Level-crossing Resonance Research Articles

Producing Conventional and Transient Amino(mercapto)methyl Radicals by Addition of Muonium to a Crystalline Thioformamide (Mes*NHCH=S).

Muonium (Mu=μ+e-) is composed of a muon of light isotope of proton (μ+) and electron (e-) and can be used as a light surrogate for a hydrogen atom. In this paper, we investigated addition of muonium to a newly synthesized Mes*-substituted thioformamide (Mes*NHCH=S, Mes*=2,4,6-tBu3C6H2). Transverse-field muon spin rotation (TF-μSR) of a solution sample of the thioformamide confirmed addition of muonium to the sulfur atom leading to the corresponding C-centered radical [Mes*NHC(H)⋅-SMu]. Density functional theory (DFT) calculations assigned a conventional amino(mercapto)methyl radical, in which both nitrogen and carbon were slightly pyramidalized, and the calculated muon hyperfine coupling constant (hfcc) including the muon isotope effect was compatible with the experimentally determined parameter. However, the muon level-crossing resonance (μLCR) spectrum of an anisotropic crystalline sample indicated two paramagnetic species, and the major product showed the considerably larger muon hfcc compared with the conventional structure of the amino(mercapto)methyl radical. The unusual transient muoniated thioformamide with the larger muon hfcc that showed rapid relaxation could be only explained by a transient structure including planarization of the nitrogen and carbon atoms in Mes*NHC(H)⋅-SMu.

µSR studies for radical reactions of unsaturated organophosphorus compounds

In this paper, the µSR studies of some unsaturated organophosphorus compounds containing heavier congeners of cyclobutane-1,3-diyl and anthracene are reviewed by discussing the usefulness of µSR for main group chemistry. The regioselective addition of muonium (Mu = [µ+e–]) to one of the skeletal phosphorus atoms in an electron-donating air-stable crystalline 1,3-diphosphacyclobutane-2,4-diyl leading to the paramagnetic 4-membered P-heterocycle was characterized by the Δ1 (ΔM = ± 1) resonance signal observed by muon (avoided) level-crossing resonance (µLCR). Meanwhile, a crystalline 1,3-diphosphacyclobutane-2,4-diyl bearing an electron-deficient nitrogen heterocyclic unit was analyzed by transverse-field muon spin rotation (TF-µSR) to characterize predominant muoniation at the skeletal radical carbon centre. A 9-phosphaanthracene bearing the trifluoromethyl (CF3) stabilizing groups at the peri positions was also investigated from the views of radical reactivity, and the regioselective addition of muonium to the skeletal sp2-type phosphorus atom was characterized by the muon hyperfine coupling (hfc) constant observed by TF-µSR and the Δ0 (ΔM = 0) signal of µLCR. The light mass of muon (Mass = 0.1134 amu) causes the larger zero-point energy and promotes the high-energy molecular structure in which the fused aromatic rings are almost flat, although the CF3 groups would prefer the non-planar saddle-like 9-phosphaanthracene skeleton.

Development of transient [formula omitted]SR method for high-flux pulsed muons

In order to expand the applicability of muon spin rotation, relaxation, and resonance (μSR) experiments with pulsed muons and to make effective use of the high-flux beam, we have developed a new experimental method “transient μSR”. In this method, μSR data for each muon pulse are tagged with external parameters such as temperature and magnetic field in real time, allowing the sample environment to be changed without interrupting data collection. As a result, continuous μSR measurements under sample conditions that vary on a time scale longer than the beam pulse interval (40 ms) are realized, and efficient beam utilization is achieved by eliminating the lag time associated with moving between discrete measurement points. The transient μSR method was applied to the study of the magnetic properties of cupric oxide (CuO) and the observation of level-crossing resonance relaxation in copper, and the method was successfully established by confirming that the results reproduce those in the previous reports.

Many-body quantum muon effects and quadrupolar coupling in solids

Strong quantum zero-point motion (ZPM) of light nuclei and other particles is a crucial aspect of many state-of-the-art quantum materials. However, it has only recently begun to be explored from an ab initio perspective, through several competing approximations. Here we develop a unified description of muon and light nucleus ZPM and establish the regimes of anharmonicity and positional quantum entanglement where different approximation schemes apply. Via density functional theory and path-integral molecular dynamics simulations we demonstrate that in solid nitrogen, α–N2, muon ZPM is both strongly anharmonic and many-body in character, with the muon forming an extended electric-dipole polaron around a central, quantum-entangled [N2–μ–N2]+ complex. By combining this quantitative description of quantum muon ZPM with precision muon quadrupolar level-crossing resonance experiments, we independently determine the static 14N nuclear quadrupolar coupling constant of pristine α–N2 to be –5.36(2) MHz, a significant improvement in accuracy over the previously-accepted value of –5.39(5) MHz, and a validation of our unified description of light-particle ZPM.

