Quadrupole Interaction Research Articles

NMR Study of AgInTe2 at Normal and High Pressures

The ternary semiconductor AgInTe2 is a thermoelectric material with a chalcopyrite-type structure, which is believed to transform into a rocksalt-type structure under high pressure. Nuclear magnetic resonance (NMR) is considered to provide unique insight into material properties on interatomic length scales, especially in the context of structural phase transitions. Here, 115In and 125Te NMR analyses are used to study AgInTe2 for ambient conditions and pressures up to 5 GPa. Magnetic field-dependent and magic angle spinning (MAS) experiments of 125Te prove strongly enhanced internuclear couplings, as well as a distribution of isotropic chemical shifts, suggesting a certain degree of cation disorder. The indirect nuclear coupling is smaller for 115In, as well as the chemical shift distribution in agreement with the crystal structure. 115In NMR is further governed by a small quadrupolar interaction (νQ ≈ 90 kHz) and shows an orders of magnitude faster nuclear relaxation in comparison to that of 125Te. At a pressure of about 3GPa, the 115In quadrupole interaction increases sharply to about 2400 kHz, indicating a phase transition to a structure with a well-defined though noncubic local symmetry, while the 115In shift suggests no significant changes of the electronic structure. The NMR signal is lost above about 5 GPa (at least up to about 10 GPa). However, upon releasing the pressure, a signal is recovered that points to the reported metastable ambient pressure phase with a high degree of disorder.

Enhanced quadrupole effects for atoms in surface spiral beams with a thin dielectric waveguide

Recently, some physical research has recognized the coupling of optical phase singularity light with quadrupole-active atomic transitions. We show that a Laguerre-Gaussian beam, when completely internally reflected at the dielectric/vacuum interface, can generate a well-defined surface spiral beam with a two-dimensional intensity distribution confined to a sub-wavelength region near the interface outside of the dielectric. The quadrupole interaction has been shown to be significantly enhanced in the case of coating the planar surface of a dielectric prism using multilayer dielectric thin films of different thicknesses. The mechanical action on the atom due to the optical forces characterized by optical quadrupole transitions could greatly facilitate the revolution of optical manipulation of neutral atoms along the dielectric/vacuum interface. The typical optical quadrupole potential, evaluated for the atomic transition, corresponds to λ=675.0nm with ΓQ=7.8×105s-1, in Cesium atoms, which is a dipole-forbidden but quadrupole-allowed transition. The parameters used to compute the optical quadrupole potential are similar to those in recent experiments. The factors controlling the general enhancement are pointed out and discussed.

Ferroquadrupolar ordering in a magnetically ordered state in ErNiAl

We conducted ultrasonic measurements to clarify whether a phase transition exists in ErNiAl, a hexagonal compound, below the antiferromagnetic transition temperature, ${T}_{\mathrm{N}}\ensuremath{\sim}6$ K. We discovered a significant elastic softening of the transverse modulus, ${C}_{66}$, accompanied by a significant ultrasonic attenuation toward ${T}_{\mathrm{Q}}=3.4$ K, which is the temperature of a sharp downward peak in other moduli, indicating a phase transition at ${T}_{\mathrm{Q}}$. The crystal field analysis reveals that the softening of ${C}_{66}$ below 80 K is due to an interlevel ${O}_{xy}$-type quadrupole interaction with a positive quadrupole-quadrupole coupling constant between the ground and excited Kramers doublets. A spontaneous expectation value of ${O}_{xy}$ emerges at ${T}_{\mathrm{Q}}$ in our crystal field model with the mean-field approximation. No quadrupolar ordering occurs in a magnetically ordered state because the degeneracy of quadrupoles is lifted by an internal magnetic field of magnetic ordering. However, our experimental and calculated results suggest that the driving force of the phase transition at ${T}_{\mathrm{Q}}$ is ${O}_{xy}$-type ferroquadrupolar ordering, implying a quadrupolar ordering in a magnetically ordered state at zero magnetic field.

