Nuclear Electric Quadrupole Interaction Research Articles

A variational model for the hyperfine resolved spectrum of VO in its ground electronic state.

A variational model for the infra-red spectrum of vanadium monoxide (VO) is presented, which aims to accurately predict the hyperfine structure within the VO XΣ-4 electronic ground state. To give the correct electron spin splitting of the XΣ-4 state, electron spin dipolar interaction within the ground state and the spin-orbit coupling between XΣ-4 and two excited states, AΠ4 and 1Σ+2, are calculated ab initio alongside hyperfine interaction terms. Four hyperfine coupling terms are explicitly considered: Fermi-contact interaction, electron spin-nuclear spin dipolar interaction, nuclear spin-rotation interaction, and nuclear electric quadrupole interaction. These terms are included as part of a full variational solution of the nuclear-motion Schrödinger equation performed using program Duo, which is used to generate both hyperfine-resolved energy levels and spectra. To improve the accuracy of the model, ab initio curves are subject to small shifts. The energy levels generated by this model show good agreement with the recently derived empirical term values. This and other comparisons validate both our model and the recently developed hyperfine modules in Duo.

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.

Coherent electrical control of a single high-spin nucleus in silicon.

Nuclear spins are highly coherent quantum objects. In large ensembles, their control and detection via magnetic resonance is widely exploited, for example, in chemistry, medicine, materials science and mining. Nuclear spins also featured in early proposals for solid-state quantum computers1 and demonstrations of quantum search2 and factoring3 algorithms. Scaling up such concepts requires controlling individual nuclei, which can be detected when coupled to an electron4-6. However, the need to address the nuclei via oscillating magnetic fields complicates their integration in multi-spin nanoscale devices, because the field cannot be localized or screened. Control via electric fields would resolve this problem, but previous methods7-9 relied on transducing electric signals into magnetic fields via the electron-nuclear hyperfine interaction, which severely affects nuclear coherence. Here we demonstrate the coherent quantum control of a single 123Sb (spin-7/2) nucleus using localized electric fields produced within a silicon nanoelectronic device. The method exploits an idea proposed in 196110 but not previously realized experimentally with a single nucleus. Our results are quantitatively supported by a microscopic theoretical model that reveals how the purely electrical modulation of the nuclear electric quadrupole interaction results in coherent nuclear spin transitions that are uniquely addressable owing to lattice strain. The spin dephasing time, 0.1 seconds, is orders of magnitude longer than those obtained by methods that require a coupled electron spin to achieve electrical driving. These results show that high-spin quadrupolar nuclei could be deployed as chaotic models, strain sensors and hybrid spin-mechanical quantum systems using all-electrical controls. Integrating electrically controllable nuclei with quantum dots11,12 could pave the way to scalable, nuclear- and electron-spin-based quantum computers in silicon that operate without the need for oscillating magnetic fields.

Loschmidt echo driven by hyperfine and electric-quadrupole interactions in nanoscale nuclear spin baths

The nuclear spin bath (NSB) dynamics and its quantum control are of importance for the storage and processing of quantum information within a semiconductor environment. In the presence of a carrier spin, primarily it is the hyperfine interaction that rules the high frequency NSB characteristics. Here, we first study the overall coherence decay and rephasings in a hyperfine-driven NSB through the temporal and spectral behaviors of the so-called Loschmidt echo (LE). Its dependence on the NSB size, initial polarization, and coupling inhomogeneity are separately investigated, which leads to a simple phenomenological expression that can accommodate all of these attributes. Unlike the prevailing emphasis on spin 1/2, the NSBs with larger spin quantum numbers are equally considered. For this case, additionally the effect of nuclear electric quadrupole interaction is taken into account where its biaxiality term is influential on the decoherence. The insights gained from model systems are then put to use for two generic realistic semiconductor systems, namely, a donor center and a quantum dot that represent small and large nanoscale NSB examples, respectively. The spectrum of LE for large quantum dots can reach the 100~MHz range, whereas, for donor centers, it reduces to a few MHz, making them readily amenable for dynamical decoupling techniques. The effect of quadrupole interaction on LE is seen to be negligible for large quantum dots, while it becomes significant for donor centers, most notably in the form of depolarizing a polarized NSB.

