Magnetism of Interacting Donors

The magnetic susceptibility of donor centers in semiconductors is calculated for the case of small interactions between closely adjacent donors. A hydrogenic model is assumed for the donor centers. The random distribution of the centers, as well as the variation of the energy of interaction with separation distance of pairs of donors, is taken into consideration. A twofold modification to the Curie law (which is correct for independent donors) is predicted by the resulting expression, namely, a curvature as well as a decrease of the slope of the Curie plot of the susceptibility versus inverse temperature. Both of these effects increase with the donor density, becoming appreciable in silicon with ${10}^{17}$-${10}^{18}$ donors/${\mathrm{cm}}^3$ and in germanium in the range around ${10}^{16}$ donors/${\mathrm{cm}}^3$. The theory is in good agreement with results of measurements.