Simultaneous measurements of nuclear-spin heat capacity, temperature, and relaxation in GaAs microstructures

Heat capacity of the nuclear spin system (NSS) in GaAs-based microstructures has been shown to be much greater than expected from dipolar coupling between nuclei, thus limiting the efficiency of NSS cooling by adiabatic demagnetization. It was suggested that quadrupole interaction induced by some small residual strain could provide this additional reservoir for the heat storage. We check and validate this hypothesis by combining nuclear spin relaxation measurements with adiabatic remagnetization and nuclear magnetic resonance experiments, using electron spin noise spectroscopy as a unique tool for detection of nuclear magnetization. Our results confirm and quantify the role of the quadrupole splitting in the heat storage within NSS and provide additional insight into fundamental, but still actively debated relation between a mechanical strain and the resulting electric field gradients in GaAs.

Electron-Nuclear Coherent Coupling and Nuclear Spin Readout through Optically Polarized VB- Spin States in hBN.

Coherent coupling of defect spins with surrounding nuclei along with the endowment to read out the latter are basic requirements for an application in quantum technologies. We show that negatively charged boron vacancies (VB-) in hexagonal boron nitride (hBN) meet these prerequisites. We demonstrate Hahn-echo coherence of the VB- spin with a characteristic decay time Tcoh = 15 μs, close to the theoretically predicted limit of 18 μs for defects in hBN. Elongation of the coherence time up to 36 μs is demonstrated by means of the Carr-Purcell-Meiboom-Gill decoupling technique. Modulation of the Hahn-echo decay is shown to be induced by coherent coupling of the VB- spin with the three nearest 14N nuclei via a nuclear quadrupole interaction of 2.11 MHz. DFT calculation confirms that the electron-nuclear coupling is confined to the defective layer and stays almost unchanged with a transition from the bulk to the single layer.

Complete crystal-field calculation of Zeeman hyperfine splittings in europium

Computational crystal-field models have provided consistent models of both electronic and Zeeman-hyperfine structure for several rare earth ions. These techniques have not yet been applied to the Zeeman-hyperfine structure of Eu$^{3+}$ because modeling the structure of the $J=0$ singlet levels in Eu$^{3+}$ requires inclusion of the commonly omitted lattice electric quadrupole and nuclear Zeeman interactions. Here, we include these terms in a computational model to fit the crystal field levels and the Zeeman-hyperfine structure of the $^7F_0$ and $^5D_0$ states in three Eu$^{3+}$ sites: the C$_{4v}$ and C$_{3v}$ sites in CaF$_2$ and the C$_2$ site in EuCl$_3$.6H$_2$O. Close fits are obtained for all three sites which are used to resolve ambiguities in previously published parameters, including quantifying the anomalously large crystal-field-induced state mixing in the C$_{3v}$ site and determining the signs of Zeeman-hyperfine parameters in all three sites. We show that this model allows accurate prediction of properties for Eu$^{3+}$ important for quantum information applications of these ions, such as relative transition strengths. The model could be used to improve crystal field calculations for other non-Kramers singlet states. We also present a spin Hamiltonian formalism without the normal assumption of no $J$ mixing, suitable for other rare earth ion energy levels where this effect is important.

Build up ‘highway’ in membrane via solvothermal annealing for high-efficient CO2 capture

Poly (ethylene oxide) (PEO) membranes are attractive for CO2 capture due to the particular dipolar–quadrupolar interaction between EO units and CO2 molecules, which offer high CO2/N2 selectivity. However, the low CO2 permeability of PEO membranes hampers their practical applications. Herein, a simple solvothermal annealing approach was proposed to enhance the flexibility of PEO chains via ‘activating’ the disengagement and rearrangement of side chains, which is essential for boosting the gas permeability. The effects of solvothermal annealing temperature, time, and solvent on the CO2/N2 separation performance were comprehensively investigated. The mechanism for the performance enhancement was proposed: a “highway” for gas transportation was built up by the released flexible side chains, which were confirmed by the mechanical and Li ion conductivity characterizations. The optimized PEO membrane offers a superior CO2 permeability of 1294 Barrer, a high CO2/N2 selectivity of 50, and 110-h long-term running stability, being beyond the 2008 Robeson’s upper bound line and promoting the practical application of PEO membranes in CO2 capture by reducing the cost.