Nuclear electric quadrupole interactions in liquids entrapped in cavities

Liquids entrapped in cavities and containing quadrupole nuclei are considered. The interaction of the quadrupole moment of a nucleus with the electric field gradient is studied. In such a system, molecules are in both rotational and translational Brownian motions which are described by the diffusion equation. Solving this equation, we show that the intra- and intermolecular nuclear quadrupole interactions are averaged to zero in cavities with the size larger than several angstroms.

Domain structure and magnetic resonance studies of ferroelastic BiVO4 revisited**Supported by The National Academy of Sciences, Republic of Korea (2014) through SHC.

Bismuth vanadate (BiVO4) is a ferroelastic material undergoing a reversible second order phase transition at 528 K(Tc) between the tetragonal and monoclinic structure. There have been experimental studies on the incommensurate domain wall (W′) which reported different orientation angles. In order to clarify this we have tried to calculate it numerically in terms of lattice constants above and below Tc by employing the theory of Sapriel, and obtained it to be either 35.9° or 54.1°. It also turns out that the shear strain (S21) in the ferroelastic phase depends on the crystal growing condition. The remaining internal stress appears to be responsible for the formation of W′ wall. The host atom nuclear magnetic resonance and the S-state impurity electron magnetic resonance are also reviewed. The nuclear electric quadrupole interaction of 51V and 209Bi in BiVO4 was evaluated in terms of the point charge model based on the crystal structure. The result of electric field gradient tensor turns out to be reasonable with experimental values. The zero-field splitting tensor of Mn2+, Fe3+ and Gd3+ are also compared, and the deduced local environment of these ions in the host are confirmed. Finally the second-order phase transition according to the Landau’s framework is found in this crystal from the temperature dependence of magnetic resonance parameters.

Hyperfine spectrum of RbBr

The molecular beam electric resonance technique has been used to conduct a high precision examination of the hyperfine spectrum of 85Rb79Br and 85Rb81Br. Coupling constants for the nuclear electric quadrupole interactions, the spin–rotation interactions, the tensor and scalar spin–spin interactions, and their dependence on vibrational and rotational state have been determined. A slightly improved value of the electric dipole moment is also obtained, and the inclusion of an electric hexadecapole interaction for the rubidium nucleus is found to somewhat improve the fit.

Investigation of parity violation in nuclear spin-rotation interaction of fluorooxirane

When it comes to the question of how signatures from parity violation in chiral molecules can be revealed, then ultra-high resolution spectroscopy techniques play a crucial role in attempts to detect such effects via line shifts. A prerequisite for this approach towards molecular parity violation is a detailed understanding of the corresponding conventional spectroscopy, including even small effects that are often neglected. Nuclear spin-rotation (NSR) interaction is one such effect that becomes appreciable only at high to ultra-high resolution and is often masked by nuclear electric quadrupole interactions (NQI) if nuclei are present with nuclear spin quantum number I larger than 1/2. Herein, NSR interactions are studied theoretically for the chiral molecules fluorooxirane and bromochlorofluoromethane (CHBrClF). For the latter molecule, NSR interactions are compared to nuclear electric quadrupole coupling contributions. The former molecule is devoid of I > 1/2 nuclei such that NSR interactions are not masked by NQI. Parity-odd contributions to NSR of 19F are computed that give rise to additional line shifts in hyperfine transitions. A detection of these nuclear spin-dependent P-odd terms could in principle give information on the nuclear anapole moment in fluorine, which arises due to parity violating interactions within the nucleus.

