Relativistic spin polarization and magnetization: Knight shift of Pt(001)

A relativistic local-density approach for including magnetic effects into scalar-relativistic electronic structure methods is presented. This method is based on a spin-only relativistic generalization of density-functional theory and on results for the relativistic homogeneous electron gas. The relativistic effects on the magnetization density are found to be important only near the nucleus and hence to affect Fermi-contact hyperfine interactions. The approach is illustrated by means of a detailed determination of the Knight shift $K$ of a thin Pt(001) film. These results show a large positive change in $K$ at the surface with respect to the bulk due to a decreased magnetization at the surface (and hence a decrease in the magnitude of the negative core polarization) plus an increased positive valence-electron contribution. The spin-only value of $K$ in the surface layer is -0.6% versus a center-layer value of -4.1% (compared with the experimental bulk value of -3.4%, which includes a positive orbital contribution). The core polarization per unpaired spin (-1.1× ${10}^6$ Oe/${\mathrm{\mu }}_{\mathit{B}}$) is in excellent agreement with experiment (-1.2× ${10}^6$ Oe/${\mathrm{\mu }}_{\mathit{B}}$). These results give both a qualitative and quantitative understanding of recent NMR experiments on small Pt particles.