Solid-state NMR signals at zero-to-ultra-low-field

Zero-to-ultra-low-field nuclear magnetic resonance (ZULF NMR) is fast emerging as a viable spectroscopic approach to study samples under conditions dominated by internal spin interactions. In the absence of the truncating effects of Zeeman interaction, the NMR signal is determined by J-coupling, dipole-dipole, and/or quadrupolar interactions. But, the low spin-precession frequencies and equilibrium spin polarisation in low external fields necessitate the use of special techniques for detecting the signals. In this article, spin evolution in ultra-low-field regime for various systems is studied and the expected NMR signals are evaluated for solid samples. The methodologies that can be used to make low-field detection feasible especially in case of solid samples are described.

Crystal-field excitations and quadrupolar fluctuations of 4f-electron systems studied by polarized light scattering

We present Raman-scattering results for three materials, CeB6, TbInO3, and YbRu2Ge2, to illustrate the essential aspects of crystal-field (CF) excitations and quadrupolar fluctuations of 4f-electron systems. For CF excitations, we illustrate how the 4f orbits are split by spin-orbit coupling and CF potential by presenting spectra for inter- and intra-multiplet excitations over a large energy range. We discuss identification of the CF ground state and establishment of low-energy CF level scheme from the symmetry and energy of measured CF excitations. In addition, we demonstrate that the CF linewidth is a sensitive probe of electron correlation by virtue of self-energy effect. For quadrupolar fluctuations, we discuss both ferroquadrupolar (FQ) and antiferroquadrupolar (AFQ) cases. Long-wavelength quadrupolar fluctuations of the same symmetry as the FQ order parameter persists well above the transition temperature, from which the strength of electronic intersite quadrupolar interaction can be evaluated. The tendency towards AFQ ordering induces ferromagnetic correlation between neighboring 4f-ion sites, leading to long-wavelength magnetic fluctuations.

Reducing the effects of weak homonuclear dipolar coupling with CPMG pulse sequences for static and spinning solids

The Carr-Purcell/Meiboom-Gill (CPMG) pulse sequence, initially introduced for measuring transverse relaxation time constants (T2), can provide significant signal enhancements for solid-state NMR (SSNMR) spectra. The proper implementation of CPMG for acquiring spectra influenced by chemical shift anisotropies (CSAs), first and/or second order quadrupolar interactions, or paramagnetic broadening has been well documented to date, as have the effects of heteronuclear dipolar coupling on CPMG echo trains and T2 lifetimes. Homonuclear dipolar coupling can also impact T2 lifetimes and CPMG echo trains; these effects have been thoroughly investigated for spectra of homonuclear dipolar coupled spin-1/2 nuclei typically acquired under static conditions that are predominantly influenced by dipolar broadening (e.g., 1H, 19F, etc.). In particular, it has been shown that short refocusing pulses with small flip angles can extend the effective T2 (T2eff, the observed T2 constant as impacted by experimental conditions) measured by CPMG sequences for strong homonuclear dipolar coupled spin-1/2 pairs under static conditions. To date, these effects have not been explored for (i) spin-1/2 nuclei that have significant CSAs and simultaneously feature weak homonuclear dipolar couplings, (ii) for quadrupolar nuclei that are also weakly homonuclear dipolar coupled, and (iii) for either of these cases under magic-angle spinning (MAS) conditions. Herein, we demonstrate that short refocusing pulses that cause small flip angles can reduce the attenuation of signal in CPMG echo trains resulting from dipolar dephasing caused by the weak homonuclear dipolar couplings. For both spin-1/2 and quadrupolar nuclei, this can lead to significant extensions in T2eff and signal enhancements of up to three times compared to conventional CPMG in favourable cases. These phenomena can occur under both static and magic-angle spinning (MAS) conditions, in the latter of which homonuclear couplings are reintroduced by rotational resonance (R2) recoupling. Experimental examples of 13C (I = 1/2), 2H (I = 1), 87Rb (I = 3/2), 23Na (I = 3/2), and 35Cl (I = 3/2) NMR under static and MAS conditions, as well as simulations of these phenomena, are shown and discussed.

Characterization of the sodium binding state in several food products by 23 Na nuclear magnetic resonance spectroscopy.

In food, salt has several key roles including conservative and food perception. For this latter, it is well-known that the interaction of sodium with the food matrix modifies the consumer perception. It is then critical to characterize these interactions in various real foods. For this purpose, we exploited the information obtained on both single and double quantum 23 Na nuclear magnetic resonance (NMR) spectroscopies. All salted food samples studied showed strong interactions with the food matrix leading to quadrupolar interactions. However, for some of them, the single quantum analysis did not match the theoretical prediction. This was explained by the presence of another type of sodium population, which did not produce quadrupolar interactions. This finding is of critical importance to perform quantitative magnetic resonance imaging (MRI) and to understand the consumer salty taste perception.