Nuclear hyperfine level pattern and hyperfine specific heat of frustrated Gd-pyrochlores Gd2 M 2O7 (M = Ti, Sn, Hf, Zr)

The nuclear contribution to the specific heat originates from the combination of a nuclear electric quadrupole interaction and a nuclear magnetic hyperfine interaction of the magnetic atoms embedded in the crystalline lattice structure. We have estimated the nuclear hyperfine level patterns of the nuclear ground state \(I_{g} = 3/2^{-}\) and the first excited state \(I_{ex} = 5/2^{+}\) at 86.5 keV of Mossbauer-active Gd155 nucleus of Gd-based pyrochlores Gd2M2O7 (M = Ti, Sn, Hf, Zr). The nuclear quadrupole and hyperfine interactions are scaled in accordance with the ratios of quadrupole and magnetic moments of \(I_{g} = 3/2^{-}\) state of Gd155 and Gd157 nuclei to get the contribution from Gd157 nucleus of Gd2M2O7 to the hyperfine specific heat Chf appropriate to its relative isotopic abundance. It is found that Chf(T) shows a Schottky hump around 6–8 mK for these pyrochlores. At temperatures much higher than the hyperfine level splitting, Chf behaves as AT − 2 with A ∼ 1–2 × 10 − 4 JK/mole-Gd which is consistent with experimental results.

All 36 exactly solvable solutions of eigenvalues for nuclear electric quadrupole interaction Hamiltonian and equivalent rigid asymmetric rotor with expanded characteristic equation listing

This paper derives all 36 analytical solutions of the energy eigenvalues for nuclear electric quadrupole interaction Hamiltonian and equivalent rigid asymmetric rotor for polynomial degrees 1 through 4 using classical algebraic theory. By the use of double-parameterization the full general solution sets are illustrated in a compact, symmetric, structural, and usable form that is valid for asymmetry parameter \(\eta \in \left({- \infty , + \infty}\right)\). These results are useful for code developers in the area of Perturbed Angular Correlation (PAC), Nuclear Quadrupole Resonance (NQR) and rotational spectroscopy who want to offer exact solutions whenever possible, rather that resorting to numerical solutions. In addition, by using standard linear algebra methods, the characteristic equations of all integer and half-integer spins I from 0 to 15, inclusive are represented in a compact and naturally parameterized form that illustrates structure and symmetries. This extends Nielson’s [1] listing of characteristic equations for integer spins out to I = 15, inclusive.

Oxygen vacancies adjacent to Cu2+ ions in TiO2 (rutile) crystals

Electron paramagnetic resonance (EPR) and electron-nuclear double resonance (ENDOR) are used to characterize Cu2+ ions substituting for Ti4+ ions in nominally undoped TiO2 crystals having the rutile structure. Illumination at 25 K with 442 nm laser light reduces the concentration of Cu2+ ions by more than a factor of 2. The laser light also reduces the EPR signals from Fe3+ and Cr3+ ions and introduces signals from Ti3+ ions. Warming in the dark to room temperature restores the crystal to its preilluminated state. Monitoring the recovery of the photoinduced changes in the Cu2+ ions and the other paramagnetic electron and hole traps as the temperature is raised from 25 K to room temperature provides evidence that the Cu2+ ions have an adjacent doubly ionized oxygen vacancy. These oxygen vacancies serve as charge compensators for the substitutional Cu2+ ions and lead to the formation of electrically neutral Cu2+-VO complexes during growth of the crystals. The Cu2+-VO complexes act as electron traps and convert to nonparamagnetic Cu+-VO complexes when the crystals are illuminated at low temperature. Complete sets of spin-Hamiltonian parameters describing the electron Zeeman, hyperfine, and nuclear electric quadrupole interactions for both the 63Cu and 65Cu nuclei are obtained from the EPR and ENDOR data. This study suggests that other divalent cation impurities in TiO2 such as Co2+ and Ni2+ may also have an adjacent oxygen vacancy for charge compensation.

