Contact Hyperfine Interaction Research Articles

Molecular Orbital Calculation of the Contact Hyperfine Interaction in N2− and N4− Radicals

Molecular Orbital Calculation of the Contact Hyperfine Interaction in N2− and N4− Radicals

Pressure dependence of F-center hyperfine interactions

We report a study of the effects of intense hydrostatic stress (10 Kbar) on the ENDOR spectra of F-centers in several alkali halides. In LiF, KCl, and KBr, the first shell contact hyperfine interaction constant, a I, increases with compression, while the second shell term, a II, decreases. In LiCl, however, d a II/d P and d a I/d P are both less than zero. We explain our experimental results, including the anomaly cf LiCl, with a model involving (1) ionic motion in a non-constant spin-density gradient and (2) ion-motion-induced perturbation of the F-center envelope function.

Spin Polarization in the Electron Gas by a Magnetic Impurity: Theory of the Excess Knight Shift

In the absence of an applied magnetic field, a process which will permit the existence of a Fermi contact hyperfine interaction at the ${\mathrm{Cu}}^{63}$ nucleus, which is not zero when summed over the randomly oriented spins of $N$ conduction electrons, is the scattering of $s$-wave electrons from the exchange potential of an open-shell impurity atom located at a distance $R$ from the Cu nucleus, and then the subsequent Fermi contact interaction at the Cu nucleus. This is a two-center scattering analog of the virtual process which is responsible for most of the Fermi contact hyperfine structure of open-shell atoms (polarization of the closed $s$ core). The first-order energy due to the Fermi contact interaction with the conduction electrons at the Cu nucleus, which have first scattered from Mn impurity atoms, is calculated as a function of $R$. It is found to change sign before $R=4.8299$ (nearest-neighbor distance), between $R=4.8299$ and $R=8$, and between $R=8$ and $R=10$ a.u., suggesting experiments in which compression or expansion can change the lattice distances and studies of the dependence on impurity concentration. The exchange potential is presented as a function of electron velocity and $R$. For completeness, the Ruderman-Kittel-Kasuya-Yosida-type spin-density waves are presented as a function of the distance from the impurity for several values of $R$. Also, for $R=0$, an estimate is made of the exchange polarization potential due to the adiabatic polarization of the impurity by the scattering electrons; it is found to be significant.

Proton Knight shifts and antiferromagnetic exchange in dimeric oxygenbridged Schiff-base–iron(III) complexes

N.m.r. data are reported for oxygen-bridged iron(III) complexes of the type (FeIIIL2)2O where L is a bidentate Schiff-base ligand. The temperature-dependence of the proton Knight shifts in the ligands has been interpreted in terms of the contact hyperfine interaction constant A and exchange integral J. The fitting of these shifts represents a novel method for the evaluation of J in such systems.

Hyperfine Contact Interaction in the Iron Atom Calculated by Many-Body Theory

Hyperfine Contact Interaction in the Iron Atom Calculated by Many-Body Theory

Proton magnetic resonance, magnetic susceptibility and Mössbauer studies of Clostridium pasteurianum rubredoxin.

Mossbauer and magnetic suspectibility studies concur in assigning high spin values to the single iron atom of rubredoxin in both redox forms. Contact shifts were observed in the NMR spectrum of the reduced form that appear to originate from pseudocontact rather than hyperfine contact interaction. The magnetic properties of rubredoxin are compared with those of another iron–sulphur protein, the eight-iron ferredoxin.

Contact hyperfine interaction and induced dynamic nuclear spin polarization

Theoretical CIDNP spectra for products formed via radical pair reactions were obtained by using the transverse Overhauser mechanism proposed by Closs and the further constraint that the saturated states have their nuclear spin configurations properly polarized according to the sign of the electron spin densities.

Hyperfine Structure in the2P2State of Atomic Lithium

Calculations by two different theoretical methods are in good agreement with each other and with available experimental data on hyperfine splitting and Zeeman level crossing of $2^{2}P$ lithium. These results show unequivocally that the contact, spin-dipolar, and orbital hyperfine interactions must be described by three independent parameters.

CORRÉLATIONS ET FONCTIONS D'ONDES RADIALESELECTRON CORRELATIONS IN THE IRON ATOM

Many-body perturbation theory is used to calculate properties of the iron atom including the effects of electron correlations. Results are given for the hyperfine contact interaction in the ground state and also for the correlation energy. Three-body correlations reduce the 3 d-3 d pair correlation energy by only fourteen percent.