Indirect NMR detection via proton of nuclei subject to large anisotropic interactions, such as 14N, 195Pt, and 35Cl, using the T-HMQC sequence.

Recently, the T-hetero-nuclear multiple quantum coherence (T-HMQC) sequence using the TRAPDOR (transfer of population in double resonance) recoupling has been introduced for the indirect detection via protons of quadrupolar nuclei with spin I = 1 (14N) or 3/2 (35Cl) in solids at fast magic-angle spinning (MAS). The sequence is simple as it only uses four rectangular pulses and exhibits low t1-noise because the recoupling pulses are applied to the indirectly detected isotope, I. We demonstrate that this sequence is applicable for the detection via protons of spin-1/2 nuclei subject to large chemical shift anisotropy, such as 195Pt. We also report the proton detection of double-quantum (2Q) coherences of 14N nuclei using this sequence. This 2Q version is more robust to the adjustment of the magic angle and the instabilities of the MAS frequencies than its parent single-quantum (1Q) version since the 2Q coherences are not broadened by the first-order quadrupole interaction. In practice, than its 1Q counterpart for the indirect detection of 14N nuclei, the 2Q variant benefits from a slightly higher resolution and comparable sensitivity. In this article, we derive for the first time the Hamiltonian that describes the spin dynamics during the TRAPDOR recoupling. This Hamiltonian demonstrates the importance of the adiabaticity parameter as well as the role of third-order terms in the effective Hamiltonian. The effects of offsets, radio-frequency field, and recoupling time on the efficiency of the T-HMQC sequence are analyzed numerically as well as with experimental detection via protons of 195Pt nuclei in a mixture of cis- and trans-platin and that of 14N and 35Cl isotopes in l-histidine HCl.

A Method for the Variational Calculation of Hyperfine-Resolved Rovibronic Spectra of Diatomic Molecules.

An algorithm for the calculation of hyperfine structure and spectra of diatomic molecules based on the variational nuclear motion is presented. The hyperfine coupling terms considered are Fermi-contact, nuclear spin-electron spin dipole–dipole, nuclear spin–orbit, nuclear spin-rotation, and nuclear electric quadrupole interactions. Initial hyperfine-unresolved wave functions are obtained for a given set of potential energy curves and associated couplings by a variation solution of the nuclear-motion Schrödinger equation. Fully hyperfine-resolved parity-conserved rovibronic Hamiltonian matrices for a given final angular momentum, F, are constructed and then diagonalized to give hyperfine-resolved energies and wave functions. Electric transition dipole moment curves can then be used to generate a hyperfine-resolved line list by applying rigorous selection rules. The algorithm is implemented in Duo, which is a general program for calculating spectra of diatomic molecules. This approach is tested for NO and MgH, and the results are compared to experiment and shown to be consistent with those given by the well-used effective Hamiltonian code PGOPHER.

Cu2+ and Cu3+ acceptors in β-Ga2O3 crystals: A magnetic resonance and optical absorption study

Electron paramagnetic resonance (EPR) and optical absorption are used to characterize Cu2+ (3d9) and Cu3+ (3d8) ions in Cu-doped β-Ga2O3. These Cu ions are singly ionized acceptors and neutral acceptors, respectively (in semiconductor notation, they are Cu− and Cu0 acceptors). Two distinct Cu2+ EPR spectra are observed in the as-grown crystals. We refer to them as Cu2+(A) and Cu2+(B). Spin-Hamiltonian parameters (a g matrix and a 63,65Cu hyperfine matrix) are obtained from the angular dependence of each spectrum. Additional electron-nuclear double resonance (ENDOR) experiments on Cu2+(A) ions give refined 63Cu and 65Cu hyperfine matrices and provide information about the nuclear electric quadrupole interactions. Our EPR results show that the Cu2+(A) ions occupy octahedral Ga sites with no nearby defect. The Cu2+(B) ions, also at octahedral Ga sites, have an adjacent defect, possibly an OH− ion, an oxygen vacancy, or an H− ion trapped within an oxygen vacancy. Exposing the crystals at room temperature to 275 nm light produces Cu3+ ions and reduces the number of Cu2+(A) and Cu2+(B) ions. The Cu3+ ions have an S = 1 EPR spectrum and are responsible for broad optical absorption bands peaking near 365, 422, 486, 599, and 696 nm. An analysis of loops observed in the Cu3+ EPR angular dependence gives 2.086 for the g value and 22.18, 3.31, and −25.49 GHz for the principal values of D (the fine-structure matrix). Thermal anneal studies above room temperature show that the Cu3+ ions decay and the Cu2+ ions recover between 75 and 375 °C.