9Be-NMR Spin–Lattice Relaxation Rate in Heavy-Fermion Superconductor UBe13

9 Be nuclear magnetic resonance (NMR) measurements have been carried out for a single crystal UBe 13 with T c =0.86 K, in order to clarify unusual properties in the normal state. For the applied field parallel to [001] direction, a well-split 9 Be NMR spectrum due to the nuclear electric quadrupole interaction is obtained in H =7 T. When the magnetic field is applied to [111] direction, the quadrupole split Be(II) lines gather around the central line. 9 Be nuclear spin–lattice relaxation rate has been measured for Be(I) and Be(II) sites for H ∥[111] in 7 T. 1/ T 1 s for both sites are found to obey √T in the temperature range of 1.5–4 K, suggesting that the antiferromagnetic spin fluctuations exist. Above 4 K, 1/ T 1 for the Be(II) site weakly depnends on temperature, whereas that for the Be(I) site is independent of temperature.

Hyperfine spectrum of RbI

The molecular beam electric resonance technique has been used to conduct a high precision examination of the hyperfine spectrum of RbI. Coupling constants for the nuclear electric quadrupole interactions, the spin-rotation interactions, the tensor and scalar spin-spin interactions, and their dependence on vibrational and rotational state have been determined.

Hyperfine spectrum of NaF

The molecular beam electric resonance technique has been used to conduct a high precision examination of the hyperfine spectrum of 23Na 19F. Coupling constants for the nuclear electric quadrupole interactions, the spin–rotation interactions, the tensor and scalar spin–spin interactions, and their dependence on vibrational and rotational state have been determined.

Zirconium–indium intermetallic compounds investigated by measurements of nuclear electric quadrupole interactions

The nuclear electric quadrupole interaction (QI) of the nuclear probe 111Cd on In sites of intermetallic compounds of the Zr–In system has been investigated as a function of temperature (15 ≤ T ≤ 1200 K) by perturbed angular correlation (PAC) spectroscopy. Zr–In compounds were synthesized by arc-melting of the metallic constituents and doped with 111In, the mother isotope of the probe nucleus by diffusion at 1200 K. Strength, symmetry and temperature coefficient of the electric field gradient (EFG) were determined for four In sites: the two 8 e-sites of ZrIn 2 and sites (2 b, 4 d) of β-ZrIn 3. The temperature dependence of the relative intensities of these sites in the PAC spectra provides information on Zr–In solid state reactions occurring during annealing of arc-molten Zr–In ingots.

Electron-nuclear double resonance study of [formula omitted] ions in [formula omitted] crystals

Electron paramagnetic resonance (EPR) and electron-nuclear double resonance (ENDOR) are used to identify and characterize V 4+ ions in a bulk single crystal of vanadium dioxide (V O 2). These S = 1 / 2 defects are observed in the as-grown crystal because an adjacent nonmagnetic M 4+ impurity, e.g., a Si 4+ ion, has destroyed the normal antiferromagnetic coupling associated with the close pairs of V 4+ ions that occur in the low-temperature monoclinic phase of V O 2. EPR spectra taken near 5 K with the magnetic field along the [110] and [001] axes show resolved hyperfine patterns due to one 51V nucleus. ENDOR spectra taken at 5 K with the magnetic field parallel to the [001] axis have large nuclear electric quadrupole splittings as a result of a significant electric field gradient at the 51V nucleus. Spin-Hamiltonian parameters describing the electron Zeeman, hyperfine, and nuclear electric quadrupole interactions are reported.

