We have made static susceptibility measurements at temperatures between 1.25 and 300 K on samples of phosphorus-doped silicon with dopant concentrations in the range 0.2$n_c$<1.3, where $n_c$ is the critical concentration for the metal-insulator transition. In this paper we discuss our results for the diamagnetism associated with the donor electrons. We find that the donor susceptibility above 60 K is diamagnetic and varies linearly with concentration. We associate the susceptibility observed at these temperatures with a diamagnetic term, ${\chi }_D$(T,n), which is of the Landau-Peierls-Pauli type, but which is linear in n. Using static susceptibility data at higher concentrations obtained by other investigators, we show that the linear behavior of ${\chi }_D$ persists up to ∼3$n_c$, i.e., within the entire impurity-‘‘band’’ region, beyond which it reverts to the $n^{1/3}$ behavior expected for a standard band. We find that published ESR susceptibility data for similar concentrations exhibit the same concentration dependence as ${\chi }_D$. Use of the ESR data has enabled us to separate out the orbital and spin contributions to the susceptibility. The average diamagnetic susceptibility per donor is found to agree with calculated values of the Larmor diamagnetism of localized electrons, and is independent of concentration over a range spanning the transition from insulating to metallic behavior; so far as the average orbital contribution of the donor electrons in the impurity ‘‘band’’ is concerned, it makes little difference whether the electrons are in localized or extended states. In addition to their possible implications for the nature of the impurity ‘‘band,’’ these results are important in that they provide a baseline against which donor susceptibility can be measured in order to determine a contribution at low temperatures which may be attributed to the presence of local moments across the metal-insulator transition.

• Received 9 July 1987

DOI:https://doi.org/10.1103/PhysRevB.37.5522