Anisotropic Knight Shift Research Articles

Nuclear Magnetic Resonance in Hexagonal Lanthanum Metal: Knight Shifts, Spin Relaxation Rates, and Quadrupole Coupling Constants

The $^{139}\mathrm{La}$ nuclear magnetic resonances in the double-hexagonal close-packed (dhcp) form of metallic lanthanum have been studied by spin-echo techniques in the frequency range 6-30 MHz and temperatures between \ensuremath{\sim}1 and 210\ifmmode^\circ\else\textdegree\fi{}K. A seven-line powder pattern due to electric quadrupole interactions is observed with $|{e}^{2}q{Q}^{(139)}{h}^{\ensuremath{-}1}|=7.8\ifmmode\pm\else\textpm\fi{}0.3$ MHz. The quadrupole splittings are identical within the experimental uncertainty for the two crystallographic sites. The Knight shifts are very different, however, $K\ensuremath{\approx}+0.63% \mathrm{and} +1.02%$ at 4\ifmmode^\circ\else\textdegree\fi{}K, and $K\ensuremath{\approx}+0.29% \mathrm{and} +0.92%$ at 210\ifmmode^\circ\else\textdegree\fi{}K. The anisotropic Knight-shift contribution is estimated to be less than 10% of the measured shifts. The average spin-lattice relaxation time for the two sites is ${T}_{1}T=0.56\ifmmode\pm\else\textpm\fi{}0.05$ sec \ifmmode^\circ\else\textdegree\fi{}K. The relaxation time for the site having the smaller Knight shift exceeds that for the other site by a factor of approximately 1.7. A comparison of the average Knight shifts and spinlattice relaxation rates in dhcp lanthanum with those in hcp scandium and yttrium leads to the conclusion that the direct $s$-contact interaction is the dominant magnetic-hyperfine mechanism in the Group-IIIB transition metals.

Magnetic Behavior of Intermetallic Compounds of Beryllium

The corroboration by NMR of the ferromagnetism of CrBe12 has prompted an NMR investigation of the magnetic properties of other beryllium intermetallic compounds. Magnetic-moment measurements of these materials show complex magnetic behavior at 4.2°K. All samples show strong paramagnetic moments and many exhibit remanence. To provide more information on this magnetic behavior, the 9Be resonance was observed in the following samples, listed in approximate order of their magnetic strength at 4.2°K: CrBe12, ZrBe2, MnBe8, FeBe11, MnBe12, NbBe3, ZrBe13, TaBe3, CrBe2, Nb2Be17, TiBe12, NbBe12, VBe12, MoBe12, TaBe12, WBe2, Ta2Be17, WBe12. Magnetization measurements are also reported for AgBe12, FeBe12, CoBe12, PtBe12, PdBe12, and AuBe12. Both the Knight shifts and the linewidths show correlation with the moment measurements. Most of the samples show small magnetic moments, positive Knight shifts, and small linewidths, ΔH, less than (800 A/m=10 Oe). ZrBe2 and MnBe8 have larger moments, negative values of K (∼−0.03% at 300°K) and larger ΔH [∼(1.2 kA/m=15 Oe) at 300°K]. CrBe12, clearly ferromagnetic, with the largest moment (of the compounds studied) has the most negative value of K (−0.19% at 300°K) and the largest ΔH [(1.83 kA/m=23 Oe) at 300°K]. From the temperature dependence of the linewidths, it appears that NbBe3 and CrBe2 may be magnetic, although much weaker than CrBe12. Anisotropic Knight shifts and first-order quadrupole effects are noted.

Nuclear Magnetic Resonance in Beryllium

NMR of $^{9}\mathrm{Be}$ in beryllium metal powder has been measured from 5 to 20 kG at 295\ifmmode^\circ\else\textdegree\fi{}K. The isotropic Knight shift is measured as (-0.0027\ifmmode\pm\else\textpm\fi{}0.0006)%; the anisotropic Knight shift $|a|<0.0003%$; and the quadrupole coupling $\frac{{e}^{2}\mathrm{qQ}}{h}$ is measured as 56.4\ifmmode\pm\else\textpm\fi{}0.3 kc/sec.

