Nutation Experiments Research Articles

Coherence of NV defects in isotopically enriched 6H-28SiC at ambient conditions

The unique spin-optical properties of NV defects in SiC, coupled with silicon carbide's advanced technology compared to diamond, make them a promising candidate for quantum technology applications. In this study, using photoinduced pulse ESR at 94 GHz (3.4 T), we reveal the room temperature spin coherence of NV defects in 6H-28SiC, purified to reduce 29Si concentration to ≈1%, four times below its natural level. We demonstrate room temperature (300 K) Hahn-echo coherence time T2 = 23.6 μs, spin–lattice relaxation time T1 = 0.1 ms, and coherent control over optically polarized NV spin states through Rabi nutation experiments. We reveal long inhomogeneous dephasing time T2* = 1.5 μs, which is about five times greater than that measured for NV defects in SiC with natural isotopic content. Our observations highlight again the potential of NV defects in 6H-28SiC, which exhibit near-infrared optical excitation and emission properties compatible with O-band fiber optics, as promising candidates for applications in quantum sensing, communication, and computation.

X-Band Single Chip Integrated Pulsed Electron Spin Resonance Microsystem.

We report on the design and characterization of a single chip integrated pulsed electron spin resonance detector operating at 9.1 GHz. The microsystem consists of an excitation microcoil, a detection microcoil, a low noise microwave preamplifier, a mixer, and an intermediate frequency (IF) amplifier. The chip area is about 0.7 mm2. To exemplify its possible applications, we report the results of single pulse, Rabi nutation, Hahn echo, two echoes, Carr-Purcell, and inversion recovery echo experiments performed on 0.02 and 0.05 nL samples of α, γ-bisdiphenylene-β-phenylallyl (BDPA) and 1% BDPA in polystyrene (BDPA:PS) at room temperature. The measured spin sensitivity is about 8 × 107 spins/Hz1/2 on a sensitive volume of about 0.1 nL. The microsystem power consumption is less than 100 mW, the radio frequency (RF) input bandwidth is 8.8 to 9.8 GHz, the IF output bandwidth is DC to 350 MHz, and the deadtime is less than 30 ns.

Use of a correction factor for the pulsecal subroutine used for pulse width calibration and identifying a hardware fault causing pulsecal to fail

Stroboscopic nutation has proved to be invaluable for pulse width calibration (P. S. C. Wu and G. Otting, Rapid pulse length determination in high-resolution NMR, J. Magn. Reson. 2005, 176, 115–119), though it is not without its issues. Herein it is proposed that a correction factor be applied to correct for the inaccuracy of the method which is dependent on the NMR system including the probe, observed nucleus, sample type set (solvent, concentration, ionic strength, etc.), temperature, etc. Poor performance of the stroboscopic nutation experiment was also found to be a harbinger of a serious hardware problem.

Selective Transition Enhancement in a g-Engineered Diradical.

A diradical with engineered g-asymmetry was synthesized by grafting a nitroxide radical onto the [Y(Pc)2]⋅ radical platform. Various spectroscopic techniques and computational studies revealed that the electronic structures of the two spin systems remained minimally affected within the diradical system. Fluid-solution Electron Paramagnetic Resonance (EPR) experiments revealed a weak exchange coupling with |J| ~ 0.014 cm-1, subsequently rationalized by CAS-SCF calculations. Frozen solution continuous-wave (CW) EPR experiments showed a complicated and power-dependent spectrum that eluded analysis using the point-dipole model. Pulse EPR manipulations with varying microwave powers, or under varying magnetic fields, demonstrated that different resonances could be selectively enhanced or suppressed, based on their different tipping angles. In particular, Field-Swept Echo-Detected (FSED) spectra revealed absorptions of MW power-dependent intensities, while Field-Swept Spin Nutation (FSSN) experiments revealed two distinct Rabi frequencies. This study introduces a methodology to synthesize and characterize g-asymmetric two-spin systems, of interest in the implementation of spin-based CNOT gates.

Dual Structure of a Vanadyl-Based Molecular Qubit Containing a Bis(β-diketonato) Ligand.