Nuclear quadrupole interaction studies ofC15RMn2hydrides (R=Y,Gd,Tb,Dy)

The nuclear electric quadrupole interaction (QI) of the probe nucleus $^{111}\text{I}\text{n}/^{111}\text{C}\text{d}$ in the paramagnetic phase of the $C15$ rare earth $(R)$--manganese hydrides (deuterides) $R{\text{Mn}}_{2}\text{H}{(D)}_{x}$, with $R=\text{Y}$, Gd, Tb, and Dy, has been investigated by perturbed angular-correlation spectroscopy. The QI between the $^{111}\text{C}\text{d}$ quadrupole moment and the electric-field gradient (EFG) at the probe nucleus on the Mn site has been measured as a function of temperature in ${\text{TbMn}}_{2}\text{H}{(D)}_{x}$ in the concentration range $0\ensuremath{\le}x\ensuremath{\le}4.3$ and in $R{\text{Mn}}_{2}\text{H}{(D)}_{x}$, $R=\text{Y}$,Gd,Dy at the highest H content of $x\ensuremath{\sim}4.3$. The relative temperature dependence of the EFG in the parent compounds $R{\text{Mn}}_{2}$ is twice as strong as in isostructural $R{\text{Al}}_{2}$ which can be related to differences in the Debye temperatures resulting from different radius ratios ${r}_{R}/{r}_{\text{Mn}}$ and ${r}_{R}/{r}_{\text{Al}}$ [Joseph-Gschneidner postulate, Scr. Metall.2, 631 (1968)]. Hydrogenation of $R{\text{Mn}}_{2}$ increases the magnitude of the EFG by a factor of 2 between $x=0$ and $x=4.3$ but leaves the relative temperature dependence almost unchanged. Only at concentrations $x>3.6$ the temperature coefficient of the QI is significantly larger than in uncharged $R{\text{Mn}}_{2}$. These results are compared with the much stronger concentration dependence and the anomalous temperature dependence of the QI of $^{111}\text{C}\text{d}$ in the $C15$ hydrides ${\text{HfV}}_{2}{\text{H}}_{x}$. Evidence for an exceptionally high H mobility in ${\text{TbMn}}_{2}{\text{H}}_{x}$ is presented. The measurements provide information on structural changes and magnetic ordering temperatures at different H concentrations.

Hyperfine spectra of KBr and KI

The molecular beam electric resonance technique has been used to conduct a high precision examination of the hyperfine spectra of 39K 79Br, 39K 81Br and 39K 127I. Coupling constants for the nuclear electric quadrupole interactions, the spin–rotation interactions, the tensor and scalar spin–spin interactions, as well as the electric dipole moment of KI, and their dependence on vibrational and rotational state have been determined. A few transitions observed for 41K 127I show a small shift in the iodine nuclear electric quadrupole interaction, and the fit improves somewhat with the inclusion of an iodine nuclear electric hexadecapole interaction term.

Microwave spectra of O2–HF and O2–DF: Hyperfine interactions and global fitting with infrared data

Spectra of the open shell complexes O(2)-HF and O(2)-DF were recorded using Fourier transform microwave spectroscopy. A complete analysis of the hyperfine structure and a global fit including microwave and infrared frequencies [W. M. Fawzy, C. M. Lovejoy, D. J. Nesbitt, and J. T. Hougen, J. Chem. Phys. 117, 693 (2002)] are reported. The Fermi contact interaction between the electron and nuclear spins, the electron spin-nuclear spin dipolar interaction, the nuclear spin-nuclear spin dipolar interaction, and the nuclear electric quadrupole interaction (for O(2)-DF) were considered in the analysis. The correspondence between the magnetic hyperfine constants and the two nuclei of the H(D)F is unambiguously established. In both O(2)-HF and O(2)-DF, the Fermi contact parameter is larger for the fluorine than for the hydrogen, while for the nuclear spin-electron spin dipolar hyperfine constants, the reverse is true. The effective angle between the HF bond and the a axis of the complex, determined from the nuclear spin-nuclear spin interaction constant, is 38(4) degrees. The same angle for the DF complex, derived from the deuterium nuclear quadrupole coupling constant, is 31(4) degrees.