Nuclear Magnetic Resonance in Bismuth Metal

The nuclear magnetic resonance in bismuth metal powder has been observed from 9 to 19 Mc/sec at 4.2\ifmmode^\circ\else\textdegree\fi{}K. The isotropic and anisotropic Knight shifts and the quadrupole coupling constant have been determined as (-1.25\ifmmode\pm\else\textpm\fi{}.30)%, (-0.3\ifmmode\pm\else\textpm\fi{}0.3)%, and 2.10\ifmmode\pm\else\textpm\fi{}.05 Mc/sec, respectively. The intrinsic linewidth was found to be 130\ifmmode\pm\else\textpm\fi{}20 kc/sec. A technique is developed to take into consideration the broadening of the observed lines due to the combined effects of the magnetic dipolar broadening and the width due to the quadrupolar splitting of each line.

Nuclear magnetic resonance in -manganese

Nuclear magnetic resonance studies have been made of manganese metal in the β modification in the temperature range 140-340 °K. It is shown that only those nuclei at one of the two crystallographically non-equivalent sites contribute to the observed resonance. These sites have axial symmetry. Detailed measurements at 295 °K of first- and second-order quadrupole interactions give the following value for the quadrupole coupling constant, e2Qq/h = 1.71 ±0.01Mc/s and for the Knight shift anisotropy, K|| - K⊥ = -0.006 ± 0.010%. The most important other source of line broadening was nuclear dipolar interaction. Consideration of its orientation dependence was necessary to explain the observed degree of asymmetry of the resonance from the powdered sample. There was also evidence for broadening due to inhomogeneity of the quadrupole coupling constant. The quadrupole coupling constant was extremely temperature dependent, decreasing by a factor 1.50 from 140 °K to 340 °K. The Knight shift decreased very slightly with increasing temperature but remained isotropic within experimental error. Theoretical calculation of the quadrupole interaction gave order-of-magnitude agreement with experiment and showed that a much larger quadrupole interaction is expected at the other crystallographic site. This probably accounts for the absence of an observable signal from nuclei at these positions. In an appendix, a calculation is made of the shape of quadrupole satellite lines in nuclear resonance from a polycrystalline sample.

Electron-Nuclear Interaction in Antimony Metal

The field gradient at the nuclei due to the conduction electrons in antimony metal is calculated using an approximation for their wave functions in keeping with available information concerning the Fermi surface of antimony metal. It is shown that the Wannier functions for antimony can be closely approximated by a set of orthogonalized atomic orbitals (OAO) which are mixed by the noncentral terms in the one-electron Hamiltonian. The mixing of the $s$-like and $p$-like OAO is seen to be analogous to the concept of $s\ensuremath{-}p$ hybridization in the simple chemical picture of the solid. Combined with earlier calculations of the field gradient due to the ion cores, the total field gradient comes out as $eq=1998\ifmmode\times\else\texttimes\fi{}{10}^{12}$ esu/${\mathrm{cm}}^{3}$ as compared to 1889\ifmmode\times\else\texttimes\fi{}${10}^{12}$ esu/${\mathrm{cm}}^{3}$, the experimental value of the gradient based on Hewitt and Williams's quadrupole-resonance data and Murakawa's values of the quadrupole moments of the ${\mathrm{Sb}}^{121,123}$ nuclei. In addition, we have calculated the direct contributions to the isotropic and anisotropic Knight shifts from the spins of the conduction electrons near the Fermi surface. These are found to be ${\ensuremath{\delta}}_{\mathrm{iso}}=+0.07%$ and ${\ensuremath{\delta}}_{\mathrm{ax}}=\ensuremath{-}0.05%$. It is hoped that when experimental values of these quantities become available in the future a comparison with the theoretical values of the direct contributions will permit an assessment of the importance of other contributors to the Knight shift such as core polarization and orbital effects.