We designed [VO(bdhb)] (1') as a new electronic qubit containing an oxovanadium(IV) ion (S = 1/2) embraced by a single bis(β-diketonato) ligand [H2bdhb = 1,3-bis(3,5-dioxo-1-hexyl)benzene]. The synthesis afforded three different crystal phases, all of which unexpectedly contain dimers with formula [(VO)2(bdhb)2] (1). A trigonal form (1h) with a honeycomb structure and 46% of solvent-accessible voids quantitatively transforms over time into a monoclinic solvatomorph 1m and minor amounts of a triclinic solventless phase (1a). In a static magnetic field, 1h and 1m have detectably slow magnetic relaxation at low temperatures through quantum tunneling and Raman mechanisms. Angle-resolved electron paramagnetic resonance (EPR) spectra on single crystals revealed signatures of low-dimensional magnetic behavior, which is solvatomorph-dependent, being the closest interdimer V···V separations (6.7-7.5 Å) much shorter than intramolecular V···V distances (11.9-12.1 Å). According to 1H diffusion ordered spectroscopy (DOSY) and EPR experiments, the complex adopts the desired monomeric structure in organic solution and its geometry was inferred from density functional theory (DFT) calculations. Spin relaxation measurements in a frozen toluene-d8/CD2Cl2 matrix yielded Tm values reaching 13 μs at 10 K, and coherent spin manipulations were demonstrated by Rabi nutation experiments at 70 K. The neutral quasi-macrocyclic structure, featuring nuclear spin-free donors and additional possibilities for chemical functionalization, makes 1' a new convenient spin-coherent building block in quantum technologies.

High-frequency high-power DNP/EPR spectrometer operating at 7 T magnetic field

One of the most essential prerequisites for the development of pulse Dynamic Nuclear Polarization (DNP) is the ability to generate high-power coherent mm-wave pulses at the electron precession frequencies corresponding to the magnetic fields of modern high-resolution NMR spectrometers. As a major step towards achieving this goal, an Extended Interaction Klystron (EIK) pulse amplifier custom-built by the Communications and Power Industries, Inc. and producing up to 140 W at 197.8 GHz, was integrated with in-house built NMR/DNP/EPR spectrometer operating at 7 T magnetic field. The spectrometer employs a Thomas Keating, Ltd. quasioptical bridge to direct mm-waves into a homebuilt DNP probe incorporating photonic bandgap (PBG) resonators to further boost electronic B1e fields. Three-pulse electron spin echo nutation experiments were employed to characterize the B1e fields at the sample by operating the homodyne 198 GHz bridge in an induction mode. Room-temperature experiments with a single-crystal high-pressure, high-temperature (HPHT) diamond and a polystyrene film doped with BDPA radical yielded < 9 ns π/2 pulses at ca. 50 W specified EIK output at the corresponding resonance frequencies and the PBG resonator quality factor of Q≈300. DNP experiments carried out in a “gated” mode by supplying 20 μs mm-wave pulses every 1 ms yielded 13C solid-effect DNP with gains up to 20 for the polystyrene-BDPA sample at natural 13C abundance. For a single-crystal HPHT diamond, the gated DNP mode yielded almost the same 13C enhancement as a low-power continuous wave (CW) mode at 0.4 W, whereas no DNP effect was observed for the BDPA/polystyrene sample in the latter case. To illustrate the versatility of our upgraded DNP spectrometer, room-temperature Overhauser DNP enhancements of 7–14 for 31P NMR signal were demonstrated using a liquid droplet of 1 M tri-phenyl phosphine co-dissolved with 100 mM of BDPA in toluene‑d8.

Quantum spin coherence and electron spin distribution channels in vanadyl-containing lantern complexes.