Photoluminescence and energy transfer of Lu3Al5O12:Ce3+, Pr3+ phosphors

Ce 3+ and Pr 3+ co−doped Lu 3 Al 5 O 12 phosphors were synthesized by the sol–gel process, and their crystal structure, photoluminescence (PL) properties, and energy transfer (ET) from the Ce 3+ to Pr 3+ were studied. The Lu 2.94− y Al 5 O 12 :0.06Ce 3+ , y Pr 3+ phosphors (0.002 ≤ y ≤ 0.008) showed the green−yellow emission from the 2 D 3/2 → 2 F 5/2, 7/2 transition of Ce 3+ and the red emission at 610 and 637 nm, which were caused by the 1 D 2 → 3 H 4 and 3 P 0 → 3 H 5 transitions of Pr 3+ , respectively. The optimal concentration of Pr 3+ for efficient ET was found to be x = 0.006. The electric quadrupole−quadrupole interaction was responsible for the concentration quenching in the Lu 2.94− y Al 5 O 12 :0.06Ce 3+ , y Pr 3+ phosphors, based on Dexter's theory. The incorporation of Pr 3+ for Lu 3+ enhanced the red PL intensity in the Lu 2.94 Al 5 O 12 :0.06Ce 3+ phosphor.

Programmable Stepwise Collective Magnetic Self-Assembly of Micropillar Arrays.

Chain-like magnetic self-organizations have been documented for micron/submicron-scale magnetic particles. However, the positions of the particles are not stationary in a sustaining fluid owing to Brownian translational motion, resulting in irregular magnetic self-assembly. Toward the development of a programmable and reversible magnetic self-assembly, we report a stepwise collective magnetic self-assembly with periodic polymeric micropillar arrays containing magnetic particles. Under an external magnetic field, the individual micropillar acts as a micromagnet; magnetic polarities of embedded ferromagnetic particles are arranged in the same direction. The nearest pillar tops undergo a pairwise assembly owing to the anisotropic quadrupolar interaction, whereas the pillar bases remain stationary because of the presence of a magnetically inert substrate. By increasing the magnetic flux density, a collective quad-body assembly of vicinal paired micropillars is accomplished, finally leading to long-range connectivity of the pillar tops. Simple evaporation of the polymeric solution yields shape-fixation of the connected micropillar architectures even after magnetic fields are removed. We investigate geometric effects on this stepwise collective magnetic self-assembly using rectangular, square, and circular micropillars. Also, we demonstrate spatially selective magnetic self-assembly (e.g., arbitrary letters) using a masking technique. Finally, we demonstrate on-demand programming of bidirectional liquid spreading through long-range ordered magnetic self-assembly.

Effect of Quadrupole of Nitrogen, as a Probe Molecule for Surface Area Estimation: XRD and HRMC Investigation

Abstract To obtain the properties of nanopores solids, N2 is usually used as probe molecule, however recently, IUPAC recommends using Ar instead. This study used experimental X-ray diffraction (XRD) analysis, Monte Carlo (MC), and hybrid reverse MC (HRMC) simulations to obtain information on the intermolecular structures of adsorbed N2 and Ar. Our results indicate that the quadrupole interaction between N2 molecules is relatively weak, and the N2 gives fairly good assessments as with Ar for porous carbons with low functional groups.