Nuclear Spin-Lattice Relaxation in Cadmium and Tin

Pulsed nuclear-magnetic-resonance measurements of the spin-lattice relaxation time ${T}_{1}$ in ${\mathrm{Cd}}^{113}$ and ${\mathrm{Sn}}^{119}$ from 77 to 820\ifmmode^\circ\else\textdegree\fi{}K are reported. An enhancement of the Korringa product ${T}_{1}TK_{\mathrm{iso}}^{}{}_{}{}^{2}$ that is constant with temperature but different in the solid and liquid states is observed. For ${\mathrm{Cd}}^{113}$, the difference between the liquid and solid enhancement is significant and can be related to a core-polarization or orbital contribution to the isotropic Knight shift ${K}_{\mathrm{iso}}$. In solid ${\mathrm{Cd}}^{113}$, the sum of these two contributions to ${K}_{\mathrm{iso}}$ is about -9% as large as the contribution from the contact hyperfine interaction and that fraction is independent of temperature. In liquid ${\mathrm{Cd}}^{113}$ and solid and liquid ${\mathrm{Sn}}^{119}$, the sum of these contributions is probably small.

ENDOR Hyperfine Constants and Lattice Distortion ofVK-Type Centers

The magnetic hyperfine dipole-dipole interaction between ${V}_{K}$-type centers (negatively charged diatomic halide molecule-ions) and the neighboring lattice nuclei has been calculated for the ${V}_{K}$ center in LiF and NaF and the ${V}_{\mathrm{KA}}$ (Li) center in NaF using the $\mathrm{F}_{2}^{}{}_{}{}^{\ensuremath{-}}$ wave function of Wahl. The calculated hyperfine constants are sensitive to the relative positions of the $\mathrm{F}_{2}^{}{}_{}{}^{\ensuremath{-}}$ molecule-ion and the neighboring nuclei. When the calculated hyperfine constants were compared with those measured in electron-nuclear double-resonance (ENDOR) experiments, the displacements of the nuclei surrounding the ${V}_{K}$-type centers were determined. In the vicinity of the center, the lattice contracts parallel to the axis of the molecule-ion and dilates perpendicular to this axis. The contact hyperfine interaction has been estimated and compared with the values measured in ENDOR experiments. The sign and order of magnitude of the contact hyperfine constants can be explained by assuming that the closed-shell orbitals of the molecule-ion are exchange-polarized.

Spin-Lattice Relaxation ofFCenters in Alkali Halides: Theory and Optical Measurements to 50 kG

We have measured the ground-state spin-lattice relaxation of $F$ centers in KBr and KI over the range of magnetic field from 0 to 50 kG, and at the temperature of 1.6\ifmmode^\circ\else\textdegree\fi{}K. Essentially continuous measurement over this large field range was made possible by a detection technique in which the magnetic circular dichroism of the optical absorption band was monitored. In the range 10 to 50 kG, the relaxation rate is predominantly that of single $F$ centers. Here, the field dependence of the relaxation rate followed very closely a curve of the form $(A{H}^{3}+B{H}^{5})coth(\frac{g\ensuremath{\beta}H}{2KT})$. The first term represents a mechanism involving phonon modulation of the hyperfine contact interaction with neighboring nuclei, and is the larger term for ${H}_{0}\ensuremath{\lesssim}25$ kG. The second term is due to relaxation via the Kronig-Van Vleck process. A theoretical evaluation of that part of the rate due to the hyperfine mechanism has produced close agreement with experimental results. In the evaluation, the interaction with the second shell of nuclei (halogens) was found to be of greatest importance for KBr and KI.

Hyperfine Contact Interactions in Oxygen Calculated by Many-Body Theory

Many-body perturbation theory, which has been used in previous atomic calculations, is applied to the calculation of the hyperfine contact interaction in the oxygen atom. Large cancellations have been found to occur between different types of diagrams. Both core polarization diagrams and also diagrams representing electron correlations have been found to contribute significantly. The final value for ${|\ensuremath{\Psi} (0)|}^{2}$ is in good agreement with that measured by Harvey.

Many-body calculation of hyperfine structure

The many-body perturbation theory of Brueckner and Goldstone is used to calculated the hyperfine contact interaction of oxygen. The calculated value for | ψ(0)| 2 is 0.0601.