We herein investigate the heterobimetallic lantern complexes [PtVO(SOCR)4] as charge neutral electronic qubits based on vanadyl complexes (S = 1/2) with nuclear spin-free donor atoms. The derivatives with R = Me (1) and Ph (2) give highly resolved X-band EPR spectra in frozen CH2Cl2/toluene solution, which evidence the usual hyperfine coupling with the 51V nucleus (I = 7/2) and an additional superhyperfine interaction with the I = 1/2 nucleus of the 195Pt isotope (natural abundance ca. 34%). DFT calculations ascribe the spin density delocalization on the Pt2+ ion to a combination of π and δ pathways, with the former representing the predominant channel. Spin relaxation measurements in frozen CD2Cl2/toluene-d8 solution between 90 and 10 K yield Tm values (1-6 μs in 1 and 2-11 μs in 2) which compare favorably with those of known vanadyl-based qubits in similar matrices. Coherent spin manipulations indeed prove possible at 70 K, as shown by the observation of Rabi oscillations in nutation experiments. The results indicate that the heavy Group 10 metal ion is not detrimental to the coherence properties of the vanadyl moiety and that Pt-VO lanterns can be used as robust spin-coherent building blocks in materials science and quantum technologies.

Molecular-Engineered Biradicals Based on the YIII-Phthalocyanine Platform

A mixed-ligand phthalocyanine/porphyrin yttrium(III) radical double-decker complex (DD) was synthesized using the custom-made 5,10,15-tris(4-methoxyphenyl)-20-(4-((trimethylsilyl)ethynyl)phenyl)porphyrin. The trimethylsilyl functionality was then used to couple two such complexes into biradicals through rigid tethers. Glaser coupling was used to synthesize a short-tethered biradical (C1) and Sonogashira coupling to synthesize longer-tethered ones (C2 and C3). Field-swept echo-detected (FSED), saturation recovery, and spin nutation-pulsed electron paramagnetic resonance experiments revealed marked similarities of the magnetic properties of DD with those of the parent [Y(pc)2]• complex, both in the solid state and in CD2Cl2/CDCl3 4:1 frozen glasses. FSED experiments on the biradicals C2 and C3 revealed a spectral broadening with respect to the spectra of DD and [Y(pc)2]• assigned to the effect of dipolar interactions in solution. Apart from the main resonance, satellite features were also observed, which were simulated with dipole-dipole pairs of shortest distances, suggesting spin delocalization on the organic tether. FSED experiments on C1 yielded spectral line shapes that could not be simulated as the integration of the off-resonance echoes was complicated by field-dependent modulations. While, for all dimers, the on-resonance spin nutation experiments yielded Rabi oscillations of the same frequencies, off-resonance nutations on C1 yielded Rabi oscillations that could be assigned to a MS = -1 to MS = 0 transition within a S = 1 multiplet. The DFT calculations showed that the trans conformation of the complexes was significantly more stable than the cis one and that it induced a marked spin delocalization over the rigid organic tether. This "spin leakage" was most pronounced for the shortest biradical C1.

Longitudinal relaxation rate measurements for different signals unveiled by nutation spectroscopy: Application to the characterization of two arrangements experienced by water in a clay network.

Nutation consists in monitoring the motion of nuclear magnetization under the application of a radiofrequency (rf) field. With an appropriate amplitude of the rf field, the nutation frequency depends on the NMR relaxation times. This property offers the possibility of differentiating species having the same Larmor frequency but differing by their relaxation times. This may occur for the composite proton NMR signal of water in complex systems. Separate nutation signals are thus observed with the possibility of measuring their longitudinal relaxation times by simply applying a saturation hard pulse, followed by an evolution interval, prior to the nutation sequence. This novel experiment has been used for studying the two sites existing for water in two kaolinite samples (one hydrated after stabilization of several months and the other nonhydrated). It turns out that water in these two sites differs essentially by its transverse relaxation time. Moreover, recovery is surprisingly biexponential for these two signals. A proper analysis of results obtained by this saturation-recovery nutation experiment provides not only the specific longitudinal relaxation rates of water in these two sites but also information about the averaging which occurs at long evolution times. This is discussed with regard of the structure and organization of the clay network. In particular, from relaxation rates at short evolution times, it is shown that this network is mainly constituted of ordered platelets, with a relatively weak proportion of randomly distributed platelets.

Exploring Photogenerated Molecular Quartet States as Spin Qubits and Qudits.