Zero-field level-crossing resonances in a small low-temperature cesium vapor cell for atomic magnetometry applications

Zero-field level-crossing resonances (LCRs) underlay one of the most robust and simplest techniques in atomic magnetometry. LCR-based miniaturized magnetic field sensors have already found relevant applications in biology and medicine. Such sensors utilize a single circularly polarized light wave to interact with alkali-metal atoms (usually Rb or Cs) and to observe the LCR in a vapor-cell transmission when a transverse magnetic field is scanned around zero value. A high-temperature regime (T ≈ 120 − 160°C) is required to achieve a desirable sensitivity of measurements. It can be a problem for some applications, especially in a multi-channel mode of operation. Here, we consider two spectroscopy techniques that can provide high-contrast and narrow LCRs under a relatively low temperature of the cell (≤60°C). These techniques imply using two light waves: the pump wave to polarize the atoms and the probe one to register the resonance. A cubic glass cell of 5×5×5 mm3 size is used in the experiments. It is filled with cesium vapors and neon as a buffer gas. The results can be used for developing a miniaturized low-power high-sensitivity magnetic field sensor for biomedical applications.

Level-crossing resonances on open atomic transitions in a buffered Cs vapor cell: Linewidth narrowing, high contrast, and atomic magnetometry applications

The ground-state Hanle effect (GSHE) in alkali-metal atomic vapors using a single circularly polarized wave underlies one of the most robust and simplest techniques in atomic magnetometry. This effect causes a narrow (subnatural-width) resonance in the light wave intensity transmitted through a vapor cell. Usually, GSHE-based sensors operate in the spin-exchange-relaxation-free (SERF) regime. However, this regime requires a relatively high temperature of vapors (150 C or higher), leading to a relatively large heat release and power consumption of the sensor head. Besides, without applying special measures, SERF regime significantly limits a dynamic range of measurements. Here, we study a pump-probe scheme involving a single elliptically polarized wave and a polarimetric detection technique. The wave is in resonance with two adjacent optical transitions in the cesium D1 line (894.6 nm) owing to their overlapping in presence of a buffer gas (Ne, 130 Torr). Using a small (0.1 cm$^3$) glass vapor cell, we demonstrate a possibility of observing subnatural-width resonances with a high contrast-to-width ratio (up to 45 %/mG) under a low-temperature (60 C) regime of operation thanks to a strong light-induced circular dichroism. Basing on a $\Lambda$ scheme of atomic energy levels, we obtain explicit analytical expressions for the line shape. The model reveals a linewidth narrowing effect due to openness of the scheme. This result is unusual for magneto-optical atomic spectroscopy because the openness is commonly considered as a undesirable effect, degrading the resonance characteristics. We estimate a sensitivity of 1.8 pT/$\surd$Hz with a 60 fT/$\surd$Hz sensitivity in the photon-shot-noise limit. The results contribute to the theory of GSHE resonances and can be applied to development of a low-temperature high-sensitivity miniaturized magnetic field sensor with an extended dynamic range.

Application of all-optical magnetometry for detection of weak magnetic fields generated by a current-carrying metallised track

A pump – probe configuration is used to register zero-field level-crossing resonances in Rb vapour contained in a cell with antirelaxation coated walls. The scheme is applied to detect the weak magnetic field generated by a current-carrying micro-wire (metallised track). Such micro-wires can be employed in neural prostheses and hybrid bionic systems as micro-electrode arrays. More specifically, the operation of such live micro-wire belonging to a neuronal – electrode interface is demonstrated, which indicates the possibility of remote testing of the operation (conducting/nonconducting) of micro-wires for in neural implants.

Fourier transform synchrotron spectroscopy of the COD-bending fundamental of CD3OD

The high-resolution Fourier transform spectrum of the CD3OD isotopologue of methanol in the region of the COD-bending fundamental band at 775 cm−1 has been recorded at the Far Infrared Beamline of the Canadian Light Source synchrotron. The torsion-rotation structure has been analyzed for sub-bands from K = 0 to 16 for both A and E torsional symmetries in the vt = 0 torsional state of the COD-bending mode. Energy term values for the excited COD-bending levels have been determined, and fitted to J(J + 1) power-series expansions to provide substate J = 0 origins. These have in turn been fitted to a basic Fourier model in order to map the torsional energy structure. The K-reduced COD-bending torsional origins follow a regular oscillatory pattern as a function of K with a significantly reduced amplitude relative to that of the vibrational ground state. With use of a simple formula for the change in the torsional constant F, the torsional barrier height V3 is found to be 440.25 cm−1, an increase of 22% relative to the ground state. The COD bend does not show evidence of anharmonic Fermi resonances with the ground torsional manifold, but J-localized level-crossing resonances coupling the 5A and 8A substates with vt = 4 ground level partners have been observed and characterized.