Nuclear Magnetic Resonance of Indium Metal at 4.2°K

The nuclear magnetic resonance spectrum of indium metal power has been measured at twelve magnetic-field points in the range of 17.0 to 30.5 kG at 4.2\ifmmode^\circ\else\textdegree\fi{}K. The analysis of this spectrum gives the isotropic Knight shift as +0.80\ifmmode\pm\else\textpm\fi{}0.02%, the anisotropic Knight shift as -0.05\ifmmode\pm\else\textpm\fi{}0.02%, and the nuclear quadrupole spliting parameter ${\ensuremath{\nu}}_{q}$ as 1.884\ifmmode\pm\else\textpm\fi{}0.002 Mc/sec. All three of these quantities were determined at each of the twelve field points, and no field dependence has been observed in this range.

Temperature dependence of the isotropic and anisotropic knight shift in polycrystalline cadmium and β-tin

The temperature dependence of the isotropic and anisotropic Knight shifts in Cd, Sn, Pb, and Al has been investigated in the temperature range 4.2–450°K. The largest temperature dependence was found in Cd in which Kiso decreases by about 27% between 444°K and 4.2°K. A smaller but still sizeable temperature dependence was found in Sn and to a lesser degree in Pb. The measurements have been related to the temperature dependence of the spin susceptibility which could be due to a very large volume dependence of the density of states at the Fermi level, N(EF). The behavior of 3Kax vs. T is shown to be due to the anisotropy of the spin susceptibility. This contribution appears to be opposite in sign to the one arising from the electron-nucleus dipole-dipole interaction. A striking feature of the measurements is the vanishing of Kax in Cd at 4.2°K. This may be related to magnetic breakdown of the spin-orbit energy gap which has been observed in some recent Fermi surface studies of this metal.

Knight Shift Anisotropy in Scandium and Yttrium and Nuclear Quadrupole Coupling in Scandium

The anisotropic Knight shift of the ${\mathrm{Sc}}^{45}$ and ${\mathrm{Y}}^{89}$ nuclear magnetic resonances (nmr) in polycrystalline scandium and yttrium metal, respectively, has been observed and measured at room temperature by means of the magnetic field dependence of the \textonehalf{} \ensuremath{\leftrightarrow} -\textonehalf{} transition. The isotropic Knight shift, ${K}_{\mathrm{iso}}$, is (0.262\ifmmode\pm\else\textpm\fi{}0.002)% for scandium and (0.367\ifmmode\pm\else\textpm\fi{}0.005)% for yttrium. The axial component of the Knight shift, ${K}_{\mathrm{ax}}$, is -(0.024\ifmmode\pm\else\textpm\fi{}0.002)% for scandium and -(0.026\ifmmode\pm\else\textpm\fi{}0.002)% for yttrium. The scandium nmr spectrum contains a central transition and three pairs of satellite lines, consistent with the $I=\frac{7}{2}$ spin of ${\mathrm{Sc}}^{45}$. The average spacing of the three pairs of satellites yields a lowest pure quadrupole frequency, ${\ensuremath{\nu}}_{\mathrm{Q}}=0.144\ifmmode\pm\else\textpm\fi{}0.002$ Mc/sec, so that the quadrupole coupling, $\frac{{e}^{2}\mathrm{Qq}}{h}=2.02\ifmmode\pm\else\textpm\fi{}0.03$ Mc/sec. Analysis of the central transition splitting yields the same value within the experimental uncertainty.

Nuclear Magnetic Resonance Study of Hyperfine Interactions in Sn3RE Intermetallic Compounds

Measurements of the 119Sn isotropic and anisotropic Knight shifts, Kiso and Kax, have been made in a series of Sn3RE intermetallic compounds (RE=La, Ce, Pr, Nd, Sm, Eu, and Yb). In particular, PrSn3 and NdSn3 have large positive, temperature-dependent shifts which are proportional to the magnetic susceptibility χM. It is proposed that the mechanism relating Kax to χM in these cases is a coupling of the 119Sn spin to the RE localized moment via the conduction electrons in a manner analogous to the pseudo-dipolar interaction between nuclear spins in heavy metals. Similarly, Kiso may be regarded as arising from an isotropic indirect coupling between f-electron spins and nuclear spins. Reasonable values of the interaction strengths are obtained.