Photogenerated molecular spin systems hold great promise for applications in quantum information science because they can be prepared in well-defined spin states at modest temperatures, they often exhibit long coherence times, and their properties can be tuned by chemical synthesis. Here, we investigate a molecular spin system composed of a 1,6,7,12-tetra(4-tert-butylphenoxy)perylene-3,4:9,10-bis(dicarboximide) (PDI) chromophore covalently linked to a stable nitroxide radical (TEMPO) by optical and electron paramagnetic resonance (EPR) techniques. Upon photoexcitation of the spin system, a quartet state is formed as confirmed by transient nutation experiments. This quartet state has spin polarization lifetimes longer than 0.1 ms and is characterized by relatively long coherence times of ∼1.8 μs even at 80 K. Rabi oscillation experiments reveal that more than 60 single-qubit logic operations can be performed with this system at 80 K. The large magnitude of the nitroxide 14N hyperfine coupling in the quartet state of PDI-TEMPO is resolved in the transient EPR spectra and leads to a further splitting of the quartet state electron spin sublevels. We discuss the properties of this photogenerated multilevel system, comprising 12 electron-nuclear spin states, in the context of its viability as a qubit for applications in quantum information science.

Accurate and Precise External Calibration Enhances the Versatility of Quantitative NMR (qNMR)

Quantitative 1H nuclear magnetic resonance (qHNMR) is a highly regarded analytical methodology for purity determination as it balances metrological rigor, practicality, and versatility well. While ideal for intrinsically mass-limited samples, external calibration (EC) qHNMR is overshadowed by the prevalence of internal calibration and perceived rather than real practical limitations. To overcome this hurdle, this study applied the principle of reciprocity, certified reference materials (caffeine as analyte, dimethyl sulfone as calibrant), and a systematic evaluation of data acquisition workflows to extract key factors for the achievement of accuracy and precision in EC-qHNMR. Automatic calibration of the 90° pulse width (90 PW) formed the foundation for the principle of reciprocity and used optimized nutation experiments, showing good agreement with values derived from manual high-precision measurement of 360 PW. Employing the automatic 90 PW calibration, EC-qHNMR with automatic vs manual tuning and matching (T&M) yielded the certified purity value within 1% error. The timing of T&M (before vs after shimming) turned out to be critically important: sufficient time is required to achieve full-temperature equilibrium relative to thermal gradients in the air inside the probe and the sample. Achievable accuracy across different NMR solvents varies with differences in thermal conductivity and leads to 2% or greater errors. With matching solvents, the demonstrated accuracy of ∼1.0% underscores the feasibility of EC-qHNMR as a highly practical research tool.

Isotope Effect in the Magneto-Optoelectronic Response of Organic Light-Emitting Diodes Based on Donor-Acceptor Exciplexes.

The isotope effect is studied in the magneto-electroluminescence (MEL) and pulsed electrically detected magnetic resonance of organic light-emitting diodes based on thermally activated delayed fluorescence (TADF) from donor-acceptor exciplexes that are either protonated (H) or deuterated (D). It is found that at ambient temperature, the exchange of H to D has no effect on the spin-dependent current and MEL responses in the devices. However, at cryogenic temperatures, where the reverse intersystem crossing (RISC) from triplet to singlet exciplex diminishes, a pronounced isotope effect is observed. These results show that the RISC process is not governed by the hyperfine interaction as thought previously, but proceeds through spin-mixing in the triplet exciplex. The observations are corroborated by electrically detected transient spin nutation experiments that show relatively long dephasing time at ambient temperature, and interpreted in the context of a model that involves exchange and hyperfine interactions in the spin triplet exciplex. These findings deepen the understanding of the RISC process in TADF materials.

Reaction: Molecular Spins as Qubits

Floriana Tuna is a Leverhulme Trust Senior Research Fellow at the University of Manchester (UoM). She holds MSc and PhD degrees in chemistry from the University of Bucharest (1989) and National Academy of Romania (1997), respectively. She worked as a visiting DAAD fellow at the University of Heidelberg (Germany), a CNRS postdoctoral fellow at ICMCB Bordeaux (France), and a Marie Curie fellow at the University of Warwick (UK) before joining UoM in 2003. She received the Romanian Academy “Ilie Murgulescu” Prize for excellence in research in 2005 and has published over 300 high-impact papers. Her major interests are in coordination chemistry, molecular magnetism, and quantum information science.

Unusually large hyperfine structure of the electron spin levels in an endohedral dimetallofullerene and its spin coherent properties.