Muonium Addition to a peri-Trifluoromethylated 9-Phosphaanthracene Producing a High-Energy Paramagnetic π-Conjugated Fused Heterocycle.

In this communication, we report muon spin rotation/resonance (μSR) studies for understanding radical reactivity of 10-mesityl-1,8-bis(trifluoromethyl)-9-phosphaanthracene. Transverse-field muon spin rotation (TF-μSR) and muon avoided level-crossing resonance (μLCR) measurements successfully visualized a paramagnetic species produced by regioselective addition of muonium (Mu) to the skeletal phosphorus atom. Density functional theory (DFT) calculations for the P-muoniation product suggested two possible isomers. Whereas the most stable isomer including the envelope-type phosphorus heterocycle shows considerably different hyperfine coupling constants (hfcs) from those of the TF-μSR and μLCR, the metastable structure accompanying the almost planar tricyclic π-conjugated skeleton could simulate the experimentally determined hfcs. The metastable planar π-conjugated paramagnetic tricyclic-fused skeleton is promoted by the larger zero-point energy due to the light muon (μ+ ), one ninth of the proton mass.

High-contrast level-crossing resonances in a small cesium vapor cell for applications in atomic magnetometry

Level-crossing (LC) resonances in alkali-metal vapors are widely used for atomic magnetometry. One of the most simple and robust techniques involves a single circularly polarized light wave, while a transverse magnetic field (Bx⊥k) is scanned around zero to observe the subnatural-linewidth resonance of electromagnetically induced transparency (EIT) in the light wave transmission. This technique allows miniaturization of the magnetic field sensor to a great extent, maintaining high sensitivity of measurements. To obtain a high quality factor of the LC resonance and, therefore, high performance of the sensor, either a high temperature (>120 °C) or an extended volume of the vapor cell (V≫1 cm3) is usually required. Here, we propose a slight modification to the commonly used configuration, which can provide high-quality LC resonances in small (≪1 cm3) vapor cells at a relatively low temperature of 60 °C or less. The modification consists in adding the second (pump) counterpropagating light wave with opposite circular polarization (σ+σ− configuration). In our experiments, the waves excite the D1-line ground-state level Fg=4 in cesium atoms in the presence of a buffer gas (Ne, 130 Torr). In the proposed scheme, a subnatural-linewidth electromagnetically induced absorption (EIA) resonance is observed. We compare parameters of the EIA resonance with those obtained in the single-wave scheme to show benefits of using the proposed σ+σ− configuration. The results have good prospects for developing a low-power miniaturized atomic magnetometer with a wide operating range.

Shift of zero-field level-crossing resonance in the Cs D1 line and its use in vector magnetometry.

We examine the level-crossing resonance in a cesium vapor cell filled with a buffer gas under counterpropagating pump and probe light waves with orthogonal linear polarizations. An optical transition Fg=4→Fe=3 is excited in the D1 line. Probe-wave transmission is analyzed versus a static magnetic field applied along the wave vectors. This configuration can provide ultrahigh-contrast electromagnetically induced absorption resonances. We report here a new, to the best of our knowledge, magneto-optical effect in the resonance shift caused by a transverse magnetic field and discuss how it can be applied in vector magnetometry.

Hydrogen-Atom Addition to Nucleobases in the Solid State: Characterization of the Corresponding Muoniated Radicals Using μSR.

The radicals formed by muonium (Mu) addition to four nucleobases (adenine, guanine, cytosine, and thymine) have been characterized by avoided level-crossing muon spin resonance (ALC-μSR). Mu is considered to be a light isotope of the hydrogen atom, and the muoniated radicals observed by ALC-μSR are isotopomers of the radicals initially produced by H addition to the nucleobases. The observed radicals have been assigned by considering the relative energies of the possible radicals reported in the literature and comparing the experimental muon and proton hyperfine coupling constants with values from previously reported electron paramagnetic resonance and ab initio calculations that have been scaled to account for the larger magnetic moment of the muon and its lighter mass compared with the proton. Mu addition is observed to occur only at secondary carbons of the purine rings in adenine and guanine. Mu adds to C8 and C2 of adenine with the relative amount being ∼70:30%, and Mu adds exclusively to C8 of guanine. Mu addition is predominantly to the secondary carbons of the pyrimidine ring in cytosine (C5 and C6 with relative yields ∼80:20%) with a small amount of addition at N3. Mu adds to both the secondary C6 and tertiary C5 in thymine with approximately equal yields as well as the O4 adduct being a minor product.

