Relevance of Knight Shift Measurements to the Electronic Density of States

The Knight shift, $$ , measures the magnetic hyperfine field at the nucleus produced by the conduction electrons which are polarized in a magnetic field. Knight shifts are often dominated by the Pauli term and, in its most simple form, can be written as $$ . Here χ is the conduction electron Pauli spin susceptibility which depends on the density of states at the Fermi level, N(E ), and 〈a〉 is an average magnetic hyperfine coupling constant associated with the wave function character at the nucleus, ∣ψ (0)∣², for conduction electrons at the Fermi surface. The Knight shift therefore provides, through 〈a〉, insight into the wave-function character associated with N(E ). Calculations of 〈a〉 involving an averaging over k-space have been attempted for a few simple metals up to the present time. For alloys and intermetallic compounds, rather different 〈a〉's are experimentally observed for different local environments, indicating that $$ samples the variation in local wave-function character, or a variation in local density of states. There is no unique way of separating the local variation of N(E ) from ∣ψ ∣(0)∣². In this article the methods developed for relating $$ to the electronic properties for most of the types of cases encountered in the literature are reviewed. We discuss "simple" metals including problems of orbital magnetism and changes in $$ caused by electronic transitions such as melting. Knight shifts and their temperature dependence in metals and intermetallic compounds involving unfilled d shells, are discussed. We give estimates of atomic hyperfine fields due to single electrons, appropriate to those cases where problems due to electronic configurations do not make deductions from experiment too ambiguous. A density of states curve calculated for Cu is given, showing the relative importance of s-p, and d character for that metal. In a qualitative sense this Cu curve implies such information for other transition metals. We discuss alloy solid solutions for the cases where a "rigid" band model might be used to explain the results, and for cases where local effects have to be taken into account. The charge oscillation and RKKY approaches and their limitations are reviewed for cases of dilute nonmagnetic and d- or f-type impurities.