We report the synthesis, ESR spectroscopic and spin coherent properties of the dimetallofullerene Sc2@C80(CH2Ph). The single-electron metal-metal bond of the Sc2 dimer inside the fullerene's cage is stabilized with the electron spin density being fully localized at the metal bond. This results in an extraordinary strong hyperfine interaction of the electron spin with the 45Sc nuclear spins with a coupling constant a = 18.2 mT (∼510 MHz) and yields a fully resolved hyperfine-split ESR spectrum comprising 64 lines. The splitting is present even at low temperatures where the molecular dynamics are completely frozen. The large extent and the robustness of the hyperfine-split spectra enable us to identify and control the well-defined transitions between specific electron-nuclear quantum states. This made it possible to demonstrate in our pulse ESR study the remarkable spin coherent dynamics of Sc2@C80(CH2Ph), such as the generation of arbitrary superpositions of the spin states in a nutation experiment and the spin dephasing times above 10 μs at temperatures T < 80 K reaching the value of 17 μs at T ≤ 20 K. These observations suggest Sc2@C80(CH2Ph) as an interesting qubit candidate and motivate further synthetic efforts to obtain fullerene-based systems with superior spin properties.

Measuring of short spin-spin relaxation times distributions using NQR nutation experiments

Experiments using nutation interferograms and nutation spectra in nuclear quadrupole resonance (NQR) are used for the first time to find the distribution of short spin-spin relaxation times in powder samples. Instead of the traditional method of the inversion of the Laplace transform, the inversion of the integral transformations of nutation interferograms and nutation spectra are used in this work. The use of the distributions of NQR relaxation times can provide new information on dynamic processes in complex molecular systems in the solid state. To illustrate the capabilities of the method, experimental results for 35Cl, 75As NQR and for 1H NMR are provided.

Proton nutation spectroscopy. Application to the quantitation of water in a kaolinite sample.

Nutation consists in monitoring the motion of nuclear magnetization under the application of a radio-frequency field. Depending on the amplitude of the rf field, the nutation frequency may be sensitive to the two longitudinal and transverse relaxation rates R1 and R2, hence the possibility of differentiating species having the same resonance frequency in the laboratory frame (the Larmor frequency) but differing by their relaxation rates, as it may occur for the composite proton NMR signal of water in complex systems. Thus, Fourier transform of the nutation curve should provide separate peaks associated with the different species involved in a composite classical NMR signal. As nutation peaks may be close to zero frequency (or even at zero frequency), their full observation requires a complex Fourier transform. This implies a second nutation curve, de-phased by 90° with respect to the first one, achieved here by a second nutation experiment preceded by a 90° hard pulse. Eventually, more accurate parameters are obtained by a non-linear least-squares analysis of the simple nutation experiment. This methodology is applied to water in a natural clay (kaolinite) and reveals the unexpected presence of two peaks which can be characterized by the relaxation rates derived from the line-widths of the nutation signals.

Salen Complexes as Fire Protective Agents for Thermoplastic Polyurethane: Deep Electron Paramagnetic Resonance Spectroscopy Investigation.

The contribution of copper complexes of salen-based Schiff bases N, N'-bis(salicylidene)ethylenediamine (C1), N, N'-bis(4-hydroxysalicylidene)ethylenediamine (C2), and N, N'-bis(5-hydroxysalicylidene)ethylenediamine (C3) to the flame retardancy of thermoplastic polyurethane (TPU) is investigated in the context of minimizing the inherent flammability of TPU. Thermal and fire properties of TPU are evaluated. It is observed that fire performances vary depending upon the substitution of the salen framework. Cone calorimetry [mass loss calorimetry (MLC)] results show that, in TPU at 10 wt % loading, C2 and C3 reduce the peak of heat release rate by 46 and 50%, respectively. At high temperature, these copper complexes undergo polycondensation leading to resorcinol-type resin in the condensed phase and thus acting as intumescence reinforcing agents. C3 in TPU is particularly interesting because it delays significantly the time to ignition (MLC experiment). In addition, pyrolysis combustion flow calorimetry shows reduction in the heat release rate curve, suggesting its involvement in gas-phase action. Structural changes of copper complexes and radical formation during thermal treatment as well as their influence on fire retardancy of TPU in the condensed phase are investigated by spectroscopic studies supported by microscopic and powder diffraction studies. Electron paramagnetic resonance (EPR) spectroscopy was fully used to follow the redox changes of Cu(II) ions as well as radical formation of copper complexes/TPU formulations in their degradation pathways. Pulsed EPR technique of hyperfine sublevel correlation spectroscopy reveals evolution of the local surrounding of copper and radicals with a strong contribution of nitrogen fragments in the degradation products. Further, the spin state of radicals was investigated by the two-dimensional technique of phase-inverted echo-amplitude detected nutation experiment. Two different radicals were detected, that is, one monocarbon radical and an oxygen biradical. Thus, the EPR study permits to deeply investigate the mode of action of copper salen complexes in TPU.