Observation of a Metastable P-Heterocyclic Radical by Muonium Addition to a 1,3-Diphosphacyclobutane-2,4-diyl.

A 1,3-diphosphacyclobutane-2,4-diyl contains a unique unsaturated cyclic unit, and the presence of radical-type centers have been expected as a source of functionality. This study demonstrates that the P-heterocyclic singlet biradical captures muonium (Mu=[μ+ e- ]), the light isotope of a hydrogen radical, to generate an observable P-heterocyclic paramagnetic species. Investigation of a powder sample of 2,4-bis(2,4,6-tri-t-butylphenyl)-1-t-butyl-3-benzyl-1,3-diphosphacyclobutane-2,4-diyl using muon (avoided) level-crossing resonance (μLCR) spectroscopy revealed that muonium adds to the cyclic P2 C2 unit. The muon hyperfine coupling constant (Aμ ) indicated that the phosphorus atom bearing the t-butyl group trapped muonium to provide a metastable P-heterocyclic radical involving the ylidic MuP(<)=C moiety. The observed regioselective muonium addition correlates the canonical formula of 1,3-diphosphacyclobutane-2,4-diyl.

Partitioning of 2-phenylethanol and limonene cosurfactants in C12E4.

Avoided level-crossing muon spin resonance (ALC-μSR) has been used to study the dynamics and local environment of spin probes formed by muonium (Mu) addition to 2-phenylethanol (PEA) and limonene (1-methyl-4-(1-methylethenyl)-cyclohexene) in an aqueous dispersion of the nonionic surfactant C12E4 (tetra(ethylene glycol) n-dodecyl ether). The spin probes derived from both cosurfactants reside within the micelles in the L1 phase and the bilayers in the Lα phase rather than in the aqueous region. The local polarity measured by the different isomers of the Mu adducts of PEA suggests there is a water gradient within the micelles and bilayers. Slow rotation of the micelles broadened the Δ1 resonances with increasing temperature in the L1 phase while narrower Δ1 resonances were observed in the Lα phase due to the rapid rotation of the spin probes around a preferred axis, which was wobbling within a cone.

Fourier transform synchrotron spectroscopy of the in-plane methyl-rocking band of CD3OH

Infrared Fourier transform spectra of the 12CD3OH isotopologue of methanol recorded at the Canadian Light Source synchrotron have been investigated in the 750–950cm−1 region to explore the torsional energy pattern of the in-plane methyl-rocking mode. The in-plane CD3-rocking band is primarily of parallel a-type character with relatively widely spaced K-structure, and the central Q-branch region is well-resolved. Sub-bands have been assigned for the vt=0 ground torsional state from K=0 to 15 for both A and E torsional species, as well as a number of sub-bands in the vt=1 excited torsional state. A variety of perturbations due to asymmetry-induced, anharmonic Fermi and level-crossing resonances is seen in the spectra. Mapping of K-reduced torsional energies determined from the upper-state term values shows that the K-dependence is severely distorted from the usual pattern of smoothly oscillating, near-sinusoidal interlocking τ-curves. Although the K=0 levels are nominally inverted for vt=0, the torsional splitting is very small with the A level higher than the E level by only 0.625cm−1, and the anomalous behavior precludes a definite conclusion about torsional inversion. However, the range of variation with K of the vt=0 CD3-rocking τ-curves is about half that of the ground vibrational state, similar to previous observations for CH3OH isotopologues, suggesting a comparable reduction of about 25% in the effective torsional barrier height for the in-plane rocking mode.

Proton, muon and13C hyperfine coupling constants of C60X and C70X (X = H, Mu)

The reaction of H atoms with fullerene C70 has been investigated by identifying the radical products formed by addition of the atom muonium (Mu) to the fullerene in solution. Four of the five possible radical isomers of C70Mu were detected by avoided level-crossing resonance (μLCR) spectroscopy, using a dilute solution of enriched (13)C70 in decalin. DFT calculations were used to predict muon and (13)C isotropic hyperfine constants as an aid to assigning the observed μLCR signals. Computational methods were benchmarked against previously published experimental data for (13)C60Mu in solution. Analysis of the μLCR spectrum resulted in the first experimental determination of (13)C hyperfine constants in either C70Mu or C70H. The large number of values confirms predictions that the four radical isomers have extended distributions of unpaired electron spin.

