Theory of Hyperfine Properties of Beryllium and Magnesium Metals

A detailed analysis of the hyperfine properties of the lighter group-II metals, beryllium and magnesium, has been carried out to understand the relation between the electronic structures of these hcp metals. The "lens" and "butterflies" of the magnesium Fermi surface have large $s$ character, leading to an appreciable value of the Knight shift $K_s$. In contrast, beryllium does not have these pieces of the Fermi surface, and this qualitatively explains the vanishingly small $K_s$ for beryllium. Core polarization (cp) plays an important role in explaining the experimental values of $K_s$. There is a basic difference between beryllium and magnesium as regards the cp contribution to the Knight shift ($K_{\mathrm{cp}}$). For beryllium, ${K_s}^{\mathrm{cp},p}$, the $p$ part of the cp contribution is negative and this, together with a small direct contribution ${K_s}^d$, leads to a vanishingly small value for $K_s$ (0.7×${10}^{-3\mathrm{}}$%), as compared to -0.25×${10}^{-2\mathrm{}}$% obtained experimentally. Orbital effects are expected to explain the remaining discrepancy in beryllium. For magnesium, ${K_s}^{\mathrm{cp}}$ is roughly 38% of ${K_s}^d$, and the total theoretical value of $K_s$ is 0.0554%, compared to the experimental value of 0.112%. The uncertainties in the exchange enhancement of ${\chi }_p$ and the role of other contributions to $K_s$ are discussed. The relaxation time in beryllium is quite large because of the small spin density, and $T_{1}T$ is found to be 1.0035×${10}^4$ deg sec as compared to 1.66×${10}^4$ obtained experimentally. No experimental value of $T_{1}T$ is available for magnesium. Our theoretical value, including exchange enhancement effects, is 0.0346×${10}^4$ deg sec. The relatively large $p$ contribution to ${K_s}^{\mathrm{cp}}$ in both the metals plays an important role in the deviation of ${K_s}^2{T}_{1}T$ from its ideal value, $\frac{{\left(\frac{{\gamma }_{\mathrm{e}}}{{\gamma }_N}\right)}^2\hslash }{4\pi {\mathrm{k}}_B}$.