Electron-Nuclear Double Resonance, Nuclear Moments, and〈r−3〉of Neodymium-143 (III) and Neodymium-145 (III) in Lanthanum Trichloride

Abstract

The electron-nuclear double resonance (ENDOR) spectra of dilute solutions of trivalent ${\mathrm{Nd}}^{143}$ and ${\mathrm{Nd}}^{145}$ ions occurring at the ${\mathrm{La}}^{+3\mathrm{}}$ ion sites in the axially symmetric La${\mathrm{Cl}}_3$ structure have been measured at the temperature of boiling He. For laboratory fields of ≈ ${10}^3$ G the frequencies ${\nu }_n$ of the ENDOR transitions are in the range $10\le {\nu }_n\le 1000$ Mc ${\sec }^{-1\mathrm{}}$. The experimental results for each nuclide have been summarized by giving values of the parameters in the spin Hamiltonian, ${\mathcal{H}}_s=\left|\beta \right|\mathrm{H}·g·\mathrm{S}+\mathrm{S}·T^{\prime }·\mathrm{I}+P^{\prime }[{I_z}^2-\frac{1}{3}I(I+1\mathrm{}\left)\right]-{\beta }_n\mathrm{H}·{g_n}^{\prime }·\mathrm{I}$, which produce a rigorous least-squares fit to the data for the two experimental conditions H ⊥ c and H∥c, where c is a vector parallel to the hexagonal axis of symmetry of the La${\mathrm{Cl}}_3$ crystal. The frequencies were fitted with rms deviations of $0.08\delta$ for H∥c and $0.3\delta$ for H ⊥ c, where $\delta$ is the average ENDOR line width, 3×${10}^5$ cps. The ${g_n}^{\prime }$ factor in the spin Hamiltonian was found to be anisotropic, with $\left|\frac{{g_{n\mathrm{II}}}^{\prime }}{{g_{n\perp }}^{\prime }}\right|=0.62\mathrm{}$. A comprehensive theoretical interpretation of the spin Hamiltonian parameters using eigenvectors precisely calculated from the best available crystal field interaction parameters yielded $\frac{\mu \left({\mathrm{Nd}}^{143}\right)}{\mu \left({\mathrm{Nd}}^{145}\right)}=+1.60883\mathrm{}\pm 0.00004$, $\mu \left({\mathrm{Nd}}^{143}\right)=-1.079\mathrm{}\pm 0.06$ nuclear magneton, $\mu \left({\mathrm{Nd}}^{145}\right)=-0.671\mathrm{}\pm 0.04$ nuclear magneton, $\frac{Q\left({\mathrm{Nd}}^{143}\right)}{Q\left({\mathrm{Nd}}^{145}\right)}=+1.96\mathrm{}\pm 0.2$, $Q\left({\mathrm{Nd}}^{143}\right)=(+0.0206\mathrm{}\pm 0.003)\times {10}^{-24\mathrm{}}$ ${\mathrm{cm}}^2$, $Q\left({\mathrm{Nd}}^{145}\right)=(+0.0105\mathrm{}\pm 0.002)\times {10}^{-24\mathrm{}}$ ${\mathrm{cm}}^2$, $〈r^{-3\mathrm{}}({\mathrm{Nd}}^{+3\mathrm{}}, 4f^3)〉=(36.9\mathrm{}\pm 4.5)\times {10}^{24}$ ${\mathrm{cm}}^{-3\mathrm{}}$. An upper limit of one part in two thousand was established for the contribution, if any, of a contact term to the hyperfine interaction. The errors quoted are estimated standard deviations of the mean based upon internal consistency. A discussion of the errors and their sources is given. In particular, the precision of the determination of the nuclear moments $\mu$ and $Q$, of $〈r^{-3\mathrm{}}〉$, and of the contact term was limited mainly by the inaccuracies of the best available values of the crystal field parameters ${A_n}^m〈r^n〉$. Numerical values of the spin Hamiltonian parameters, crystal field eigenvectors, and relevant interaction multiplicative factors are tabulated.