Competing multipolar orders in a face-centered cubic lattice: Application to the osmium double perovskites

In 5$d^2$ Mott insulators with strong spin-orbit coupling, the lowest pseudospin states form a non-Kramers doublet, which carries quadrupolar and octupolar moments. A family of double perovskites where magnetic ions form a face-centered cubic (fcc) lattice was suggested to unveil an octupolar order offering a rare example in $d$-orbital systems. The proposed order requires a ferromagnetic (FM) octupolar interaction, since the antiferromagnetic (AFM) Ising model is highly frustrated on the fcc lattice. A microscopic model was recently derived for various lattices: for an edge-sharing octahedra geometry, AFM Ising octupolar and bond-dependent quadrupolar interactions were found when only dominant inter- and intraorbital hopping integrals were taken into account. Here we investigate all possible intra- and interorbital exchange processes and report that interference of two intraorbital exchanges generates a FM octupolar interaction. Applying the strong-coupling expansion results together with tight-binding parameters obtained by density functional theory, we estimate the exchange interactions for the osmium double perovskites, Ba$_2$BOsO$_6$ (B=Mg,Cd, and Ca). Using classical Monte Carlo simulations, we find that these systems are close to the phase boundary between AFM type-I quadrupole and FM octupole orders. We also find that exchange processes beyond second-order perturbation theory including virtual processes via pseudospin-triplet states may stabilize an octupolar order.

Predicting the phase equilibria of binary mixtures containing carbon dioxide + n-alkanols from a quadrupolar SAFT-VR approach

The vapor–liquid equilibria of binary mixtures containing carbon dioxide + n-alkanols is studied in the framework of the statistical associating fluid theory for potentials of variable range (SAFT-VR). The effect of the quadrupole moment of carbon dioxide on the phase equilibria is considered into the original SAFT-VR approach by incorporating an additional contribution to the Helmholtz free energy due to quadrupole–quadrupole interactions. The carbon dioxide is modeled as two spherical segments tangentially bonded with an axial quadrupolar moment. The n-alkanol molecules are represented as chains of spherical monomer segments with three associating sites to describe the hydrogen bonding interactions between the molecules. The association effects are taken into consideration by using the first-order thermodynamic perturbation theory of Wertheim. The attractive interactions between monomer segments and site-site associative interactions have been accounted for by using a square-well intermolecular potential. The pure component parameters for carbon dioxide and n-alkanols (from methanol to 1-decanol) are obtained by fitting the SAFT-VR approach to experimental saturated liquid density and vapor pressure. These optimized parameters are used to determine the vapor–liquid equilibria of the mixtures. The pressure-composition and density-composition projections predicted by SAFT-VR for the carbon dioxide + n-alkanols are in good agreement with the experimental data. A significant improvement in the description of the vapor–liquid equilibria of binary mixtures containing carbon dioxide + n-alkanols is obtained with the quadrupolar contribution compared with the results obtained from the original SAFT-VR. The optimized molecular parameters are rescaled in order to determine critical lines and the types of phase behavior. The critical lines and critical points are predicted by the original SAFT-VR approach and the quadrupolar version of the SAFT-VR in good agreement with experimental data. The inclusion of the quadrupolar interactions, present in the carbon dioxide, avoids the treatment of these interactions in an effective way via the square-well potential of variable range. The results of the present work are useful for further exploration of adsorption-extraction of n-alkanols in supercritical fluids.

Quantifying the quadrupolar interaction by 45Sc-NMR spectroscopy of single crystals

Single crystals of the compound [{Sc(H2O)5(μ-OH)}2]Cl4 ⋅ 2H2O were studied by 45Sc-NMR, with the effect of the quadrupolar coupling interaction on the spectra of the spin-7/2 nucleus analysed in the hierarchical framework of perturbation theory. Orientation-dependent spectra acquired at B0 = 17.6 T showed strong second-order effects due to the comparatively large coupling constant of χ = |14.613 ± 0.006| MHz, with an associated asymmetry parameter of ηQ = 0.540 9 ± 0.000 4. By analysing the splittings of the ±3/2 satellites, which in good approximation are subjected to first-order effects only, the full quadrupolar coupling tensor could be determined. The second-order effects caused by this tensor were calculated according to theoretical predictions for all orientations, and subtracted from both the centres of gravity of the satellites, and the central transitions. This allowed extraction of the full chemical shift tensor, with the eigenvalues being δ11 = (5.6 ± 0.9) ppm, δ22 = (12.4 ± 0.9) ppm, and δ33 = (38.5 ± 0.9) ppm. In spectra acquired at a lower magnetic field of B0 = 9.4 T, third-order effects could be detected, and similarly quantified using analytical expressions.