Theory of Indirect Nuclear Interactions in Rubidium and Cesium Metals

A quantitative evaluation has been made of the Ruderman-Kittel and pseudodipolar parameters ${A}_{\mathrm{ij}}$ and ${B}_{\mathrm{ij}}$ for ${\mathrm{Rb}}^{85}$ and ${\mathrm{Cs}}^{133}$ nuclei in the respective metals using one-orthogonalized-plane-wave functions and calculated band structures. All the possible mechanisms that contribute to ${A}_{\mathrm{ij}}$ and ${B}_{\mathrm{ij}}$ have been considered. For ${A}_{\mathrm{ij}}$, about 90.54 and 92.25% of the total contribution for rubidium and cesium, respectively, are found to arise from the second-order effect of the contact hyperfine interaction. For ${B}_{\mathrm{ij}}$, the corresponding figures are 89.95 and 88.84%, arising from one order each in the electron-nuclear contact and dipole interactions. For each mechanism, the calculation involves an integration over the region of k space within the Fermi surface. The integrand is composed of three k-dependent factors, an expectation value over the wave functions, a density-of-states term, and a phase factor which depends on the distance between the nuclei. The final result depends sensitively on the $k$ dependence of these factors, and in some cases there is a cancellation between positive and negative contributions from different regions of k space. In the light of this, a critical analysis is made of earlier approximations, where some of the k-dependent factors were replaced by their values at the Fermi surface. Self-consistency and correlation effects are explicitly included, and produce less than 10% correction for ${A}_{\mathrm{ij}}$ and ${B}_{\mathrm{ij}}$ in both metals. Our calculated values for ${A}_{\mathrm{ij}}$ are 22.73 and 124.65, respectively, for rubidium and cesium, as compared to recent experimental values 51\ifmmode\pm\else\textpm\fi{}5 and 200\ifmmode\pm\else\textpm\fi{}10 cps. For ${B}_{\mathrm{ij}}$, the calculated values are 0.398 and 2.330, as compared to experimental values 11.80 and 35.00 cps. Possible sources for the discrepancies, and additional factors whose inclusion could lead to improved agreement with experiment, are discussed.

Paramagnetic Resonance and Optical Study of Cupric Amine Complexes

The EPR spectra of complexes of CuCl2, CuBr2, CuF2, and Cu (NO3)2 with primary, secondary, and tertiary amines were obtained at 77°K and room temperature. In a nonpolar solvent, 1:1 ether/ethanol, the g value and the hyperfine splitting constant were found to depend on both the amine ligands and the anion, whereas in water, the g value and hyperfine constant depend on the amine ligands but do not depend on the anions. Optical spectra of these systems taken at room temperature also show the same amine ligand and anion dependence. The anion dependence of the spin-Hamiltonian parameters can be explained by admitting admixtures of excited states with 4s character into the singly occupied orbital through vibronic coupling. This vibronic coupling assumption is also consistent with the effect of the amine ligands on the contact hyperfine interaction.

Electron Paramagnetic Resonance of Copper in Beryllium Oxide

Paramagnetic-resonance absorption of copper-doped single crystals of beryllium oxide has been investigated at 9 GHz. The best-fit values to a spin Hamiltonian with $S=\frac{1}{2}$ are $|{g}_{\ensuremath{\parallel}}|=1.709\ifmmode\pm\else\textpm\fi{}0.002$, $|{g}_{\ensuremath{\perp}}|=2.379\ifmmode\pm\else\textpm\fi{}0.001$, $|{A}_{\ensuremath{\parallel}}|=(50\ifmmode\pm\else\textpm\fi{}1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$, $|{A}_{\ensuremath{\perp}}|=(108\ifmmode\pm\else\textpm\fi{}1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$, and $|Q|=(11\ifmmode\pm\else\textpm\fi{}1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$, where the hyperfine values refer to the ${\mathrm{Cu}}^{63}$ isotope, for which $I=\frac{3}{2}$. The observations are interpreted as due to ${\mathrm{Cu}}^{2+}$ substitutional for beryllium at normal lattice sites. Crystal-field theory which incorporates covalent bonding has been used to interpret these results in terms of the $3{d}^{9}$ configuration of ${\mathrm{Cu}}^{2+}$ in ${C}_{3v}$ symmetry. The experimental results are shown to be consistent with the theory, which yields an orbital reduction factor of 0.6, and values for $〈{r}^{\ensuremath{-}3}〉$ and the contact hyperfine interaction close to those for the free ion. The results are also compared with some other cases of $3{d}^{9}$ ions in tetrahedral coordination.