Nuclear magnetic resonance line shape study in metallic powders in presence of axially symmetric anisotropic knight shift

The absorption and dispersion line shapes in a powder sample of a metal displaying axially symmetric anisotropic Knight Shift have been studied. An unambiguous way to derive from the experimental data precise values for K ax, K iso and the width and shape of the zero-field symmetric broadening is presented and applied to the cases of tin and cadmium metals for different temperatures. Even a small temperature dependence of the different parameters can be detected, and the usefulness of such measurements to obtain information on the band structure of non-cubic metals is discussed.

Quadrupole Coupling and Knight Shift Anisotropy in "hcp" Lanthanum

The nuclear magnetic resonance of ${\mathrm{La}}^{139}$ has been observed in hcp polycrystalline lanthanum metal at 25.6 kOe and 300\ifmmode^\circ\else\textdegree\fi{}K. The recorded pattern at 15.5 Mc/sec displays a central line and one pair of satellite lines. The position and shape of the central line yields an isotropic Knight shift of (0.685\ifmmode\pm\else\textpm\fi{}0.020)% and an axial shift of (0.046\ifmmode\pm\else\textpm\fi{}0.020)%. The satellite spacing yields a lowest pure quadrupole frequency ${\ensuremath{\nu}}_{Q}=101\ifmmode\pm\else\textpm\fi{}4$ kc/sec or $\frac{{e}^{2}\mathrm{qQ}}{h}=(1.41\ifmmode\pm\else\textpm\fi{}0.06)$ Mc/sec. A calculation of the lattice electric field gradient is made for the $\mathrm{ABAC}$ stacking sequences, yielding 0.540\ifmmode\times\else\texttimes\fi{}${10}^{22}$ and 0.487\ifmmode\times\else\texttimes\fi{}${10}^{22}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ for the so-called $A$ and $B$ (or $C$) layer sites, respectively, by the method of plane-wise summation of de Wette. Improved values of the nuclear electric quadrupole moment, $Q({\mathrm{La}}^{139})=0.21$ b, and the Sternheimer antishielding factor, ${\ensuremath{\gamma}}_{\ensuremath{\infty}}({\mathrm{La}}^{3+})=\ensuremath{-}73.5$, are adopted and discussed. The sign of the conduction-electron electric field gradient is shown to be negative.

Nuclear magnetic resonance line shape study in metallic powders in presence of axially symmetric anisotropic knight shift

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The dependence of the anisotropic knight shift on crystal symmetry

The magnetic field at a nucleus in a metal due to the electron-nuclear spin dipole interaction produces the anisotropic Knight shift. We show here that, in the absence of spin-orbit and electron spin-spin dipole coupling terms, the shift is zero in cubic materials as a general group-theoretical consequence of symmetry, and that we need make no specific assumptions about the electron wave functions such as they are p-like or d-like etc. as in previous discussions. Neglecting the same terms, we derive the formulae for the angular dependence of the shift on the orientation of the magnetic field relative to crystallographic axes for single crystals of the six non-cubic systems. These results are obtained with an independent-particle model for the conduction electrons, but we will find that they are unaffected if we take the Coulomb interactions fully into account. Finally, we give an expression for the anisotropic Knight shift with spin-orbit coupling included in a certain approximation. Diamagnetic effects are neglected throughout.

Sign of the Conduction Electron Contribution to the Electric Field Gradient in Metals

Evidence is presented for the lattice and conduction electron contributions to the electric field gradient having opposite sign in the case of pure BETA -tin, and correlation between the conduction electron contribution and the anisotropic Knight shift in metals is suggested. (R.E.U.)

Knight Shift and Quadrupole Interaction in Tc Metal

The nuclear magnetic resonance of the ${\mathrm{Tc}}^{99}$ nucleus in technetium metal has been observed. The shape and position of the resonance are due to combinations of isotropic and anisotropic Knight shifts, first and second order quadrupole interactions, and dipolar broadening. The various contributions have been separated by studying the characteristics of the resonance as a function of frequency.