Investigating the compatibility of PEEK polymer for the fabrication of sample cells for use in muon spin spectroscopy

Polyether ether ketone (PEEK) is a thermoplastic polymer with a wide range of applications due to its chemical inertness and thermal stability, and for these reasons sample cells for gas and liquid phase μSR have been constructed from PEEK. Muon levelcrossing resonance (μLCR) studies of PEEK revealed a broad, strong μLCR signal that, we hypothesize, is due to multiple overlapping resonances from the various muonium (Mu) adducts of PEEK. To investigate this, two monomer units from PEEK (4,4'-dihydroxybenzophenone and para-dimethoxybenzene) were studied in solution using transverse-field muon spin rotation (TF-μSR) and μLCR. Two different muoniated radicals were formed by Mu addition to 4,4/- dihydroxybenzophenone and one radical was formed in para-dimethoxybenzene. The μSR spectra were assigned by comparing the experimentally measured muon and proton hyperfine coupling constants with values calculated for the possible structures using Gaussian-09 software with the B3LYP functional and 6-31G basis set. Good agreement was found for cyclohexadienyl- type radicals formed by Mu addition to the benzene rings of the monomer units. We can also infer that these radicals are being formed in PEEK, and based on this we conclude that sample cells made of PEEK are unsuitable for many types of μSR experiment.

Detection and decoherence of level-crossing resonances of8Li in Cu

Level-crossing resonances are observed for spin-polarized ${}^{8}$Li in copper at 200 K. The positions of the resonances as a function of magnetic field and crystal orientation are a precise measure of the induced quadrupolar interaction on the nearest-neighbor Cu spins and provide unambiguous evidence that ${}^{8}$Li occupies a substitutional site. The resonances are detected as enhancements in the ${}^{8}$Li spin relaxation rate and are much broader than predicted from a static spin Hamiltonian. A strong collision model is used to extract a decoherence time as a result of the dipolar coupling of the ${}^{8}$Li-Cu subsystem to the surrounding nuclear spin bath.

Dual Reactivity of a Stable Zwitterionic N-Heterocyclic Silylene and Its Carbene Complex Probed with Muonium

The reactivity of the multifunctional cyclic silylene 4 and its carbene complex 5 have been investigated by a combination of muon spin spectroscopy and computation. The free radicals formed by muonium (Mu) addition to 4 were identified, showing that there are two dominant sites of free radical attack: on the Si atom and on the exocyclic methylene carbon. Reaction of muonium with 5 also produced two radicals, but with markedly different hyperfine constants. For both compounds avoided level-crossing resonance spectra and calculation of hyperfine constants show that one of the radicals results from Mu addition to the methylene group, yielding radicals 4a and 5a. Each contains a muoniated methyl group, −CH2Mu, which undergoes restricted rotation with respect to the plane of the ring. For 4 the second product is readily assigned as the muoniated silyl radical 4b, on the grounds of its high muon hyperfine constant (716 MHz). The second product from 5 shows instead a very small coupling constant, 19 MHz, assigna...

High-resolution spectroscopy of the C–N stretching band of methylamine

The C-N stretching infrared fundamental of CH(3)NH(2) has been investigated by high-resolution laser sideband and Fourier transform synchrotron spectroscopy to explore the energy level structure and to look for possible interactions with high-lying torsional levels of the ground state and other vibrational modes. The spectrum is complicated by two coupled large-amplitude motions in the molecule, the CH(3) torsion and the NH(2) inversion, which lead to rich spectral structure with a wide range of energy level splittings and relative line intensities. Numerous sub-bands have been assigned for K values ranging up to 12 for the stronger a inversion species for the v(t) = 0 torsional state, along with many of the weaker sub-bands of the s species. The C-N stretching sub-state origins have been determined by fitting the upper-state term values to J(J + 1) power-series expansions. For comparison with the ground-state behaviour, both ground and C-N stretch origins have been fitted to a phenomenological Fourier series model that produces an interesting pattern with the differing periodicities of the torsional and inversion energies. The amplitude of the torsional energy oscillation increases substantially for the C-N stretch, while the amplitude of the inversion energy oscillation is relatively unchanged. Independent inertial scale factors ρ were fitted for the torsion and the inversion and differ significantly in the upper state. The C-N stretching vibrational energy is determined to be 1044.817 cm(-1), while the effective upper state B-value is 0.7318 cm(-1). Several anharmonic resonances with v(t) = 4 ground-state levels have been observed and partially characterized. A variety of J-localized level-crossing resonances have also been seen, five of which display forbidden transitions arising from intensity borrowing that allow determination of the interaction coupling constants.