Nuclear Spin-Lattice Relaxation in Hexagonal Transition Metals: Titanium

The nuclear magnetic resonance of $^{47}\mathrm{Ti}$ and $^{49}\mathrm{Ti}$ has been observed in hexagonal close-packed titanium metal in the temperature range $T=1\ensuremath{-}4\ifmmode^\circ\else\textdegree\fi{}$K. Measurements of the line profile and relaxation rates were carried out at 12.5 MHz by pulsed nuclear resonance techniques. Since the gyromagnetic ratios of $^{47}\mathrm{Ti}$ and $^{49}\mathrm{Ti}$ are nearly identical, the resonances of the two isotopes were superimposed. A partially resolved first-order quadrupole spectrum having a total width exceeding 8 kOe was observed, yielding a probable assignment ${h}^{\ensuremath{-}1}{e}^{2}q{Q}^{47}\ensuremath{\approx}{h}^{\ensuremath{-}1}{e}^{2}q{Q}^{49}\ensuremath{\approx}7.7$ MHz. The average Knight shift is estimated to be $K=(+0.4\ifmmode\pm\else\textpm\fi{}0.2)%$. The spin-lattice relaxation times ${T}_{1}$, which are quite long (${T}_{1}T=150\ifmmode\pm\else\textpm\fi{}20$ sec\ifmmode^\circ\else\textdegree\fi{}K), provide evidence that the conduction-electron states at the Fermi level are predominantly $d$-like. The theory of nuclear spin-lattice relaxation in hexagonal transition metals is treated in the tight-binding approximation. Contact, core-polarization, orbital, and dipolar hyperfine interactions are considered. The magnitudes of the orbital and dipolar contributions to the spin-lattice relaxation rate depend on the orientation of the magnetic field relative to the hexagonal $c$ axis. In the presence of $s\ensuremath{-}d$ mixing, the contact contribution is found to interfere destructively with one of the components of the core-polarization contribution. The predicted total relaxation rates are shown to depend more strongly on the orbital admixture coefficients than is the case in cubic transition metals. The relatively large number of parameters in the theory precludes a unique fit to the experimental results for titanium. In general, however, the calculated rates exceed the observed rate by a factor of 2-3 over a wide range of parameter values. The apparent discrepancy is attributed to the combined effects of (1) the electron-phonon enhancement of the electronic specific heat and (2) $s\ensuremath{-}d$ interference effects. The former effect causes the "bare" electron density of states to be overestimated, while the latter leads to an overestimate of the sum of contact and core-polarization contributions to the relaxation.

NMR Evidence for Contact Hyperfine Coupling in Paramagnetic UF4

AbstractThe F19 NMR absorption in powdered UF4 is investigated in the temperature range 122 to 433 °K at magnetic fields between 10000 and 5000 G. The fluorine absorption pattern in this paramagnetic material with seven nonequivalent F‐sites in the unit cell is reproduced qualitatively by a sum of six asymmetric component lines (H∥ ‐– H⊥)−1/2 × (H–H⊥)−1/2, some of which are shifted in the high field direction, and some in the low field direction. The occurrence of low‐field shifted components provides evidence of contact hyperfine interaction between the magnetic electrons and the fluorine nuclei whereas the occurrence of high‐field shifted components may arise from indirect coupling through electron transfer, and indicates partial covalent bonding between the magnetic electrons and the surrounding fluorine ions. This is supported by magnetic susceptibility and EPR data.

Spin-Orbit Coupling and the Knight Shift in Nontransition-Metal Superconductors

The Knight shift ${K}_{s}$ of nontransition-metal superconductors is discussed in terms of three contributions, namely: (a) The Van Vleck part of the contact shift attributed to the spin-orbit coupling force of the periodic potential which, in the presence of an external magnetic field, causes virtual high-energy rearrangements of conduction electrons near and inside the Fermi surface; (b) that part of the contact shift which is attributed to low-energy rearrangements of conduction electrons and affected by spin-reversing scattering; and (c) the diamagnetic orbital shift. For the calculation of (a), Wannier's theory of a Bloch electron in a magnetic field is generalized to the original Pauli Hamiltonian ${\mathcal{H}}_{0}$, describing the relativistic dynamical behavior of a conduction electron in the effective periodic potential of the lattice. This leads to an effective Hamiltonian which couples only Bloch-type spinors of the same band index, but of the same and of different spin indices. With the help of the eigenfunctions of ${\mathcal{H}}_{0}$, the hyperfine contact interaction is treated by perturbation theory. To arrive at simple expressions for the corresponding Knight shift and nuclear spin-relaxation time, valid for arbitrary strength of spin-orbit coupling, the energy-band function in the absence of the field is approximated by a parabola. Formulas for (b) and (c) are taken from the literature. The relative importance of the three contributions to ${K}_{s}$ is discussed for Al, Sn, and Hg, where the Knight shift has been observed in the normal and in the superconducting states. If one assumes that spin-reversing scattering is caused merely by spin-orbit interactions at atomic imperfections such as displaced surface atoms of small particles, and not by paramagnetic impurities, one finds that in Al neither of the two spin-orbit coupling effects is sufficiently strong to account for more than \ensuremath{\sim}2% of the residual shift ${K}_{s}(0)$. For the experimental Sn sample, (a) and (b) have the ratio 1:3 and, together with the orbital shift, can account for $\frac{2}{3}$ of the observed ${K}_{s}(0)$. For Hg, (a) and (b) are of comparable magnitude at $T=0$ and together account for more than \textonehalf{} of the observed shift ${K}_{s}(0)$.