Ultra-broadband coplanar waveguide for optically detected magnetic resonance of nitrogen-vacancy centers in diamond.

We report on coplanar waveguides (CPWs) designed for optically detected magnetic resonance of nitrogen-vacancy (NV) centers in diamonds. A broad band up to 15.8 GHz has been realized, which ensures that the electron spins can be manipulated under external magnetic fields up to 5000 G. The conversion factor of CPW has been measured by Rabi nutation experiments, which ranges from 6.64 G W-1/2 to 10.60 G W-1/2 in the frequency band from 0.76 GHz to 17.3 GHz. Broadband CPWs also provide high quality control pulses due to the minimization of the distortion. These characteristics will find potential applications in NV-based quantum information processing and single spin magnetometry.

Measurement of short transverse relaxation times by pseudo-echo nutation experiments

Very short NMR transverse relaxation times may be difficult to measure by conventional methods. Nutation experiments constitute an alternative approach. Nutation is, in the rotating frame, the equivalent of precession in the laboratory frame. It consists in monitoring the rotation of magnetization around the radio-frequency (rf) field when on-resonance conditions are fulfilled. Depending on the amplitude of the rf field, nutation may be sensitive to the two relaxation rates R1 and R2. A full theoretical development has been worked out for demonstrating how these two relaxation rates could be deduced from a simple nutation experiment, noticing however that inhomogeneity of the rf field may lead to erroneous results. This has led us to devise new experiments which are the equivalent of echo techniques in the rotating frame (pseudo spin-echo nutation experiment and pseudo gradient-echo experiment). Full equations of motion have been derived. Although complicated, they indicate that the sum of the two relaxation rates can be obtained very accurately and not altered by rf field inhomogeneity. This implies however an appropriate data processing accounting for the oscillations which are superposed to the echo decays and, anyway, theoretically predicted. A series of experiments has been carried out for different values of the rf field amplitude on samples of water doped with a paramagnetic compound at different concentrations. Pragmatically, as R1 can be easily measured by conventional methods, its value is entered in the data processing algorithm which then returns exclusively the value of the transverse relaxation time. Very consistent results are obtained that way.

Magnetic flux tailoring through Lenz lenses for ultrasmall samples: A new pathway to high-pressure nuclear magnetic resonance.

A new pathway to nuclear magnetic resonance (NMR) spectroscopy for picoliter-sized samples (including those kept in harsh and extreme environments, particularly in diamond anvil cells) is introduced, using inductively coupled broadband passive electromagnetic lenses, to locally amplify the magnetic field at the isolated sample, leading to an increase in sensitivity. The lenses are adopted for the geometrical restrictions imposed by a toroidal diamond indenter cell and yield signal-to-noise ratios at pressures as high as 72 GPa at initial sample volumes of only 230 pl. The corresponding levels of detection are found to be up to four orders of magnitude lower compared to formerly used solenoidal microcoils. Two-dimensional nutation experiments on long-chained alkanes, CnH2n+2 (n = 16 to 24), as well as homonuclear correlation spectroscopy on thymine, C5H6N2O2, were used to demonstrate the feasibility of this approach for higher-dimensional NMR experiments, with a spectral resolution of at least 2 parts per million. This approach opens up the field of ultrahigh-pressure sciences to one of the most versatile spectroscopic methods available in a pressure range unprecedented up to now.