mu/s. This time is shortened above 100 K by thermally activated radical molecule motions with activation energy 85 cm/sup -1/. The electron spin echo envelope modulation (ESEEM) spectrum shows unresolved peaks at /sup 1/H indicating strong molecular dynamics and delocalisation of the unpaired electron.

Dephasing relaxation of the electron spin echo of the vibronic Cu(H(2)O)(6) complexes in Tutton salt crystals at low temperatures.

Two-pulse electron spin echo (ESE) measurements of the phase relaxation (phase memory time T(M)) were performed in a series of Tutton salt crystals M(I)(2)M(II)(SO(4))(2).6X(2)O (M(I)=NH(4), K, Cs; M(II)=Zn, Mg; X=H, D) weakly doped with Cu(2+) ions (c approximately equal to 10(18) ions/cm(3)) in temperature range 4-60 K where ESE signals were detectable. The ESE decay was strongly modulated with proton (or deuteron) frequencies and described by the decay function V(2tau)=V(0)exp(-btau-mtau(2)) with the mtau(2) term being temperature independent and negligible above 20 K. Various mechanisms leading to the tau- or tau(2)-type ESE decay are reviewed. The m and b coefficients for nuclear spectral diffusion (NSD), electron spectral diffusion (SD), and instantaneous diffusion (ID) were calculated in terms of existing theories and the resulting rigid lattice T(0)(M) times were found to be close one to another within the crystal family with average values: 17.5 micros (NSD protons), 200 micros (NSD deuterons), 8 micros (SD), and 5 micros (ID). The ID dominates but the calculated effective T(M)(0) is longer than the experimental T(M)(0)=2 micros. This is due to a nonuniform distribution of the Cu(2+) ions with a various degree of the disorder in the studied crystals. The acceleration of the dephasing rate 1/T(M) with temperature is due to the mechanisms producing exp(-btau) decay. They are reviewed and two of them were found to be operative in Tutton salt crystals: (a) Excitations to the vibronic levels of energy Delta leading to the temperature dependence 1/T(M)=B exp(-Delta/kT), with the vibronic levels produced by strong Jahn-Teller effect, and (b) spin-lattice relaxation processes being effective above 50 K. Based on the Delta values being on the order of 100 cm(-1), the scheme of vibronic levels in the Tutton salts is presented, and the independence of the Delta on temperature proves that the adiabatic potential surface shape of Jahn-Teller active Cu(H(2)O)(6) complexes is not affected by temperature below 65 K.

Electron spin relaxation in pseudo-Jahn-Teller low-symmetry Cu(II) complexes in diaqua(L-aspartate)Zn(II).H(2)O crystals.

Low-temperature (4-55 K) pulsed EPR measurements were performed with the magnetic field directed along the z-axis of the g-factor of the low-symmetry octahedral complex [(63)Cu(L-aspartate)(2)(H2O)2] undergoing dynamic Jahn-Teller effect in diaqua(L-aspartate)Zn(II) hydrate single crystals. Spin-lattice relaxation time T(1) and phase memory time T(M) were determined by the electron spin echo (ESE) method. The relaxation rate 1/T(1) increases strongly over 5 decades in the temperature range 4-55 K. Various processes and mechanisms of T(1)-relaxation are discussed, and it is shown that the relaxation is governed mainly by Raman relaxation processes with the Debye temperature Theta(D)=204 K, with a detectable contribution from disorder in the doped Cu(2+) ions system below 12 K. An analytical approximation of the transport integral I(8) is given in temperature range T=0.025-10Theta(D) and applied for computer fitting procedures. Since the Jahn-Teller distorted configurations differ strongly in energy (delta(12)=240 cm(-1)), there is no influence of the classical vibronic dynamics mechanism on T(1). Dephasing of the ESE (phase relaxation) is governed by instantaneous diffusion and spectral diffusion below 20 K with resulting rigid lattice value 1/T(0)(M)=1.88 MHz. Above this temperature the relaxation rate 1/T(M) increases upon heating due to two mechanisms. The first is the phonon-controlled excitation to the first excited vibronic level of energy Delta=243 cm(-1), with subsequent tunneling to the neighbor potential well. This vibronic-type dynamics also produces a temperature-dependent broadening of lines in the ESEEM spectra. The second mechanism is produced by the spin-lattice relaxation. The increase in T(M) is described in terms of the spin packets forming inhomogeneously broadened EPR lines.

Combined optical and microwave approach for performing quantum spin operations on the nitrogen-vacancy center in diamond

Electron spin echoes were performed on nitrogen-vacancy $(\mathrm{N}\ensuremath{-}V)$ centers in diamond using optical polarization and detection and 35 GHz microwave control. The experiments demonstrate an approach to quantum information in the solid state. A phase memory time of $3.6 \ensuremath{\mu}\mathrm{s}$ was measured, and coupling of the electronic spin to the ${}^{14}\mathrm{N}$ nuclear spin was observed. Because of the favorable properties of the $\mathrm{N}\ensuremath{-}V$ center, interesting extensions of these single-qubit operations can be proposed.

Electron spin relaxation of the Jahn–Teller Cu(H 2O) 6 complex in Cs 2Zn(SO 4) 2·6H 2O crystals

The electron spin–lattice and phase relaxation times were measured by electron spin echo (ESE) method in the temperature range 10–50 K, where Jahn–Teller dynamics of the Cu(H 2O) 6 complexes is too slow to dominate in the EPR spectra of Cu 2+ in Cs 2Zn(SO 4) 2·6H 2O. The spin–lattice relaxation is governed by ordinary the two-phonon Raman processes which overdominate the effects expected from the Jahn–Teller dynamics. It allowed us to determine the Debye temperature of Cs 2Zn(SO 4) 2·6H 2O crystals as Θ D =220 K. The ESE amplitude decay is governed by nuclear spectral diffusion below 23 K with phase memory time T M =5 μs. At this temperature a broadening of the lines in FT-ESE spectrum (pseudo-ENDOR spectrum) appears, and then a continuous acceleration of the phase relaxation on heating is observed. This is due to the excitations to the vibronic level of energy 71 cm −1 in the deepest well of the potential energy surface.

Decay of spontaneous echoes in amorphous [formula omitted] at very low temperatures

Using a two-pulse excitation sequence we have generated spontaneous polarization echoes in B 2 O 3 glass samples and have investigated the decay of the echoes at different temperatures. In principle, this type of experiment allows a direct measurement of the phase memory time τ 2 of tunneling states. Our experiments show that the echo dephasing in amorphous B 2 O 3 is much faster compared to that in previously investigated SiO 2 glasses.

Off-centre dynamic Jahn-Teller effect studied by electron spin relaxation of Cu2+ ions in SrF2 crystal

Temperature cw-EPR and pulsed EPR electron spin echo experiments were performed for a low concentration of Cu2+ ions in cubic SrF2 crystals. The well resolved EPR spectrum at low temperatures (below 30 K) with parameters g = 2.493, g = 2.083, A = 121, A = 8.7, A(19F) = 135, A(19F) = 33.0 (A-values in 10-4 cm-1) is transformed continuously into a single broad line above 225 K on heating, due to the g-factor shift and EPR line broadening. These data along with the angular variation EPR data are described in terms of a pseudo-Jahn-Teller effect of (T2g+A2u)(a1g+eg+t1u) type producing six off-centre positions of the Cu2+ ion in the fluorine cube. Above 30 K a two-step averaging g-factor process occurs and is governed by vibronic dynamics between potential wells of the off-centre positions. This dynamics governs the electron spin relaxation in the whole temperature range. The electron spin-lattice relaxation rate 1/T1 grows rapidly by six orders of magnitude in the temperature range 30-100 K and is determined by the Orbach-type process with excitations to two excited vibronic levels of energy 83 and 174 cm-1. For higher temperatures the relaxation is dominated by overbarrier jumps leading to the isotropic EPR spectrum above 225 K. The phase memory time TM has the rigid lattice value 3.5 µs determined by nuclear spectral diffusion and its temperature variation is governed by the vibronic dynamics indicating that the excitations between vibronic levels produce a dephasing of the electron spin precessional motion.

Low temperature dynamics of hydrazinium ions in lithium hydrazinium sulphate (LHS) studied by electron spin echo (ESE) technique

The temperature dependence of the phase memory time T M in γ-irradiated lithium hydrazinium sulphate, LiN 2H 5SO 4, single crystal has been measured in the temperature range 4.2–290 K. Two minima in T M( T) at 115 and 175 K were observed. The low-temperature T M minimum has been identified as due to librational motions of the N 2H 5 + hydrazinium ion with an activation energy of 0.045 eV. The T M minimum at 175 K has been assigned to rotation of the –NH 3 + end of the hydrazinium ion with an activation energy of 0.074 eV. The activation energies have been compared with the results of a previous NMR and Raman spectroscopic studies of this crystal.